QUINTESSENCE: - Infomathsinfomathsonline.com/Que_papers/All Chapters 1-20-Old Questions.doc · Web view... the intersection of any two of the subsets ... 3y = 5 and 3x – 4y = 7

INFOMATHSOLD QUESTIONS-CW1 OLD QUESTIONS-CW1

SETS & RELATIONS 1. The binary relation on the integers defined by R =

{(a, b) : |b – a| 1} is HCU-2012

(a) Reflexive only (b) Symmetric only (c) Reflexive and Symmetric (d) An equivalence relation

2. Set of all subsets is a PUNE-2012

(a) power set (b) equal sets (c) equivalent sets (d) None of these

3. In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is NIMCET-2012(a) 22 (b) 33 (c) 10 (d) 45

4. Let X be the universal set for sets A and B. If n(A) = 200, n(B) = 300 and n(A ∩ B) = 100, then n(A'∩ B') is equal to 300 provided in n(X) is equal to

NIMCET-2011(a) 600 (b) 700 (c) 800 (d) 900

5. In a college of 300 students, every student reads 5 news papers and every news paper is read by 60 students. The number of news paper is

NIMCET-2011(a) atleast 30 (b) atmost 20 (c) exactly 25 (d) exactly 28

6. If A = {1, 2, 3}, B = {4, 5, 6}, which of the following are relations from A to B?

BHU-2011(a) {(1, 5), (2, 6), (3, 4), (3, 6)}(b) {(1, 6), (3, 4), (5, 2)}(c) {(4, 2), (4, 3), (5, 1)}(d) B A

7. The number of subsets of an n elementric set is BHU-2011

(a) 2n (b) n (c) 2n (d)

8. If A = {a, b, d, l}, B = {c, d, f, m} and C = {a, l, m, o}, then C (A B) is given by

BHU-2011(a) {a, d, l, m} (b) {b, c, f, o}(c) {a, l, m} (d) {a, b, c, d, f, l, m, o}

In question 9 and 10, for sets X and Y, X Y is defined as X Y = (X – Y) (Y – X)9. If P = {1,2, 3, 4}, Q = {2, 3, 5, 8}, R = {3, 6, 7, 9}

and S = {2, 4, 7, 10} then (P Q) (R S) is HCU-2011

(a) {4, 7} (b) {1, 5, 6, 10}(c) {1, 2, 3, 5, 6 8, 9, 10} (d) None of the above

10. If X, Y, Z are any three subsets of U, then the subset of U consisting of elements which belong to exactly two of the sets X, Y, Z is

HCU-2011(a) (X Y) (Y Z) (Z X)(b) (X Y) (Y Z) (Z X)(c) ((X Y) Z) – ((X Y) Z)(d) None of the above

11. Let A = {1, 2, 3, 4}. The cardinality of the relation R = {(a,b)| a divides b} over A is : PU CHD-2011(A) 10 (B) 9 (C) 8 (D) 4

12. If X={8n –7n–1\nN } and Y= {49(n–1)\nN} then:PU CHD-2010

(A) X Y (B) Y X (C) X=Y (D) XUY=N13. The relation R={(1,1) (2,2), (3,3), (1,2), (2,3), (1,3) }

on the set A ={1,2,3} is : PU CHD-2010

(A) reflexive but not symmetric (B) reflexive but not transitive(C) symmetric and transitive (D) neither symmetric nor transitive

14. Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = (3, 6, 9, 12) Then the relation is :

PU CHD-2009(a) reflexive and transitive only (b) reflexive only (c) and equivalence relation (d) reflexive and symmetric only

15. For real numbers x and y, we write xRy

is an irrational number. Then the relation R is KIITEE-2010(a) reflexive (b) symmetric (c) transitive (d) None of these

16. If X = {4n – 3n – 1: n N} and Y = {9(n – 1) : n N}, then X Y is equal to

KIITEE-2010(a) X (b) Y (c) N (d) None of these

17. If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets A B and B A are :

KIITEE-2010(a) 299 (b) 992 (c) 100 (d) 18

18. If A, B and C are three sets such that A B = A C and A B = A C, then KIITEE-2010(a) A = C (b) B = C (c) A B = (d) A = B

19. In a city 60% read news paper A, 40% read news paper B and 30% read C, 20% read A and B, 30% read A and C, 10% read B and C. Also 15% read paper A, B and C. The percentage of people who do not read any of these news papers is (PGCET – 2009)(a) 65% (b) 15% (c) 45% (d) None of these

20. The total number of relations that exist from the set A with m elements into the set A A is

(NIMCET – 2009)(a) m2 (b) m3 (c) m (d) None of these

21. If P = {(4n – 3n - 1) / n N} and Q = {(9n - 9) / n N}, then P Q is equal to

(NIMCET – 2009)(a) N (b) P (c) Q (d) None of these

22. A1, A2, A3 and A4 are subsets of a set U containing 75 elements with the following properties : Each subset contains 28 elements; the intersection of any two of the subsets contains 12 elements; the intersection of any three of the subsets contains 5 elements; the intersection of all four subsets contains 1 elements. The number of elements belongs to none of the four subsets is

(NIMCET – 2009)(a) 15 (b) 17 (c) 16 (d) 18

23. From 50 students taking examination in Mathematics, Physics and Chemistry, 37 passed Mathematics, 24 Physics and 43 Chemistry. At most 19 passed Mathematics and Physics, at most 29 Mathematics and Chemistry and atmost 20 Physics and Chemistry. The largest possible number that could have passed all three examinations is

(NIMCET - 2009)(a) 10 (b) 12 (c) 9 (d) None of these

24. Let the sets A = {2, 4, 6, 8 …} and B = {3, 6, 9, 12, …} and n (A) = 200, n(B) = 250 then

(KIITEE – 2009)(a) n(A B) = 67 (b) n(A B) = 66(c) n (A B) = 450 (d) n(A B) = 380

25. Let R be relation on the set of positive integers defined as follows: aRb iff 4a + 5b is divisible by 9 then R is

(Hyderabad Central University – 2009)(a) Reflexive only (b) Reflexive and symmetric but not transitive(c) Reflexive and transitive but not symmetric

1 INFOMATHS/MCA/MATHS/OLD QUESTIONS

INFOMATHS(d) An Equivalence relation

26. The set having only one subset is (Hyderabad Central University – 2009)

(a) { } (b) {0} (c) {{}} (d) None of these 27. If R and S are equivalence relations on a set A, then

(Hyderabad Central University – 2009)(a) R S is an equivalence relation (b) R S is an equivalence relation (c) Both A and B are true (d) Neither A nor B is true

28. Identify the wrong statement from the following :NIMCET-2010

(a) If A and B are two sets, then A- B= A (b) If A,B and C are sets, then (A - B) – C = (A – C)-(B

- C)(C) If A and B are two sets, then = (D)

If A, B and C are sets, then A B A B29. A survey shows that 63% of the Americans like

cheese where as 76% like apples. If x% of the Americans lie both cheese and apples, then we have

NIMCET-2010(a) x 39 (b) x63(c) 39x63 (d) N.O.T

30. Suppose P1, P2, … P30 are thirty sets each having 5 elements and Q1, Q2, …. Qn are n sets with 3

elements each. Let and each

element of S belongs to exactly 10 of the Pi S and exactly 9 of the Qj s. Then, n is equal to

(MCA : NIMCET - 2008)(a) 15 (b) 3 (c) 45 (d) None

31. If A = {1, 2, 3}, B = {a, b, c, d}. The number of subsets in the Cartesian product of A & B is

(Pune– 2007)(a) 212 (b) 27 (c) 12 (d) 7

32. In an election 10 per cent of the voters on the voters’ list did not cast their votes and 50 voters cast their ballot papers blank. There were exactly two candidates. The winner was supported by 47 per cent of all the voters in the list and he got 306 more than his rival. The number of voters in the list was

(IP University : – 2006)(a) 6400 (b) 6603 (c) 7263 (d) 8900 (e) N.O.T

33. Only one of the following statements given below regarding elements and subsets of the set {2, 3, {1, 2, 3}} is correct. Which one is it?

(IP University : – 2006)(a) {2, 3} {2, 3, {1; 2, 3}} (b) 1 (2, 3, {1, 2, 3}}(c) {2, 3} (2, 3, {1, 2, 3}} (d) {1, 2, 3,} {2, 3, {1, 2, 3}}

34. Which set is the subset of all given sets? (Karnataka PG-CET : - 2006)

(a) {1, 2, 3, 4, …} (b) {1}(c) {0} (d) { }

35. A set contains (2n + 1) elements. If the number of subsets which contain at most n elements is 4096, then the value of n is

(NIMCET – 2009)(a) 28 (b) 21 (c) 15 (d) 6

36. If set A has 6 elements, B has 4 elements and C has 8 elements, the maximum number of elements in (B – C) (A B) C is

(Hyderabad Central University – 2009)(a) 18 (b) 12 (c) 16 (d) 24

37. Let A be a set with 10 elements. The total number of relations that can be defined on A that are both reflexive and asymmetric is

(Hyderabad Central University – 2009)

(a) 245 (b) 255 (c) (d) None

of these

THEORY OF EQUATIONS

1. If the equation x4 – 4x3 + ax2 + bx + 1= 0 has four positive roots then a =?

BHU-2012(a) 6, -4 (b) -6, 4 (c) 6, 4 (d) -6, -4

2. Let P(x) = ax2 + bx + c and Q(x) = - ax2 + bx + c, where ac 0. Then for the polynomial P(x) Q(x)

HCU-2012(a) All its roots are real (b) None of its roots are real (c) At least two of its roots are real (d) Exactly two of its roots are real

3. Let p(x) be the polynomial x3 + ax2 + bx + c, where a, b and c are real constants. If p(–3) = p(2) = 0 and p'(–3) < 0, which of the following is a possible value of c ?

PU CHD-2012(A) – 27 (B) – 18 (C) – 6 (D) – 3

4. Which of the following CANNOT be a root of a polynomial in x of the form 9x5 + ax3 + b, where a and b are integers?

PU CHD-2012

(A) – 9 (B) – 5 (C) (D)

5. If and are the root of 4x2 + 3x + 7 = 0, then the

value of is :

PU CHD-2012

(A) (B) (C) (D)

6. If a, b, c are real numbers such that a2 + b2 + c2 = 1, then ab + bc + ca

PU CHD-2012(A) 1/2 (B) – 1/2 (C) 2 (D) – 2

7. If the roots of the equation ax2 + bx + c = 0 are real and of the form α/ (α -1) and (α + 1) / α then the value of (a + b + c)2 is :

PU CHD-2011(A) b2 – 4ac (B) b2 – 2ac (C) 2b2 – ac (D) b2 – 3ac

8. If a2 + b2+ c2 = 1, then ab + bc + ca lies in the interval :

PU CHD-2011

(A) (B)

(C) (D)

9. The roots of the equation |x2 x 6 | x 2 are : PU CHD-2010(A) – 2, 1, 4 (B) 0, 2, 4 (C) 0, 1, 4 (D) – 2, 2, 4

10. If one root of the equation ax2 + bx + c = 0 is twice the other then :

PU CHD-2010(A) 2a2 = 3c2 (B) 2b2 = 3ac(C) 2b2 = 9ac (D) b2 = ac

11. If both the roots of the quadratic equation x2 – 2kx + k2 + k – 5 = 0 are less than 5, then k lies in the interval PU CHD-2009(a) (5, 6] (b) (6, ) (c) (-, 4) (d) [4, 5]

12. The function f(a) and f(b) are of same sign and f(x) = 0 then the function : PU CHD-2009(a) has either no root or even number of roots

between a and b (b) must have at least one root between a and B (c) has either no root or odd number of roots

between a and b (d) has complex root

13. How many real solutions does the equation x7 + 14x5

+ 16x3 + 30x – 560 = 0 have? KIITEE-2010

(a) 7 (b) 1 (c) 3 (d) 514. If the rots of the quadratic equation x2 + px + q = 0

are tan 30 and tan 15, respectively, then the value of 2 + q – p is KIITEE-2010(a) 3 (b) 0 (c) 1 (d)2


INFOMATHS15. The number of real solutions of the equation x2 – 3|x|

+ 2 = 0 is KIITEE-2010

(a) 2 (b) 4 (c) 1 (d) 316. The roots of the quadratic equation x2 + x – 1 = 0

are PGCET-2010

(a) (b)

(c) (d)

17. The roots of the quadratic equation x2 – x – 1 = 0 are (PGCET – 2009)

(a) (b)

(c) (d)

18. Let , be the roots of the equation (x – a) (x – b) = c, c 0, then the roots of the equation (x + ) (x + ) + c = 0 are

(Hyderabad central university - 2009)(a) a, - b (b) – a, b (c) – a, - b (d) a, b

19. The number of roots of the equation |x2 – x - 6| = x + 2 is

(NIMCET - 2008)(a) 2 (b) 3 (c) 4 (d) None

20. If esin x – e-sin x – 4 = 0 then the number of real values of x is

(KIITEE – 2008)(a) 0 (b) 1 (c) infinite (d) None

21. The values of x and y satisfying the equations:

and are. (MP

combined – 2008)(a) x = 9, y = 1 (b) x = 6, y = 1 (c) x = 6, y = 2 (d) x = 3, y = 2

22. If x2 + x – 2 is a factor of the polynomial x4 + ax3 + bx2 – 12x + 16 then the ordered pair (a, b) =

(ICET – 2007)(a) (-3, 8) (b) (3, - 8) (c) (-3, - 8) (d) (3, 8)

23. If and then (x, y) =

(ICET – 2007)

(a) (b)

(c) (d)

24. The maximum value of the expression 5 + 6x – x2 is (ICET – 2007)

(a) 11 (b) 12 (c) 13 (d) 14

25. If one root of the equation ax2 + bx + c = 0 is double the other root, then, (ICET – 2005)(a) b2 = 9ac (b) 2b2 = 3ac (c) b = 2a (d) 2b2 = 9ac

26. The maximum value of the expression 2 + 5x – 7x2

is ICET–2005

(a) (b) (c) (d)

27. The solution of the equation x2/3 – 3x1/3 + 2 = 0 is (Pune – 2007)

(a) 1, 2 (b) 1, 8 (c) 2, 6 (d) 1, 428. Which of the following may be true for a quadratic

equation ( is real)? (Pune – 2007)

(a) If is a root, 1/ is also a root (b) If is a root, - is also a root(c) If is a root, i is also a root (d) If i is a root, -i is also a root

29. If a + b + c = 0 then one root of the equation ax2 – bx + c = 0 is

(Pune – 2007)

(a) (b) (c) (d)

30. If x2 + ax + 10 = 0 and x2 + bx – 10 = 0, have a common root then a2 – b2 equal to (Karnataka PG-CET – 2006)(a) 10 (b) 20 (c) 30 (d) 40

31. If ax2 + bx + c = 0 lx2 + mx + n = 0

have reciprocal roots then: (UPMCAT– 2002)

(a) (b)

(c) (d) None of these

32. Given a b; The roots of (a – b)x2 – 5(a – b)x + (b – a) = 0 are:

(UPMCAT– 2002)(a) Real and equal (b) real and different (c) complex (d) None of these

33. If the real number x when added to its inverse gives the minimum value of the sum, then the value of is equal to

NIMCET-2012(a) – 2 (b) 2 (c) 1 (d) – 1

34. The equation (cos p – 1)x2 + (cos p) x + sin p = 0 where x is a variable has real roots. Then the interval of p is

NIMCET-2012(a) (0, 2π) (b) (-π, 0)

(c) (d) (0, π)

35. Number of real roots of 3x5 + 15x – 8 = 0 is NIMCET-2012

(a) 3 (b) 5 (c) 1 (d) 036. The least integral value of K for which (K–2) x2 + K+

8x + 4 > 0 for all x R, isNIMCET-2011

(a) 5 (b) 4 (c) 3 (d) 637. Solution set of inequality

is

NIMCET-2011(a) (–2, –1) (b) (–2, 3) (c) (–1, 3) (d) (3, ∞)

38. If α, β are the roots of the equation x2 − 2x + 4 = 0 then the value of α6 + β6 is

NIMCET-2011(a) 64 (b) 128 (c) 256 (d) 132

39. If 2x4 + x3 – 11x2 + x + 2 = 0, then the value of

are

(NIMCET - 2009)

(a) (b) (c) (d)

40. If x < - 1 and 2|x+1| - 2x = |2x - 1| + 1, then the value of x is

(NIMCET - 2009)(a) –2 (b) 2 (c) 0 (d) none


INFOMATHS41. The number of distinct integral values of ‘a’

satisfying the equation 22a – 3(2a + 2) + 25 = 0 is (NIMCET - 2009)

(a) 0 (b) 1 (c) 2 (d) 342. The set of real values of x satisfying |x - 1| 3 and |

x – 1| 1 is (KIITEE - 2009)

(a) [2, 4] (b) [-2, 0] [2, 4](c) (- , 2] [4, ) (d) None of these

43. If , are non real numbers satisfying x3 – 1 = 0

then the value of is equal to

(KIITEE - 2009)(a) 0 (b) 3 + 1 (c) 3 (d) None of these

44. The number of positive real roots for the following polynomial P(x) = x4 + 5x3 + 5x2 – 5x – 6 is

(Hyderabad central university - 2009)(a) 0 (b) 1 (c) 2 (d) 3

45. If a, b are the roots of x2 + px + 1 = 0 and c, d are roots of x2 + qx + 1 = 0, the value of E = (a – c) (b – c) (a + d) (b + d) is (NIMCET - 2008)(a) p2 – q2 (b) q2 – p2 (c) q2 + p2 (d) None

46. If then x4 + x3 – 4x2 + x + 1 = (ICET

– 2005)(a) x2(y2 + y – 2) (b) x2(y2 + y – 3) (c) x2(y2 + y – 4) (d) x2(y2 + y – 6)

47. Which of the following may be true for a quadratic equation ( is real)?

Pune-2007(a) If is a root, 1/ is also a root (b) If is a root, - is also a root(c) If is a root, i is also a root (d) If i is a root, -i is also a root

48. If a + b + c = 0 then one root of the equation ax2 – bx + c = 0 is

Pune-2007

(a) (b) (c) (d)

49. If and are the roots of |x2 + x + 5| + 6x + 1 = 0 then +

(Pune– 2007)(a) 7 (b) –7 (c) 5 (d) –5

50. x R, The solution set of the inequality|x – 4| + | x – 6| + |x – 8| 15, is (IP. University : Paper – 2006)(a) [1, 11] (b) [2, 12] (c) [0, 10] (d) [3, 10](e) None of these

51. x R. The solution set of the inequality 10[x]2 – 17[x] – 6 0 (where [x] denotes the greatest integer less than or equal to) is

(IP. University :– 2006)

(a) [0, 3) (b) [-1, 2) (c) (0, 3] (d) [-1, 3] 52. The solution set for real x of the equation

is (IP. University :–

2006)

(a) (b) (c) (d)

(e) None of these 53. If a is a positive integer, and the roots of the

equation 7x2 – 13x + 2a are rational numbers, then the smallest value of a is

(IP. University : Paper – 2006)(a) 1 (b) 2 (c) 3 (d) 4 (e) N.O.T

54.(UPMCAT : paper – 2002)

(a) x = - 1, x = 9 (b) x = - 1 (c) x = 9 (d) None of these

55. If , then the value of expression 4x3 +

2x2 – 8x + 7, is equal to BHU-2011

(a) 10 (b) 5 (c) 0 (d) – 2 56. The number of quadratic equations which remain

unchanged by squaring their roots, is BHU-2011

(a) zero (b) four (c) two (d) infinite

SEQUENCE & SERIES

1. The sum of the series upto n-

terms is: PU CHD-2012

(A) (B)

(C) (D)

2. The harmonic mean of two numbers is 4. The arithmetic mean A and geometric mean G of these two numbers satisfy the equation 2A + G2 = 27. The two numbers are : PU CHD-2012(A) 3, 6 (B) 4, 5 (C) 2, 7 (D) 1, 8

3. In a geometric progression, (p + q)th term is m and (p - q)th term is n, then pth term is :

PU CHD-2011(A) m/n (B) (C) (D)

4. The arithmetic mean of 9 observations is 100 and that of 6 observations is 80, then the combined mean of all the 15 observations will be :

PU CHD-2011(A) 100 (B) 80 (C) 90 (D) 92

5. If in a GP sum of n terms is 255, the last term is 128 and the common ratio is 2, then the value of n is equal to

BHU-2011(a) 2 (b) 4 (c) 8 (d) 16

6. If the ratio of the sum of m terms and n terms of an AP be m2 : n2, then the ratio of its mth and nth terms will be

BHU-2011

(a) (b)

(c) (d)

7. The harmonic mean of the roots of the equation is

BHU-2011(a) 2 (b) 4 (c) 6 (d) 8

8. Arithmetic mean of two positive numbers is

and their geometric mean is 15. The larger of the two numbers is

HCU-2011(a) 30 (b) 20 (c) 24 (d) None of the above

9. Let A (x1, y1), B(x2, y2), C(x3, y3) and D(x4, y4) be four points such that x1, x2, x3, x4 and y1, y2, y3, y4 are both in arithmetic progression. Then the area of the quadrilateral ABCD is

HCU-2011(a) 0(b) greater than 1 (c) less than 1 (d) Depends on the coordinates of A, B, C, D

10. If x, 2x+2, 3x+3 are in G.P then the 4th term is :PU CHD-2010

(A) 27 (B) –27 (C) 13.5 (D) –13.5


INFOMATHS11. is equal to : PU

CHD-2010

(A) (b)

(c) (d)

12. If a, b, c are in A.P., p, q, r are in H. P. and ap, bq, cr

in G.P. , then is equal to

NIMCET-2010

(a) (b) (c) (d)

13. Which of the following statement is correct? PU CHD-2009(a) A.M. < G.M. < H.M. (b) A.M. > G.M. > H.M. (c) A.M. > G.M. < H.M. (d) H.M. < A.M. < G.M.

14. The sum to infinite terms of the series

is KIITEE-

2010(a) 3 (b) 4 (c) 6 (d) 2

15. Sum up to 10 terms of 1 + 3 + 5 + 7 + …. Is PGCET-2010(a) 100 (b) 102 (c) 103 (d) 104

16. Sum of 43 + 83 + 123 + …. + 403 is (PGCET – 2009)(a) 193600 (b) 183600 (c) 194600 (d) 183700

17. In a geometric progression, if the sum of the first four term is equal to 15 and the sum of the second, third, fourth and fifth terms is 30, then the sixth term equals to (KIITEE – 2009)(a) 16 (b) 32 (c) 48 (d) 64

18. If H is the Harmonic mean between P and Q, then

is

NIMCET-2012

(a) 2 (b)


19. If three positive real number a, b, c (c > a) are in H.P., then log (a + c) + log (a – 2b + c) is

NIMCET-2011(a) 2 log (c – b) (b) 2 log (a + c) (c) 2 log (c – a) (d) log a + log b + log c

20. The sum of 112 + 122 +….+ 302

NIMCET-2011(a) 8070 (b) 9070 (c)1080 (d) 9700

21. Suppose a, b, c are in A.P. with common difference d. Then e1/c, eb/ac, e1/a are (NIMCET – 2008)(a) A.P. (b) GP. (c) H.P. (d) None

22. If H1, H2, …., Hn are n harmonic means between a

and b, a b, then the value of is

equal to(NIMCET -2008)

(a) n + 1 (b) n – 1 (c) 2n (d) 2n + 3 23. If nc4, nc5 and nc6 are in arithmetic progression then n

is (KIITEE – 2008)(a) 9 (b) 8 (c) 17 (d) 14

24. If the second term of an arithmetic progression is 20 and its fifth term is double the first then the sum to 20 terms of the series is

(ICET – 2007)(a) 64 (b) 108 (c) 1080 (d) 2160

25. If = b2 then 1/3 1/9 1/27, … = (ICET – 2007)(a) a (b) b (c) 1/a (d) 1/b

26. If m is the arithmetic mean of a1, a2, ….. an then the arithmetic mean of a1 + , a2, + …. an + is

(ICET – 2007)(a) m (b) m + (c) m + (d) m

27. The geometric mean between a2 and b2 is ICET – 2005

(a) |ab| (b) a2b2 (c) ab (d)

28. If K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an arithmetic progression then, K is

(ICET – 2005)(a) 4 (b) 3 (c) 1 (d) 4

29. If a > 1, b > 1 and a + b = ab and if

then

(ICET – 2005)(a) 0 (b) 2 (c) 1 (d) 3

30. If tn is the nth term of an arithmetic progression with first term ‘a’ and common difference “d” then,

(ICET – 2005)

(a) na + (n – 1)d (b) n(a + nd) (c) na + (n + 1)d (d) na + (2n – 1)d

31. In a polygon, the smallest angle is 88 and common difference is 10, the number of sides is :

UPMCAT– 2002 (a) 10 (b) 8 (c) 5 (d) N.O.T.

BINOMIAL THEOREM1. The coefficient of x3 in the expansion of (1 + x)3 (2 +

x2)10 is :PU CHD-2012

(A) 214 (B)

(C) (D)

2. In the binomial expansion of (a – b)n, n 5, the sum

of 5th and 6th terms is zero. Then equals:

BHU-2012

(a) (b) (c) (d)

3. If nCr-1 = 36, nCr = 84 and nCr+1 = 126, then the value of r is equal to :

BHU-2012(a) 1 (b) 2 (c) 3 (d) 4

4. Let and f = fractional part of x. Then x(1 – f) is equal to

HCU-2012(a) 1 (b) 2 (c) (d) 7

5. Coefficient of xyz-2 in (x – 2y + 3z-1)4 is Pune-2012

(a) -216 (b) 216 (c) -110 (d) 3006. The sum of 20C8 + 20C9 + 21C10 + 22C11 – 23C11 is

NIMCET-2012(a) 22C12 (b) 23C12 (c) 0 (d) 21C10


INFOMATHS7. If for n N, then the value of

is NIMCET-

2011(a) nA (b) –nA (c) 0 (d) A

8. If the coefficient of x7 in the expansion of

is equal to the coefficient of x-7 in the

expansion of , then

BHU-2011

(a) pq = 1 (b)

(c) p + q = 1 (d) p – q = 1 9. The coefficient of x15 the product

(x – 1) (2x – 1) (22x – 1) (23x – 1) …. (215 x – 1) is equal to

BHU-2011(a) 2120 – 2108 (b) 2105 – 2121 (c) 2120 – 2105 (d) 2120 – 2104

10. The nth term of the series is

BHU-2011

(a) (b)

(c) 20(5n + 3) (d)

11. The remainder when 599 is divided by 13 is : PU CHD-2011(A) 6 (B) 8 (C) 9 (D) 10

12. If the co–efficient of x7 in the expansion of

and the coefficient of x-7 in the

expansion of are equal then ab is equal

to : PU CHD-2010

(A) 1 (B) 2 (C) 3 (D) 413. What is the value of factorial zero (0!)?

PU CHD-2009(a) 10 (b) 0 (c) 1 (d) – 1

14. If (1+x)n = ao + a1x + a2 x2 +….an xn ,then

NIMCET-

2010

(a) (b)

(c) (d)

15. 49n + 16n – 1 is divisible by KIITEE-2010(a) 3 (b) 19 (c) 64 (d) 29(e) None of these

16. In the Binomial expansion of (a – b)n, n 5, the sum

of 5th and 6th terms is zero, then equals:

KIITEE-2010

(a) (b) (c) (d)

17. If the last term in the Binomial expansion of

is then the 5th term from

the beginning isKIITEE-2010(a) 210 (b) 420 (c) 105 (d) None of these

18. If (1 + x – 2x2)6 = 1 + a1x + a2x2 + … + a12x12, then the value of a2 + a4 + a6 + … + a12 is

(NIMCET – 2009)(a) 1024 (b) 64 (c) 32 (d) 31

19. Let tn = n(n!) then is equal to

(KIITEE – 2009)(a) 15! – 1 (b) 16! – 1 (c) 15! + 1 (d) None of these

20. The sum of 2nCr is equal to (KIITEE

– 2009)(a) n 22n – 1 (b) 2n-1 + 1 (c) 22n – 1 (d) None of these

21. is

equal to (KIITEE – 2009)

(a) for even values of n only

(b) for odd values of n only

(c) for all n N

(d) None of these22. The coefficient of a8 b10 in the expansion of (a + b)18

is (KIITEE – 2009)

(a) 18C8 (b) 18C10 (c) 218 (d) None of these

23. In the expansion of the constant term

is (KIITEE – 2009)

(a) 15C6 (b) - 15C6 (c) 0 (d) 124. The middle term in the expansion of

is

(KIITEE – 2009)(a) 2nCn (b) –2nCn (c) –2nCn-1 (d) None of these

25. What is the value of the ten’s digit in the sum 1! + 2! + 3! + … + 2008! Hyderabad Central Univ. – 2009(a) 0 (b) 1 (c) 9 (d) 4

26. Value of (for n, a

positive integer) depends on Hyderabad Central Univ. – 2009(a) Value of A (b) Value of n (c) neither A nor n (d) Both A and n

27. In the expression (x + 1) (x + 4) (x + 9) (x + 16) … (x + 400) the coefficient of x19 is

(NIMCET – 2008)(a) 2870 (b) 210 (c) 4001 (d) 1900

28. The sum of the numerical co-efficients in the

expansion of is

KIITEE – 2008(a) 212 (b) 1 (c) 2 (d) None


INFOMATHS29. The co-efficients of x3 in the expansion of (1 – x +

x2)5 is KIITEE – 2008

(a) 10 (b) – 20 (c) – 30 (d) – 50 30. In the expansion of (1 + x + x2)-3 the coefficient of x6

will be : (MP combined – 2008)(a) 9 (b) 3 (c) 1 (d) – 3

31. If (1 + x)n = C0 + C1x + C2x2 + … + Cnxn then C0C1 + C1C2 + C2C3 + … + Cn-1 Cn will be equal to:

(MP combined – 2008)

(a) (b)

(c) (d)

32. In the expansion of the term

independent of x will be (MP combined – 2008)

(a) (b) (c) (d)

33. The coefficient of the term independent of x in the

expansion of is

ICET - 2007

(a) (b) (c) (d) None

34. If the 21st and 22nd terms in the expression (1 + 6a)24

are equal then a = ICET - 2007

(a) 7/8 (b) 8/7 (c) 5/8 (d) 8/5

35. The coefficient of x4 in is ICET

– 2005

(a) (b) (c) (d)

36. If the 5th term of is 10, then, x = ICET

– 2005(a) 6 (b) – 6 (c) 9 (d) 8

37. = ICET – 2005

(a) (b)

(c) (d)

38. The remainder in the divisor of 340 by 23 is Pune– 2007(a) 13 (b) 12 (c) 14 (d) 15

39. (12! + 1) is divisible by Pune– 2007

(a) 11 (b) 13 (c) 14 (d) 7

40. The sum equals IP

Univ.– 2006

(a) (b) (c) (d) (e) N.O.T

41. The coefficient of x6 in the expansion of (1 + x2)3 (2 + x4)10 is

IP Univ. Paper – 2006(a) 214 (b) 31

(c) (d)

(e) None of these

42. The sum is equal to : MP

Paper – 2004

(a) (b) (c) (d)

43. The term independent of x in is MP

Paper – 2004(a) third (b) fifth (c) sixth (d) seventh

44. UPMCAT paper –

2005

(a) (b)


45. Coefficient of x4 in log (1 + x + x2) is : UPMCAT paper – 2005 (a) 5/12 (b) 13/12 (c) -5/12 (d) N.O.T

46. If b is taken to be positive, then the following series

is equal to :

UPMCAT– 2005 (a) 1 (b) 1/4 (c) 1/2 (d) 1/3

47. In the expression , the term independent

of x is equal to : UPMCAT– 2005 (a) 10C5 (b) 10C3 (c) 10C6 (d) None of these

48. The value of is equal to

KIITEE – 2008(a) 9 (n – 4) (b) 5 (2n – 9) (c) 10n (d) None

49. The sum of the series is

equal to KIITEE – 2008

(a) n.2n-1 + a (b) 0 (c) a (d) None

EXPONENTIAL AND LOGARITHMIC SERIES 1. If log103 = 0.477, the number of digits in 340 is : PU

CHD-2011(A) 18 (B) 19 (C) 20 (D) 21

2. The sum of the series

is infinity is : MP COMBINED - 2008

(a) loge 2 (b) loge 5 (c) (d)


INFOMATHS3. Coefficient of x5 in the expansion of

is : MP COMBINED - 2008

(a) (b) (c) (d)

4. Value of the series:

to

infinity is : MP COMBINED - 2008(a) 2 (b) 1 (c) e2 (d) e

5. The value of the series :

to infinity is :

MP COMBINED - 2008

(a) loge2 (b)

(c) (d) 1 – loge2 6. Find the sum of the infinite series

.

MP Paper – 2004 (a) e (b) e-2 (c) 1/e (d) None of these

7. If inf. coeff. of xn is

UPMCAT Paper - 2002

(a) (b) (c) (d)

PERMUTATIONS & COMBINATIONS 1. How many words can be formed out of the letters of

the word ‘PECULIAR’ beginning with P and ending with R ?

PU CHD-2012(A) 100 (B) 120 (C) 720 (D) 150

2. If M = {1, 2, 3, 4, 5, 7, 8, 10, 11, 14, 17, 18}. Then how many subsets of M contains only odd integers.

Pune-2012(a) 26 (b) 212 (c) 211 (d) None of these

3. No. of seven digit integers with sum of digits equal to 10, formed by digits 1, 2, 3 only are

Pune-2012(a) 55 (b) 66 (c) 77 (d) 88

4. How many nos. between 1 and 10,000 which are either even, ends up with 0 or have the sum of their digits divisible by 9.

Pune-2012(a) 5356 (b) 5456 (c) 5556 (d) 5656

5. The number of words that can be formed by using the letters of the word Mathematics that start as well as end with T is

NIMCET-2012(a) 80720 (b) 90720 (c) 20860 (d) 37528

6. The number of different license plates that can be formed in the format 3 English letters (A …. Z) followed by 4 digits (0, 1 ….. 9) with repetitions allowed in letters and digits is equal to

NIMCET-2012(a) 263 × 104 (b) 263 + 104 (c) 36 (d) 263

7. In which of the following regular polygons, the number of diagonals is equal to number of sides?

NIMCET-2012(a) Pentagon (b) Square (c) Octagon (d) Hexagon

8. 100 ! = 1 2 3 ….. 100 ends exactly in how many zeroes?

HCU-2011(a) 24 (b) 10 (c) 11 (d) 21

9. Let a and b be two positive integers. The number of factors of 5a7b are

HCU-2011(a) 2(a+b) (b) a + b + 2 (c) ab + 1 (d) (a + 1) (b + 1)

10. A polygon has 44 diagonals, the number of its sides is

NIMCET-2011, PU CHD-2011(a) 9 (b) 10 (c) 11 (d) 12

11. The number of ways of forming different nine digit numbers from the number 223355888 by rearranging its digit so that the odd digits occupy even positions is

NIMCET-2011(a) 16 (b) 36 (c) 60 (d)

18012. There are n numbered seats around a round table.

Total number of ways in which n1(n1 < n) persons can sit around the round table, is equal to

BHU-2011(a) (b) (c) (d)

13. The number of subsets of a set containing n distinct object is

BHU-2011(a) nC1 + nC2 + nC3 + nC4 + …… + nCn (b) 2n – 1 (c) 2n + 1 (d) nC0 + nC1 + nC2 + ….. + nCn

14. A five digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done is : PU CHD-2011(A) 216 (B) 600 (C) 240 (D) 3125

15. Total number of ways in which five + and seven – signs can be arranged in a line such that no two + signs occur together is :

PU CHD-2010(A) 56 (B) 42 (C) 28 (D) 21

16. All letters of the word AGAIN are permuted in all possible ways and the words so formed (with or without meaning) are written in dictionary order then the 50th word is : PU CHD-2010(A) NAAGI (B) NAAIG (C) IAANG (D) INAGA

17. How many ways are there to arranged the letters in the word GARDEN with the vowels in alphabetical order? PU CHD-2009(a) 120 (b) 480 (c) 360 (d) 240

18. A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is : KIITEE-2010(a) 346 (b) 140 (c) 196 (d) 280

19. How many different words can be formed by jumbling the word MISSISSIPPI in which no two S are adjacent? KIITEE-2010(a) 8.6C4.7C4 (b) 6.78C4 (c) 6.8.7C4 (d) 7.6C4.8C4

20. The number of ways in which 6 men and 5 women can dine at a roundtable, if no two women are to sit together is given by

KIITEE-2010(a) 6! 5! (b) 30 (c) 5! 4! (d) 7! 5!

21. Total number of divisors of 200 are PGCET-2010(a) 10 (b) 6 (c) 12 (d) 5

22. How many different paths in the xy-plane are there from (1, 3) to (5, 6) if a path proceeds one step at a time by going either one step to the right (R) or one step upward (U)? (NIMCET – 2009)(a) 35 (b) 40 (c) 45 (d) None of these

23. There are 10 points in a plane. Out of these 6 are collinear. The number of triangles formed by joining these points is

(NIMCET – 2009)


INFOMATHS(a) 100 (b) 120 (c) 150 (d) None of these

24. A man has 7 friends. The number of ways in which he can invite one or more of his friends to a party is (KIITEE – 2009)(a) 132 (b) 116 (c) 127 (d) 130

25. The number of ways in which the letter of word ARTICLE can be rearranged so that the odd places are always occupied by consonants is

(KIITEE – 2009)(a) 576 (b) 4C3 4! (c) 2(4!) (d) None of these

26. Nine hundred distinct n – digit positive numbers are to be formed using only the digits 2, 5, 7. The smallest value of n for which this is possible is

(KIITEE – 2009)(a) 6 (b) 8 (c) 7 (d) 9

27. Total number of 6 – digit numbers in which all the odd digits and only odd digits appear is

(KIITEE – 2009)

(a) (b) (c) 6! (d) N.O.T

28. Find the total number of ways a child can be given at least one rupee from four 25 paise coins, three 50 paise coins and two one-rupee coins HYDERABAD CENTRAL UNIVERSITY - 2009(a) 53 (b) 51 (c) 54 (d) 55

29. How many 5-digit prime numbers can be formed using the digits 3, 5, 7, 2 and 1 once each?

HYDERABAD CENTRAL UNIVERSITY - 2009(a) 1 (b) 5! – 4! (c) 0 (d) 5!

30. If there are 20 possible lines connecting non-adjacent points of a polygon, how many sides does it have?

HYDERABAD CENTRAL UNIVERSITY - 2009(a) 12 (b) 10 (c) 8 (d) 9

31. From 5 different green balls, four different blue balls and three different red balls, how many combinations of balls can be chosen taking at least one green and one blue ball?

HYDERABAD CENTRAL UNIVERSITY - 2009(a) 60 (b) 3720 (c) 4096 (d) None of these

32. The number of even proper factors of 1008 is HYDERABAD CENTRAL UNIVERSITY - 2009

(a) 24 (b) 22 (c) 23 (d) 25

33. An eight digit number divisible by 9 is to be formed by using 8 digits out of the digits 0, 1, … 9 without replacement. The number of ways in which this can be done is NIMCET - 2008(a) 9! (b) 2(7!) (c) 4(7!) (d) 36(7!)

34. The number of ordered pairs (m, n), m, n {1, 2, … 100} such that 7m + 7n is divisible by 5 is

NIMCET - 2008(a) 1250 (b) 2000 (c) 2500 (d) 5000

35. Twenty apples are to be given among three boys so that each gets atleast four apples. How many ways it can be distributed?

KIITEE - 2008(a) 22C20 (b) 90 (c) 18C8 (d) None

36. The number of arrangements of the letters of the word SWAGAT taking three at a time is

KIITEE - 2008(a) 72 (b) 120 (c) 14 (d) None

37. The number of points (x, y, z) in space, whose each co-ordinate is a negative integer such that x + y + z + 12 = 0 is KIITEE - 2008(a) 110 (b) 385 (c) 55 (d) None

38. There are three piles of identical yellow, black and green balls and each pile contains at least 20 balls. The number of ways of selecting 20 balls if the number of black balls to be selected is twice the number of yellow balls is. KIITEE - 2008(a) 6 (b) 7 (c) 8 (d) 9

39. x1, x2, x3 N. The number of solutions of the equations x1. x2. x3 = 24300 is

IP Paper – 2006(a) 480 (b) 512 (c) 560 (d) 756

40. In how many different ways can the letters of the word DISTANCE can be arranged so that all the vowels come together

Karnataka PG-CET paper – 2006(a) 720 (b) 4320 (c) 4200 (d) 3400

41. In a chess tournament each of the six players will play every other player exactly once. How many matches will be played during the tournament?

Karnataka PG-CET paper – 2006(a) 12 (b) 15 (c) 30 (d) 36

42. In an objective type examination, 120 objective type questions are there : each with 4 options P, Q, R and S. A candidate can choose either one of these options or can leave the question unanswered. How many different ways exist for answering this question paper?

NIMCET – 2008 (a) 5120 (b) 4120 (c) 1205 (d) 1204

43. A four digit number a3a2a1a0 is formed from digits 1 … 9 such that

if ai + 1 is even otherwise i =

0, 1, 2 is the smallest integer larger than a and is the largest integer smaller than a. The

smallest value that a3 can have is (Hyderabad Central University - 2009)

(a) 5 (b) 7 (c) 9 (d) 144. Four students have to be chosen – 2 girls as captain

and vice – captain and 2 boys as captain and vice – captain. There are 15 eligible girls and 12 eligible boys. In how many ways can they be chosen if Sunitha is sure to be captain?

HYDERABAD CENTRAL UNIVERSITY - 2009(a) 114 (b) 1020 (c) 360 (d) 1848

45. From city A to B, there are 3 different roads. From B to C there are 5 and from C to D there are 2 different roads. Laxman has to go from A to D attending to some work in B and C on the way and has to come back in the reversed order. In how many ways can he complete his journey if he does not take the exact same path while coming back? HYDERABAD CENTRAL UNIVERSITY - 2009(a) 250 (b) 870 (c) 90 (d) 100

46. The number of ways in which 12 blue balls, 12 green balls and one black ball can be arranged in a row with the black ball in the middle and arrangements of the colours of balls being symmetrical about the black ball, is IP Paper – 2006

(a) (b)

(c) (d)

47. A contractor hires k people for a job and they complete the job in x days. A month later he gets a contract for an identical job. At this time he has with him k + m + n people for the job, the number of days it will require for them to complete it, is IP Paper – 2006

(a) x + m + n (b)

(c) (d)

48. A student took five papers in an examination, where the full marks were the same for each paper. The marks obtained by the student in these papers were in the proportion 6:7:8:9:10. The student obtained 3/5 of the total full marks. The number of papers in


INFOMATHSwhich the student obtained less than 45 per cent marks is

IP Paper – 2006(a) 2 (b) 3 (c) 4 (d) None of these

35. A set contains (2n + 1) elements. If the number of subsets which contain at most n elements is 4096, then the value of n is

(NIMCET – 2009)(a) 28 (b) 21 (c) 15 (d) 6

23. If nc4, nc5 and nc6 are in arithmetic progression then n is (KIITEE – 2008)(a) 9 (b) 8 (c) 17 (d) 14

TRIGONOMETRY 1. Let be an angle such that 0 < < /2 and tan (/2)

is rational. Then which of the following is true? HCU-2012

(a) Both sin (/2) and cos(/2) are rational(b) tan() is irrational (c) Both sin () and cos() are rational(d) none of the above

2. If then

is equal toHCU-2012

(a) 1+cot (b) 1-cot (c) – 1 – cot (d) – 1+cot

3. The value of is

HCU-2012

(a) tan274 (b) (c) cot 8 (d) tan 16

4. The value of

PU CHD-2012 (A) cos 34° (B) sin 34°(C) cot 56° (D) tan 56°5. The maximum value of sin(x + /6) + cos(x + /6) in

interval (0, /2) is attained at(A) /12 (B) /6 (C) /3 (D) 2

6. If cos + sin = cos, then cos – sin is equal to

PU CHD-2012(A) sin (B) sec

(C) (D)

7. If sin = then =

Pune-2012

(a) (b) (c) (d)

8. If A – B then (1 + tan A) (1 – tan B) is equal to

NIMCET-2012(a) 2 (b) 1 (c) 0 (d) 3

9. Which of the following is correct?NIMCET-2012

(a) sin 1 > sin 1 (b) sin 1 < sin 1

(c) sin 1 = sin 1 (d)

10. If two towers of heights h1 and h2 subtend angles 60 and 30 respectively at the midpoint of the line joining their feet, then h1 : h2 is

NIMCET-2012(a) 1 : 2 (b) 1 : 3 (c) 2 : 1 (d) 3 : 1

11. If and

, then tan (2α) =

NIMCET-2012

(a) (b) (c) (d)

12. If sin2x = 1 – sinx, then cos4x + cos2x = NIMCET-2012

(a) 0 (b) 1 (c) 2/3 (d) – 1 13. The value of cot-1 (21) + cot-1 (13) + cot-1 (-8) is

NIMCET-2012

(a) 0 (b) π (c) 8 (d)

14. If sin (cos) = cos (sin), then sin 2 =NIMCET-2012

(a) (b) (c) (d)

15. If cosec , then tan A is :

BHU-2012

(a) (b) (c) (d)

16. The value(s) of is (are):

BHU-2012

(a) (b) (c) (d)

17. If A + B + C = and , then :

BHU-2012

(a) (b) (c) (d)

18. If sinx + sin2x = 1, then the value of cos12 x + 3cos10x + 3cos8x + cos6x is

BHU-2012(a) – 1 (b) 1 (c) – 2 (d) 2

19. If the angle of elevation of a cloud at a height h above the level of water in a lake is and the angle of depression of its image in the lake is , then the height of the cloud above the surface of the lake is not correct:

BHU-2012

(a) (b)

(c) (d)

20. If the angles of elevation of the top and bottom of a flag staff fixed at the top of a tower at a point distant a from the foot of a tower are and , then height of the flag staff is :

BHU-2012(a) a (sin - sin ) (b) a (cos - cos )(c) a (cot - cot ) (d) a (tan - tan )

21. The solution of the equation

is : BHU-2012

(a) (b)

(c) x = 1 (d) x = 0


INFOMATHS22. If then x is :

BHU-2012

(a) 0 (b) (c) (d)

23. The value of is equal to :

BHU-2012

(a) (b) (c) (d)

24. If , then the value of is

HCU-2011(a) 1/2 or 2 (b) 1/2 or – 2 (c) 3/4 or – 2 (d) 3/4 or 2

25. The value of sin 30° cos 45° + cos 30° sin 45°[no correct answer was given in choices, correct

answer should be ]

NIMCET-2011

(a) (b) (c) (d)

26. The solution of Δ ABC given that B = 45°, C = 105° and c = is

NIMCET-2011

(a) A = 30°, c = , b =

(b) A = 30°, c = , b =

(c) B = 30°, c = , b =

(d) B = 30°, c = , b =

27. If , then the value of a cos 2θ + b sin 2θ is

NIMCET-2011

(a) b (b) a (c) (d)

28. The general solution of is:NIMCET-2011

(a) (b)

(c) No solutions (d)

29. The value of is

NIMCET-2011, BHU-2011

(a) 1 (b) (c) (d) 2

30. If sin x, cos x and tan x are in GP, then the value of cot6x – cot2x is:

NIMCET-2011(a) 2 (b) – 1 (c) 1 (d) 0

31. The greatest angle of the triangle whose three sides are x2 + x + 1, 2x + 1 and x2 – 1 is

NIMCET-2011(1) 150° (2) 90° (3) 135° (4) 120°

32. The general value of θ satisfying the equation 2sin2 θ − 3sin θ − 2 = 0 is

NIMCET-2011

(a) (b)

(c) (d)

33. In a ABC, cosec A(sin B cos C + cos B sinC) equals BHU-2011

(a) (b) (c) 1 (d) 0

34. The value of tan 9 - tan 27 - tan 63 + tan 81 is BHU-2011

(a) 1 (b) 2 (c) 3 (d) 4

35. If , then the value of cos

is

BHU-2011

(a) (b) (c) (d)

36. From the top of a lighthouse 60 m high with its base at the sea-level, the angle of depression of a boat is 15. The distance of the boat from the foot of the lighthouse is

BHU-2011

(a) (b)

(c) (d)

37. The general solution of the trigonometrical equation sinx + cosx = 1 is given by

BHU-2011(a) x = 2n, n = 0, 1, 2, …

(b) x = 2n + , n = 0, 1, 2, …..

(c)

(d)

38. If sin = sin , then the angle and are related by BHU-2011

(a) = 2n + (-1)n (b) = n (c) = n + (-1)n (d) = (2n + 1) +

39. The value of cos 10 - sin 10 is BHU-2011

(a) positive (b) negative (c) 0 (d) 1

40. In a triangle ABC, R is circumradius and 8R2 = a2 +b2+c2. The triangle ABC is NIMCET-2010 (a) Acute angled (b) Obtuse angled

(c) Right angled (d) N.O.T

41. If sin-1 then x is

equal to NIMCET-2010

(a) a (b) b (c) (d)

42. The value of cot 200 -4 cos 200 is NIMCET-2010

(a) 1 (b) -1 (c) 0 (d) N.O.T43. If tan A – tan B = x and cot B – cot A = y, then cot (A

– B) is equal to KIITEE-2010

(a) (b) (c) (d)

(e) None of these


INFOMATHS44. If cos ( – ) = a, and cos ( – ) = b, then sin2 ( – )

+ 2ab cos ( – ) is equal to KIITEE-2010

(a) a2 + b2 (b) a2 – b2 (c) b2 – a2 (d) – a2 – b2 (e) None of these

45. The number of ordered pairs (,) where , (-,)

satisfying cos ( - ) = 1 and is

KIITEE-2010(a) 0 (b) 1 (c) 2 (d) 4(e) None of these

46. If tan = (1 + 2-x)-1, tan = (1 + 2x+1)-1, then + equals

KIITEE-2010

(a) (b) (c) (d)

(e) None of these47. If tan (cos) = cot(sin), then the value of

is equal to

KIITEE-2010

(a) (b) (c) (d)

(e) None of these

48. Solution of the equation is

KIITEE-2010

(a) x = 3 (b)

(c) x = 0 (d) None of these(e) None of these

49. The value of

KIITEE-

2010

(a) (b) (c) (d)

50. In ABC, a = 2, b = 3 and then B is equal

to KIITEE-2010

(a) 30 (b) 60 (c) 90 (d) 120

51. The value of is

PGCET-2010

(a) 0 (b) 1 (c) (d)

52. From a point 100 meters above the ground, the angles of depression of two objects due south on the ground are 60 and 45. The distance between the object is PGCET-2010

(a) mts (b) mts

(c) mts (d) None of these

53. The greatest angle of ABC whose sides are a = 5, b and c = 5, is

PGCET-2010(a) 45 (b) 100 (c) 120 (d) 60

54. The value of

(PGCET– 2009)(a) (b)

(c) (d) 55. The elevation of the tower 100 meters away is 30.

The length of the tower is (PGCET paper – 2009)

(a) mts (b) mts

(c) mts (d) mts

56. The smallest angle of a ABC whose sides are a = 1, is (PGCET paper –

2009)(a) 20 (b) 90 (c) 75 (d) 15

57. If

then is

equal to (MCA : NIMCET – 2009)

(a) (b) (c) (d)

58. The number of solutions for

is

(MCA : NIMCET – 2009)(a) zero (b) one (c) two (d) infinite

59. If , then x is

(MCA : NIMCET – 2009)(a) 1/6 (b) 1/3 (c) 1/2 (d) 1/4

60. If A = cos2 + sin4, then for all values of (MCA : NIMCET – 2009)

(a) 1 A 2 (b)

(c) (d)

61. If sin-1 x + cos-1 (1 – x) = sin-1 (-x), then x satisfies the equation

(MCA : NIMCET – 2009)(a) 2x2 – x + 2 = 0 (b) 2x2 – 3x = 0 (c) 2x2 + x – 1 = 0 (d) None of these

62. The equation sin4x + cos4x + sin2 x + = 0 is solvable for

(MCA : NIMCET – 2009)

(a) (b) – 3 1

(c) (d) – 1 1

63. The number of values of the triple t(a, b, c) for which a cos 2x + b sin2x + c = 0 is satisfied by all real x is (MCA : KIITEE – 2009)(a) 0 (b) 2 (c) 3 (d) infinite

64. has the value

(KIITEE – 2009)(a) sin A sin B cos C (b) 0(c) 1 (d) None of these

65. The number of solution of |cos x| = sin x, 0 x 4, is (MCA : KIITEE – 2009)(a) 8 (b) 2 (c) 4 (d) None of these

66. The formula holds for (MCA : KIITEE – 2009)


INFOMATHS(a) x (-1, 0) (b)

(c) x [0, 1] (d)

67. The value of

(KIITEE – 2009)(a) 17/6 (b) 7/16 (c) 6/17 (d) None of these

68. If cos-1 x > sin-1x, then (KIITEE – 2009)

(a) x < 0 (b) –1 < x < 0

(c) (d)

69. Consider the function on R. Let

x1 and x2 be two real values such that f(x1) = f(x2). Then x1 – x2 is always of the form

Hyderabad Central University - 2009(a) (b)

(c) (d)

70. Two persons are standing at different floors of a tall building and are looking at a statue that is 100 metres far from the building. Angle of inclination of the person at higher floor is 60 and that of the person at lower floor is 45. What is the distance between the two persons? Hyderabad Central University - 2009

(a) (b)

(c) (d) 71. The maximum value of (cos 1) (cos 2) …. (cos n)

where 0 1, 2, n /2 and (cot 1) (cot 2) … (cot n) = 1 is

NIMCET – 2008

(a) (b) (c) (d) 1

72. If cos + cos = a, sin + sin = b and is the arithmetic mean between and , then sin 2 + cos 2 is equal to

NIMCET - 2008(a) (b)

(c) (d) None

73. If (1 + tan 1) (1 + tan2) … (1 + tan 45) = 2n, then the value of n is

NIMCET - 2008(a) 21 (b) 22 (c) 23 (d) 24

74. The value of sin 12 and 48 sin 54 NIMCET - 2008(a) sin 30 (b) sin230 (c) sin330 (d) cos3 30

75. The value of

terms is equal to MCA : KIITEE – 2008

(a) 0 (b) 1 (c) (d) None

76. In a ABC, a = 5, b = 4 and then the

side c is MCA : KIITEE – 2008

(a) 3 (b) 6 (c) 2 (d) None

77. In a ABC, A = 90. Then

MCA : KIITEE – 2008

(a) (b) (c) (d)

None

78. If in a ABC, 3a = b + c then is

equal to KIITEE – 2008

(a) 1 (b) (c) 2 (d) None

79. cos-1 (cos x) = x is satisfied by KIITEE – 2008(a) x R (b) x [-1, 1](c) x [0, ] (d) None

80. The value of is KIITEE –

2008


81. A tower casts a shadow 100, long when the elevation of a source of light is at 45. What is the height of the tower?

KARNATAKA - 2007(a) (b) 100m (c) 10m (d) m

82. From the top of a light house 360 m height, the angles of depression of the top and bottom of a tower are observed to be 30 and 60 respectively. What is the height of the tower?

KARNATAKA - 2007(a) 200m (b) 210m (c) 190m (d) 240m

83. The greatest angle of a triangle with sides 7, 5 and 3 is KARNATAKA - 2007(a) 60 (b) 90 (c) 120 (d) 135

84. For a triangle XYZ, if X , Y = 2, Z then X is

KARNATAKA - 2007(a) 45 (b) 60 (c) 75 (d) 30

85. A wire of length 20 cm is bent so as to form an arc of a circle of radius 12 cm. The angle subtended at the center is

KARNATAKA - 2007(a) 3/5 radians (b) 5/3 radians (c) 1/3 radians (d) 5 radians

86. A circular metallic ring of radius 1 foot is reshaped into a circular arc of radius 80 ft. The area of the sector formed is

KARNATAKA - 2007(a) 20 sq ft. (b) 40 sq. ft (c) 80 sq. ft (d) 60 sq. ft

87. If A, B, C, D are angles of a cyclic quadrilateral then cos A + cos B + cos C + cos D is

KARNATAKA – 2007, UP-2002(a) 1 (b) 0 (c) 2 (d) 3

88. If x cos - y sin = and x sin + y cos then x2 + y2

ICET - 2007(a) 2 (b) 2 (c) 2 + 2 (d) 2 – 2

89. If (0 < < 90 and the matrix

has no inverse than

ICET - 2007(a) 30 (b) 45 (c) 60 (d) 75

90. It then sin f() + cos

ICET -


INFOMATHS(a) (b)

(c) (d)

91. If A + C = B, then, tan A tan B tan C = ICET – 2005(a) tan B – tan A + tan C (b) tan B + tan A – tan C (c) tan B – tan A + tan C (d) tan A + tan B + tan C

92. If a flag staff of 6 metres height, placed on the top of a tower throws a shadow of metres along the ground, then, the angle in degrees that the sun makes with the ground is

ICET–2005(a) 30 (b) 45 (c) 60 (d) 75

93. If , then, for 0 < < 90

ICET – 2005

(a) (b) (c) (d)

94. The general solution of the equation sin2 – sin2 - 15cos2 = 0 is given by equals

IP University : Paper – 2006(a) n + tan-1 3 or m - tan-1 5 (b) n - tan-1 3 or m + tan-1 5 (c) n - tan-2 2 or m + tan-1 6 (d) n - tan-1 7 or m - tan-1 3 (e) None of these

95. When the length of the shadow of a pole is equal to a height of the pole, then the elevation of source of light is

Karnataka PG-CET Paper – 2006(a) 30 (b) 45 (c) 60 (d) 75

96. If tan A + cot A = 4 then tan4 A + cot4 A is equal to Karnataka PG-CET Paper – 2006

(a) 110 (b) 194 (c) 88 (d) 19497. If one side of a triangle is double of another side and

the angle opposite to these sides differ by 60, then the triangle is Karnataka PG-CET Paper – 2006(a) right angled (b) an obtuse angled (c) an acute angled (d) None of these

98. If sin A = sin B and cos A = cos B, then Karnataka PG-CET Paper – 2006

(a) A = n + B (b) A = n - B (c) A = 2 n + B (d) A = 2n - B

99. If tan-1 x + tan-1 y = /4, then Karnataka PG-CET Paper – 2006

(a) x + y + xy = 1 (b) x + y – xy = 1 (c) x + y + xy + 1 = 1 (d) x + y – xy + 1 = 0

100. The equation 3 cos x + 4 sin x = 6 has _____ solution

Karnataka PG-CET Paper – 2006(a) finite (b) infinite (c) one (d) no

101. The value of sin x(1 + cos x) is maximum at: MP: MCA Paper - 2004

(a) /3 (b) /2 (c) /6 (d) 3/4

102. UPMCAT : Paper – 2002

(a) 117 (b) 3/7 (c) -1/7 (d) None of these

103. Cos40 + Cos80 + Cos 160 is equal to : UPMCAT : Paper – 2002

(a) -1 (b) 0 (c) 1 (d) N.O.T. 104. A, B, C are in A.P. b:c then A is equal

to : UPMCAT : Paper – 2002 (a) 103.5 (b) 98.5 (c) 101.5 (d) None of these

105. If two stones are 500 meters apart. The, angle of depressions being 30 and 45 as seen by aeroplane what is the altitude the plane is flying:

UPMCAT : Paper – 2002 (a) mts (b) mts (c) mts (d) None of these

106. is equal to :

UPMCAT : Paper – 2002

(a) (b) (c) (d) None of these

107. If cosec x + cot x = 2 sin x, where 0 ≤ x ≤ 2π In then:

UPMCAT : Paper – 2002 (a) x = π/3, 5 π/3 (b) x = π/3, 5π/6 (c) x = π/3, π (d) None of these

108. In a cyclic quadrilateral ABCD, sin (A + C) is equal to : UPMCAT : Paper – 2002 (a) 1/2 (b) 1 (c) – 1 (d) 0

109. The maximum value of 3cosx + 4sinx + 5 is: UPMCAT : Paper – 2002

(a) 10 (b) 0 (c) 5 (d) None of these

110. The sides of a triangle are a, b and , then the greatest angle is :

UPMCAT : Paper – 2002 (a) 60 (b) 90 (c) 120 (d) None of these

111. sin[cot-1 cos(tan-1 y)] is equal to : UPMCAT : Paper – 2002

(a) (b)


112. If then C is:

UPMCAT : Paper – 2002 (a) 90 (b) 60 (c) 30 (d) 45

PROBABILITY 1. All the coefficients of the equation ax2 + bx + c = 0

are determined by throwing a six-sided un-biased dice. The probability that the equation has real roots is

HCU-2012 (a) 57/216 (b) 27/216 (c) 53/216 (d) 43/216

2. Suppose 4 vertical lines are drawn on a rectangular sheet of paper. We name the lines

and respectively. Suppose two players A and B join two disjoint pairs of end points within A1 to A4 and B1 to B4 respectively without seeing how the other is marking.What is the probability that the figure thus formed has disconnected loops?

HCU-2012 (a) 1/3 (b) 2/3 (c) 3/6 (d) 1/6

3. In a village having 5000 people, 100 people suffer from the disease Hepatitis B. It is known that the accuracy of the medical test for Hepatitis B is 90%. Suppose the medical test result comes out to be positive for Anil who belongs to the village, then what is the probability that Anil is actually having the disease.

HCU-2012 (a) 0.02 (b) 0.16 (c) 0.18 (d) 0.3

4. Let A, B and C be the three events such thatP(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(A B) = 0.08, P(A C) = 0.28, P(A B C) = 0.09.If P(A B C) 0.75, then P(B C) satisfies :

PU CHD-2012(A) P(B C) ≤ 0.23 (B) P(B C) ≤ 0.48


INFOMATHS(C) 0.23 ≤ P(B C) ≤ 0.48 (D) P(B C) ≤ 0.15

5. A number is chosen from each of the two sets {1, 2, 3, 4, 5, 6, 7, 8, 9} and {1, 2, 3, 4, 5, 6, 7, 8, 9}. If P denotes the probability that the sum of the two numbers be 10 and Q the probability that their sum be 8, then (P + Q) is

PU CHD-2012

(A) (B) (C) (D)

6. Let P(E) denote the probability of event E. Given P(A)

= 1, P(B) , the values of P(A|B) and P (B|A)

respectively are NIMCET-2012

(a) (b) (c) (d)

7. A determinant is chosen at random from the set of all determinants of matrices of order 2 with elements 0 and 1 only. The probability that the determinant chosen is non-zero is

NIMCET-2012(a) 3/16 (b) 3/8 (c) 1/4 (d) None of these

8. Coefficients of quadratic equation ax2 + bx + c = 0 are chosen by tossing three fair coins where ‘head’ means one and ‘tail’ means two. Then the probability that roots of the equation are imaginary is

NIMCET-2012(a) 7/8 (b) 5/8 (c) 3/8 (d) 1/8

9. A problem in Mathematics is given to three students

A, B and C whose chances of solving it are

respectively. If they all try to solve the problem, what is the probability that the problem will be solved? NIMCET-2012, MP-2008(a) 1/2 (b) 1/4 (c) 1/3 (d) 3/4

10. If a fair coin is tossed n times, then the probability that the head comes odd number of times is

NIMCET-2012

(a) (b) (c) (d) None of

these11. One hundred identical coins each with probability P

of showing up heads re tossed. If 0 < P < 1 and the probability of heads showing on 50 coins is equal to that of heads on 51 coins; then the value of P is

NIMCET-2012

(a) (b) (c) (d)

12. Let P be a probability function on S = (l1, l2, l3, l4)

such that . Then P(l1)

is BHU-2012

(a) 7/18 (b) 1/3 (c) 1/6 (d) 1/513. The probability that A, B, C can solve problem is

respectively they attempt independently,

then the probability that the problem will solved is : BHU-2012

(a) 1/9 (b) 2/9 (c) 4/9 (d) 2/3

14. In a single throw with two dice, the chances of throwing eight is :

BHU-2012(a) 7/36 (b) 1/18 (c) 1/9 (d) 5/36

15. A single letter is selected at random from the word “probability”. The probability that it is a vowel, is :

BHU-2012

(a) 3/11 (b) 4/11 (c) 2/11 (d) 016. An unprepared student takes a five question true-

false exam and guesses every answer. What is the probability that the student will pass the exam if at least four correct answers is the passing grade?

HCU-2011(a) 3/16 (b) 5/32 (c) 1/32 (d) 1/8Answer questions 17 and 18 using the following text: In a country club, 60% of the members play tennis, 40% play shuttle and 20% play both tennis and shuttle. When a member is chosen at random,

17. What is the probability that she plays neither tennis nor shuttle?

HCU-2011(a) 0.8 (b) 0.2 (c) 0.5 (d) 0.4

18. If she plays tennis, what is the probability ability that she also plays shuttle?

HCU-2011(a) 2/3 (b) 2/5 (c) 1/3 (d) 1/2

19. If E is the event that an applicant for a home loan in employed C is the event that she possesses a car and A is the event that the loan application is approved, what does P(A|E C) represent in words?

HCU-2011(a) Probability that the loan is approved, if she is employed and possesses a car (b) Probability that the loan is approved, if she is either employed or possesses a car (c) Probability that the loan is approved, if she is neither employed nor possesses a car.(d) Probability that the loan is approved and she is employed, given that she possesses a car

20. An anti-aircraft gun can take a maximum of four slots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth slots are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane then is

NIMCET-2011(a) 0.5 (b) 0.7235 (c) 0.6976 (d) 1.0

21. A random variable X has the following probability distributionx 0 1 2 3 4 5 6 7 8 P(X = x) a 3a 5a 7a 9a 11a 13a 15a 17a Then the value of ‘a’ is

NIMCET-2011(a) 1/81 (b) 2/82 (c) 5/81 (d) 7/81

22. Three coins are thrown together. The probability of getting two or more heads is

BHU-2011(a) 1/4 (b) 1/2 (c) 2/3 (d) 3/8

23. If four positive integers are taken at random and are multiplied together, then the probability that the last digit is 1, 3, 7 or 9 is :

PU CHD-2010

(A) (B) (C) (D)

24. The numbers X and Y are selected at random (without replacement) from the set (1, 2, .....3N). The probability that x2 – y2 is divisible by 3 is :

PU CHD-2010

(A) (B) (C) (D)

25. Probability of happening of an event A is 0.4 Probability that in 3 independent trials, event A happens atleast once is:PU CHD-2009(a) 0.064 (b) 0.144 (c) 0.784 (d) 0.4

26. A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P(A B) is : PU CHD-2009(a) 3/5 (b) 0 (c) 1 (d) 1/6


INFOMATHS27. India plays two matches each with West Indies and

Australia. In any match the probabilities of India getting points 0, 1 and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability f India getting at least 7 points is NIMCET-2010 (a) 0.8750 (b) 0.0875 (c) 0.0625 (d)

0.025028. A coin is tossed three times The probabilities of

getting head and tail alternatively is NIMCET-2010

(a) 1/11 (b) 2/3 (c) 3/4 (d) 1/429. One hundred identical coins, each with probability P

of showing up a head, are tossed. If 0 < p < 1 and if the probability of heads on exactly 50 coins is equal to that of heads on exactly 51 coins then the value of p, is NIMCET-2010

(a) (b) (c) (d)

30. A dice is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is

KIITEE-2010(a) 8/3 (b) 3/8 (c) 4/5 (d) 5/4

31. If A and B are events such that

then is

KIITEE-2010(a) 5/12 (b) 3/8 (c) 5/8 (d) 1/4

32. If A and B are any two mutually exclusive events, then P(A|AB) is equal to

(PGCET– 2009)(a) P(AB) (b) P(A)/(P(A) + P(B)) (c) P(B)/P(AB) (d) None of these

33. A man has 5 coins, two of which are double – headed, one is double – tailed and two are normal. He shuts his eyes, picks a coin at random, and tosses it. The probability that the lower face of the coin is a head is (NIMCET – 2009)(a) 1/5 (b) 2/5 (c) 3/5 (d) 4/5

34. A and B are independent witnesses in a case. The probability that A speaks the truth is ‘x’ and that B speaks the truth is ‘y’. If A and B agree on a certain statement, the probability that the statement is true is (NIMCET – 2009)

(a) (b)

(c) (d)

35. Let A and B be two events such that

and .

Then events A and B are (NIMCET – 2009)

(a) independent but not equally likely(b) mutually exclusive and independent (c) equally likely and mutually exclusive(d) equally likely but not independent.

36. The probability that a man who is 85 yrs. old will die before attaining the age of 90 is 1/3. A1, A2, A3 and A4 are four persons who are 85 yrs. old. The probability that A1 will die before attaining the age of 90 and will be the first to die is

(NIMCET – 2009)

(a) (b) (c) (d)

37. An anti aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The

probabilities of hitting the plane at first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane then is

(MCA : NIMCET – 2009)(a) 0.6972 (b) 0.6978 (c) 0.6976 (d) 0.6974

38. Let A = [2, 3, 4, …., 20, 21] number is chosen at random from the set A and it is found to be a prime number. The probability that it is more than 10 is

(MCA : KIITEE – 2009)(a) 9/10 (b) 1/5 (c) 1/10 (d) None of these

39. Find the probability that a leap year will contain either 53 Tuesday or 53 Wednesdays.

HYDERABAD CENTRAL UNIVERSITY - 2009(a) 1/5 (b) 2/5 (c) 2/3 (d) 3/7

40. Probability that atleast one of A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then P(A') + P(B') is

HYDERABAD CENTRAL UNIVERSITY - 2009(a) 0.9 (b) 1.15 (c) 1.1 (d) 2

41. The sum of two positive real numbers is 2a. The probability that product of these two numbers is not less than 3/4 times the greatest possible product is

HYDERABAD CENTRAL UNIVERSITY - 2009(a) 1/2 (b) 1/3 (c) 1/4 (d) 9/16

42. If two events A and B such that P(A') = 0.3, P(B) = 0.5 and P(A B) = 0.3, then P(B/AB') is :

NIMCET - 2008(a) 1/4 (b) 3/8 (c) 1/8 (d) None

43. A pair of unbiased dice is rolled together till a sum of either 5 or 7 is obtained. The probability that 5 comes before 7 is.

NIMCET - 2008(a) 3/5 (b) 2/5 (c) 4/5 (d) None

44. A letter is taken at random from the letters of the word ‘STATISTICS’ and another letter is taken at random from the letters of the word ‘ASSISTANT’. The probability that they are the same letter is.

NIMCET - 2008

(a) (b) (c) (d)

45. A six faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even, is.

NIMCET - 2008(a) 4/8 (b) 5/8 (c) 6/8 (d) 7/8

46. A letter is known to have come from either TATANAGAR or CALCUTTA. On the envelope, just two consecutive letters, TA, are visible. The probability that the letter has come from CALCUTTA is

NIMCET - 2008(a) 4/11 (b) 1/3 (c) 5/12 (d) None

47. A card is drawn from a pack. The card is replaced and the pack is reshuffled. If this is done six times, the probability that 2 hearts, 2 diamonds and 2 club cards are drawn is. KIITEE – 2008

(a) (b)

(c) (d) None

48. Two balls are drawn at random from a bag containing 6 white, 4 red and 5 black balls. The probability that both these balls are black, is :

MP COMBINED – 2008(a) 1/21 (b) 2/15 (c) 2/21 (d) 2/35

49. 6 boys and 6 girls sit in a row randomly. The probability that all the girls sit together is :

MP COMBINED – 2008

(a) (b) (c) (d)


INFOMATHS50. Probabilities of three students A, B and C to pass an

examination are respectively , and . The

probability that exactly one student will pass is: MP COMBINED – 2008

(a) (b) (c) (d)

51. Different words are written with the letters of PEACE. The probability that both E’s come together is :

MP COMBINED – 2008(a) 1/3 (b) 2/5 (c) 3/5 (d) 4/5

52. The probability of throwing 6 at least one in four throws of a die is: MP COMBINED – 2008

(a) (b) (c) (d)

53. An untrue coin is such that when it is tossed the chances of appearing head is twice the chances of appearance of tail. The chance of getting head in one toss of the coin is :

MP COMBINED – 2008(a) 1/3 (b) 1/2 (c) 2/3 (d) 1

54. The probability of randomly chosing 3 defectless bulbs from 15 electric bulbs of which 5 bulbs are defective, is :

MP COMBINED – 2008

(a) (b) (c) (d)

55. Probability of four digit numbers, which are divisible by three, formed out of digits 1, 2, 3, 4, 5 is : MP COMBINED – 2008(a) 1/5 (b) 1/4 (c) 1/3 (d) 1/2

56. Let A and B be two events with P(A) = 1/2, P(B) = 1/3 and P(A B) = 1/4 , What is P(A B)?

KARNATAKA - 2007(a) 3/7 (b) 4/7 (c) 7/12 (d) 9/122

57. If three unbiased coins are tossed simultaneously then the probability of getting exactly two heads is

ICET - 2007(a) 1/8 (b) 2/8 (c) 3/8 (d) 4/8

58. A person gets as many rupees as the number he gets when an unbiassed 6 – faced die is thrown. If two such dice are thrown the probability of getting Rs. 10 is. ICET - 2007(a) 1/12 (b) 5/12 (c) 13/10 (d) 19/10

59. Let E be the set of all integers with 1 in their units place. The probability that a number n chosen from [2, 3, 4, … 50] is an element of E is

ICET - 2007(a) 5/49 (b) 4/49 (c) 3/49 (d) 2/49

60. A and B independent events. The probability that

both A and B occur is and the probability that

neither of them occurs is 1/6. Then the probability of occurrence of A is. ICET – 2005(a) 5/6 (b) 1/2 (c) 1/12 (d) 1/18

61. 8 coins are tossed simultaneously. The probability of getting atleast six heads is

ICET – 2005

(a) (b) (c) (d)

62. If two dice are tossed the probability of getting the sum at least 5 is PUNE Paper – 2007

(a) (b) (c) (d)

63. A and B play a game of dice. A throws the die first. The person who first gets a 6 is the winner. What is the probability that A wins?

PUNE Paper – 2007(a) 6/11 (b) 1/2 (c) 5/6 (d) 1/6

64. A player is going to play a match either in the morning or in the afternoon or in the evening all possibilities being equally likely. The probability that he wins the match is 0.6, 0.1 and 0.8 according as if the match is played in the morning, afternoon or in the evening respectively. Given that he has won the match, the probability that the match was played in the afternoon is

IP Univ. Paper – 2006

(a) (b) (c) (d) (e)

65. The probabilities that a husband and wife will be alive 20 years from now are given by 0.8 and 0.9 respectively. What is the probability that in 20 years at least one, will be alive?

Karnataka PG-CET : Paper – 2006 (a) 0.98 (b) 0.02 (c) 0.72 (d) 0.28

66. A bag contains 4 white and 3 black balls and a second bag contains 3 white and 3 black balls. If a ball is drawn from each of the bags, then the probability that both are of same colour is :

MP Paper – 2004

(a) (b) (c) (d)

67. The probability of getting atleast 6 head in 8 trials is: MP– 2004

(a) (b) (c) (d)

68. Prob. of getting an odd number or a no. less than 4 in throwing a dice is :

MP– 2004(a) 1/3 (b) 2/3 (c) 1/2 (d) 3/5

69. Given A and B are mutually exclusive events. IFP (B) = 0. 15, P(A B) = 0.85, P(A) is equal to UPMCAT Paper – 2002(a) 0.65 (b) 0.3 (c) 0.70 (d) N.O.T.

70. In a pack of 52 cards, the probability of drawing at random such that it is diamond or card king is :

UPMCAT Paper – 2002(a) 1/26 (b) 4/13 (c) 3/13 (d) 1/4

71. Given A and B are mutually exclusive events. if:P (A B) = 0.8, P(B) = 0.2 then P(A) is equal to UPMCAT–2002(a) 0.5 (b) 0.6 (c) 0.4 (d) N.O.T.

72. Two dice are thrown once the probability of getting a sum 9 is given by : UPMCAT Paper – 2002(a) 1/12 (b) 1/18 (c) 1/6 (d) N.O.T.

73. In a pack of 52 cards. Two cards are drawn at random. The probability that it being club card is :

UPMCAT Paper – 2002

(a) (b) (c) (d) N.O.T.

74. If P(A' B') is equal to 19/60 then P(AB) is equal to

UPMCAT Paper – 2002

(a) (b) (c) (d) N.O.T.

75. If the events A and B are mutually exclusive then P (A B) is given by : UPMCAT Paper – 2002(a) P(A) + P(B) (b) P(A)P(B) (c) P(A) P(B/A) (d) N.O.T.

76. If A and B are two events, the prob. that exactly one of them, occurs in given by: UPMCAT Paper – 2002

(a) (b)



INFOMATHS77. A bag contains 6 red and 4 green balls. A fair dice is

rolled and a number of balls equal to that appearing on the dice is chosen from the urn at random. The probability that all the balls selected are red is.

NIMCET – 2008 (a) 1/3 (b) 3/10 (c) 1/8 (d) none

78. A number x is chosen at random from (1, 2, …. 10). The probability that x satisfies the equation (x – 3) (x – 6) (x – 10) = 0 is

ICET - 2007(a) 2/5 (b) 3/5 (c) 3/10 (d) 7/10

TWO DIMENSIONAL GEOMETRY 1. Find the equation of the graph xy = 1 after a

rotation of the axes by 45 degrees anti-clockwise in the new coordinate system (x', y').

HCU-2012

(a) x'2 – y'2 = 1 (b)

(c) (d)

2. The number of points (x, y) satisfying (i) 3x - 4y = 25 and (ii) x2 + y2 25 is

HCU-2012(a) 0 (b) 1 (c) 2 (d) infinite

3. A point P on the line 3x + 5y = 15 is equidistant from the coordinate axes. Then P can lie in

HCU-2012(a) Quadrant I only (b) Quadrant I or Quadrant III only (c) Quadrant I or Quadrant II only (d) any Quadrant

4. A circle and a square have the same perimeter. Then HCU-2012

(a) their areas are equal (b) the area of the circle is larger (c) the area of the square is larger (d) the area of the circle is times the area of the square

5. The eccentricity of the ellipse x2 + 4y2 + 8y – 2x + 1 = 0 is :

PU CHD-2012

(A) (B) (C) (D)

6. The orthocenter of the triangle formed by the lines xy = 0 and x + y = 1 is :

PU CHD-2012(A) (1/2, 1/2) (B) (1/3, 1/3)(C) (1/4, 1/4) (D) (0, 0)

7. The distance between the parallel lines y = 2x + 4 and 6x = 3y + 5 is

PU CHD-2012, NIT-2010

(A) (B) 1 (C) (D)

8. The lines 2x – 3y = 5 and 3x – 4y = 7 are the diameters of a circle of area 154 square units. Then the equation of this circle is ( = 22/7)

PU CHD-2012(A) x2 + y2 + 2x – 2y = 62 (B) x2 + y2 + 2x – 2y

= 47(C) x2 + y2 – 2x + 2y = 47 (D) x2 + y2 – 2x + 2y

= 629. The focus of the parabola y2 – x – 2y + 2 = 0 is :

PU CHD-2012(A) (1/4, 0) (B) (1, 2) (C) (3/4, 1) (D) (5/4,

1)10. The medians of a triangle meet at (0, –3). While its

two vertices are (–1, 4) and (5, 2), the third vertex is at

PU CHD-2012(A) (4, 5) (B) (–1, 2) (C) (7, 3) (D) (– 4, – 15)

11. The area of the triangle having the vertices (4, 6), (x, 4), (6, 2) is 10 sq units. The value of x is

PU CHD-2012(A) 0 (B) 1 (C) 2 (D) 3

12. The position of reflection of point (4, 1) w.r.to line y = x – 1 is

Pune-2012(a) (-4, -1) (b) (1, 2) (c) (2, 3) (d) (3, 4)

13. 6x2 + 12x + 8 – y = 0 has its standard form as? Pune-2012

(a) (b)


14. If a given point is P(10,10) and the Eq. of circle is(x – 1)2 + (y – 2)2 = 144. Where does the pt. lies

Pune-2012(a) inside (b) on (c) outside (d) None of these

15. The point on the curve y = 6x = x2, where the tangent is parallel to x – axis is

NIMCET-2012(a) (0, 0) (b) (2, 8) (c) (6, 0) (d) (3, 9)

16. If (4, - 3) and (-9, 7) are the two vertices of a triangle and (1, 4) is its centroid, then the area of triangle is

NIMCET-2012

(a) (b) (c) (d)

17. The equation of the ellipse with major axis along the x-axis and passing through the points (4, 3) and (-1, 4) is

NIMCET-2012(a) 15x2 + 7y2 = 247 (b) 7x2 + 15y2 = 247 (c) 16x2 + 9y2 = 247 (d) 9x2 + 16y2 = 247

18. If the circles x2 + y2 + 2x + 2ky + 6 = 0 and x2 + y2

+ 2ky + k = 0 intersect orthogonally, then k is NIMCET-2012

(a) 2 of (b) – 2 or

(c) 2 or (d) – 2 or

19. Focus of the parabola x2 + y2 – 2xy – 4(x + y – 1) = 0 is

NIMCET-2012(a) (1, 1) (b) (1, 2) (c) (2, 1) (d) (0, 2)

20. If e and er be the eccentricities of a hyperbola and

its conjugate, then

NIMCET-2012(a) 0 (b) 1 (c) 2 (d) None of these

21. The straight line passes through the point and makes an angle of 60 with the x-axis. The length of the intercept on it between the point P and the line is :

BHU-2012(a) 1.5 (b) 2.5 (c) 3.5 (d) 4.5

22. The equation of the straight line passing through the point of intersection of 4x + 3y – 8 = 0 and x + y – 1 = 0, and the point (-2, 5) is :

BHU-2012(a) 9x + 7y – 17 = 0 (b) 4x + 5y + 6 = 0 (c) 3x – 2y + 19 = 0 (d) 3x – 4y – 7 = 0

23. The angle between the two straight line represented by the equation 6x2 + 5xy – 4y2 + 7x + 13y – 3 = 0 is:

BHU-2012

(a) (b)

(c) (d)

24. The equation of circle passing through (-1, 2) and concentric with x2 + y2 – 2x – 4y – 4 = 0 is :

BHU-2012(a) x2 + y2 – 2x – 4y + 1 = 0 (b) x2 + y2 – 2x – 4y + 2 = 0


INFOMATHS(c) x2 + y2 – 2x – 4y + 4 = 0 (d) x2 + y2 – 2x – 4y + 8 = 0

25. The radius of the circle on which the four points of intersection of the lines (2x – y + 1) (x – 2y + 3) = 0 with the axes lie, is :

BHU-2012

(a) 5 (b) (c) (d)

26. The focal distance of a point on the parabola y2 = 8x is 4. Its ordinates are :

BHU-2012(a) 1 (b) 2 (c) 3 (d) 4

27. The straight line x cos + y sin = p touches the

ellipse if :

BHU-2012(a) p2 = a2 cos2 - b2 sin2 (b) p2 = a2 cos2 + b2 sin2(c) p2 = a2 sin2 - b2 cos2 (d) p2 = a2 sin2 + b2 cos2

28. If the line lx + my = n touches the hyperbola

if :

BHU-2012(a) a2l2 – b2m2 = n2 (b) al – bm = n (c) a2l2 + b2m2 = n2 (d) al + bm = n

29. For the conic , the sum of reciprocals

of the segments of any focal chord is equal to : BHU-2012

(a) l (b) 2l (c) (d)

30. The equation of tangent at (2, 2) of the curve xy2 = 4 (4 – x) is :

BHU-2012(a) x – y = 4 (b) x + y = 4 (c) x – y = 2 (d) x + y = 2

31. A curve given in polar form as r = a(cos() + sec ()) can be written in Cartesian form as

HCU-2011(a) x(x2 + y2) = a(2x2 + y2) (b)

(c) (d) y = atan + x

32. The relation that represents the shaded region in the figure given below is

HCU-2011(a) y x (b) |y| |x| (c) y |x| (d) |y| x

33. The area enclosed within the lines |x| + |y| = 1 isNIMCET-2011

(a) 1 (b) 2 (c) 3 (d) 434. If 2x + 3y – 6 = 0 and 9x+ 6y – 18 = 0 cuts the axes

in concyclic points, then the center of the circle is: NIMCET-2011

(a) (2, 3) (b) (3, 2) (c) (5, 5) (d) (5/2, 5/2)35. The number of distinct solutions (x, y) of the system

of equations x2 = y2 and (x – a)2 + y2 = 1 where ‘a’ is any real number, can only be

NIMCET-2011

(a) 0, 1, 2, 3, 4 or 5 (b) 0, 1 or 3 (c) 0, 1, 2 or 4 (d) 0, 2, 3 or 4

36. The vertex of parabola y2 − 8y +19 = x isNIMCET-2011

(a) (3, 4) (b) (4, 3) (c) (1, 3) (d) (3, 1)37. The eccentricity of ellipse 9x2 + 5y2 − 30y = 0 is

NIMCET-2011

(a) (b) (c) (d) 38. Point A is a + 2b, P is a and P divides AB in the ratio

of 2 : 3. The position vector of B is BHU-2011

(a) 2a – b (b) b – 2a (c) a – 3b (d) b39. If the position vectors of A and B are a and b

respectively, then the position vector of a point P which divides AB in the ratio 1 : 2 is

BHU-2011

(a) (b)

(c) (d)

40. The straight line touches the curve

y = be-x/a at the point BHU-2011

(a) where it crosses the y-axis (b) where it crosses the x-axis (c) (0, 0) (d) (1, 1)

41. Every homogeneous equation of second degree in x and y represent a pair of lines

BHU-2011(a) parallel to x-axis (b) perpendicular to y-axis (c) through the origin (d) parallel to y-axis

42. The difference of the focal distances of any point on

the hyperbola is

BHU-2011(a) a (b) 2a (c) b (d) 2b

43. If in ellipse the length of latusrectum is equal to half of major axis, then eccentricity of the ellipse is

BHU-2011

(a) (b) (c) (d)

44. An equilateral triangle is inscribed in the parabola y2 = 4ax whose vertex is at the vertex of the parabola. The length of its side is

BHU-2011(a) (b) (c) (d)

45. Two circles x2 + y2 = 5 and x2 + y2 – 6x + 8 = 0 are given. Then the equation of the circle through their point of intersection and the point (1, 1) is

BHU-2011(a) 7x2 + 7y2 – 18x + 4 = 0 (b) x2 + y2 – 3x + 1 = 0 (c) x2 + y2 – 4x + 2 = 0 (d) x2 + y2 – 5x + 3 = 0

46. The equation represents a

BHU-2011(a) straight line (b) circle (c) parabola (d) pair of lines

47. The coordinates of the orthocenter of the triangle formed by the lines 2x2 – 2y2 + 3xy + 3x + y + 1 = 0 and 3x + 2y + 1 = 0 are

BHU-2011

(a) (b)

(c) (d)


INFOMATHS48. The angle between the asymptotes of the hyperbola

27x2 – 9y2 = 24 is NIMCET-2010(a) 60 (b) 120 (c) 30 (d) 150

49. If any tangent to the ellipse intercepts

equal length l on the axes, then l = NIMCET-2010(A) a2 + b2 (B) (C) (a2 +b2)2 (D) N.O.T

50. If a p, b q, c r and = 0, then the value

of + is NIMCET-

2010 (a) 0 (b) 1 (c) -1 (d) 2

51. The number of integral values of m for which the x coordinate of the point of intersection of the lines 3x + 4y = 9 and y = mx + 1 is also an integer is

KIITEE-2010(a) 2 (b) 0 (c) 4 (d) 1

52. The pair of straight lines joining the origin to the common point of x2 + y2 = 4 and y = 3x + c perpendicular if c2 is equal to

KIITEE-2010(a) 20 (b) 13 (c) 1/5 (d) 1

53. Intercept on the line y = x by the circle x2 + y2 – 2x = 0 is AB. Equation of the circle on AB as diameter is

KIITEE-2010(a) x2 + y2 + x – y = 0 (b) x2 + y2 – x + y = 0(c) x2 + y2 + x + y = 0 (d) x2 + y2 – x – y = 0

54. The locus of a point which moves such that the tangents from it to the two circles x2 + y2 – 5x – 3 = 0 and 3x2 + 3y2 + 2x + 4y – 6 = 0 are equal is

KIITEE-2010(a) 2x2 + 2y2 + 7x + 4y – 3 = 0 (b) 17x + 4y + 3 = 0 (c) 4x2 + 4y2 – 3x + 4y – 9 = 0 (d) 13x – 4y + 15 = 0

55. If a 0 and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y2

= 4ax and x2 = 4ay, then KIITEE-2010

(a) d2 + (3b – 2c)2 = 0 (b) d2 + (3b + 2c)2 = 0 (c) d2 + (2b – 3c)2 = 0 (d) d2 + (2b + 3c)2 = 0

56. The distances from the foci of P (a, b) on the ellipse

are KIITEE-

2010

(a) (b)


57. The locus of a point P(,) moving under the condition that the line y = x + is a tangent to the

hyperbola is

KIITEE-2010(a) an ellipse (b) a circle (c) a parabola (d) a hyperbola

58. It the foci of the ellipse and the

hyperbola coincide, then the value

of b2 is

KIITEE-2010(a) 3 (b) 16 (c) 9 (d) 12

59. The medians of a triangle meet at (0, - 3) and two vertices are at (-1, 4) and (5, 2). Then the third vertex is at

KIITEE-2010(a) (4, 15) (b) (-4, 15) (c) (-4, 15) (d) (4, -15)

60. The length of the perpendicular drawn from the point (3, - 2) on the line 5x – 12y – 9 = 0 is

PGCET-2010


61. If the lines x – 6y + a = 0, 2x + 3y + 4 = 0 and x + 4y + 1 = 0 are concurrent, then the value of ‘a’ is

PGCET-2010(a) 4 (b) 8 (c) 5 (d) 6

62. the angle between the lines represented by x2 + 3xy + 2y2 = 0 is

PGCET-2010(a) tan-1(2/3) (b) tan-1(1/3) (c) tan-1(3/2) (d) None of these

63. If the circle 9x2 + 9y2 = 16 cuts the x-axis at (a, 0) and (-a, 0), then a is

PGCET-2010(a) 2/3 (b) 3/4 (c) 1/4 (d) 4/3

64. The length of the perpendicular drawn from the point (1, 1) on the 15x + 8y + 45 = 0 is

(PGCET paper – 2009)(a) 3 (b) 4 (c) 5 (d) 2

65. The equation of the line passing through the point of intersection 2x – y + 5 = 0 and x + y + 1 = 0 and the point (5, - 2) is

(PGCET paper – 2009)(a) 3x + 7y – 1 = 0 (b) x + 2y + 1 = 0 (c) 5x + 6y + 3 = 0 (d) None of these

66. The point of intersection of the lines represented by 2x2 – 9xy + 4y2 = 0 is

(PGCET paper – 2009)(a) (0, 0) (b) (0, 1) (c) (1, 0) (d) (1, 1)

67. If y = x + c is a tangent to the circle x 2 + y2 = 8, then c is

(PGCET paper – 2009)(a) 3 (b) 2 (c) 4 (d) 1

68. The equation of the parabola whose vertex is (1, 1) and focus is (4, 1) is

(PGCET paper – 2009)(a) (y – 1)2 = 12(x – 1) (b) (y – 2)2 = 13(x – 2) (c) (y – 1)2 = 10(x + 1) (d) None of these

69. If the distance of any point (x, y) from the origin is defined as d(x, y)= max (|x|, |y|), then the locus of the point (x, y) where d(x, y) = 1 is MCA : NIMCET – 2009, KIITEE-2010(a) a square of area 1 sq. unit (b) a circle of radius 1 (c) a triangle (d) a square of area 4 sq. units

70. Let ABC be an isosceles triangle with AB = BC. If base BC is parallel to x-axis and m1, m2 are slopes of medians drawn through the angular points B and C, then (MCA : NIMCET – 2009)(a) m1m2 = - 1/2 (b) m1 + m2 = 0 (c) m1m2 = 2 (d) (m1 – m2)2 + 2m1m2=0

71. The straight lines and

meet on

(MCA : NIMCET – 2009)(a) a parabola (b) an ellipse (c) a hyperbola (d) a circle

72. The equation of the line segment AB is y = x, if A and B lie on the same side of the line mirror 2x – y = 1 the image of AB has the equation

(MCA : KIITEE - 2009)(a) 7x – y = 6 (b) x + y = 2


INFOMATHS(c) 8x + y = 9 (d) None of these

73. The point (-1, 1) and (1, -1) are symmetrical about the line

(MCA : KIITEE - 2009)(a) y + x = 0 (b) y = x (c) x + y = 1 (d) None of these

74. The product of perpendiculars drawn from the point (1, 2) to the pair of lines x2 + 4xy + y2 = 0 is

(MCA : KIITEE - 2009)(a) 9/4 (b) 9/16 (c) 3/4 (d) None of these

75. The centroid of the triangle whose three sides are given by the combined equation (x2 + 7xy + 12y2) (y – 1) = 0 is

(MCA : KIITEE - 2009)

(a) (b)


76. Two distinct chords drawn from the point (p, q) on the circle x2 + y2 = px + qy, where pq 0 are bisected by the x-axis then

(MCA : KIITEE - 2009)(a) |p| = |q| (b) p2 = 8q2 (c) p2 < 8q2 (d) p2 > 8q2

77. The length of the latus rectum of the parabola x = ay2 + by + c is

(MCA : KIITEE - 2009)(a) a/4 (b) 1/4a (c) 1/a (d) a/3

78. The equation of the tangent to the x2 – 2y2 = 18 which is perpendicular to the line x – y = 0

(MCA : KIITEE - 2009)(a) x + y = 3 (b) x + y =3/2 (c) x + y + 2 = 0 (d)

79. The sides of the rectangle of the greatest area that can be inscribed in the ellipse x2 + 2y2 = 8, are given by

HYDERABAD CENTRAL UNIVERSITY - 2009(a) (b) (c) (d)

80. The equation of the circle having the chord x – y = 1

of the circle as a

diameter is HYDERABAD CENTRAL UNIVERSITY - 2009

(a)

(b)

(c)

(d)

81. Loci of a point equidistant to (2, 0) and x = - 2 is HYDERABAD CENTRAL UNIVERSITY - 2009

(a) y2 = 8x (b) y2 = 4x (c) x2 = 2y (d) x2 = 16y

82. Given two fixed points A(-3, 0) and B(3, 0) with AB = 6, the equation of the locus of point P which moves such that PA + PB = 8 is HYDERABAD CENTRAL UNIVERSITY - 2009

(a) (b)

(c) (d)

83. If y = mx bisects the angle between the lines x2

(tan2 + cos2) + 2xy tan - y2 sin2 = 0 when =

/3, then the value of is NIMCET - 2008

(a) 1 (b) (c) (d)

84. If a, b, c are the roots of the equation x3 – 3px2 + 3qx – 1 = 0, then the centroid of the triangle with

vertices and is at the point

NIMCET - 2008

(a) (p, q) (b)

(c) (p + q, p – q) (d) (3p, 3q) 85. Equation of the common tangent touching the circle

(x – 3)2 + y2 = 9 and the parabola y2 = 4x above the x – axis is NIMCET - 2008(a) (b) (c) (d)

86. The coordinates of a point on the line x + y = 3 such that the point is at equal distances from the lines |x| = |y| are KIITEE - 2008(a) (3, 0) (b) (-3, 0) (c) (0, - 3) (d) None

87. Lines are drawn through the point P (-2, -3) to meet the circle x2 + y2 – 2x – 10y + 1 = 0. The length of the line segment PA, A being the point on the circle where the line meets the circle is.

KIITEE - 2008(a) (b) 16 (c) 48 (d) None

88. If the common chord of the circles x2 + (y - )2 = 16 and x2 + y2 = 16 subtend a right angle at the origin then is equal to. MCA : KIITEE - 2008(a) (b) (c) 4 (d) 8

89. The equation of any tangent to the circle x2 + y2 – 2x + 4y – 4 = 0 is

KIITEE - 2008(a) (b) (c) (d) None

90. The equation of the circle whose two diameters are 2x – 3y + 12 = 0 and x + 4y – 5 = 0 and the area of

which is 154 sq. units, will be :

MP COMBINED - 2008(a) x2 + y2 + 6x – 4y + 36 = 0 (b) x2 + y2 + 3x – 2y + 18 = 0(c) x2 + y2 – 6x + 4y + 36 = 0 (d) x2 + y2 + 6x – 4y – 36 = 0

91. The circle x2 + y2 – 2x + 2y + 1 = 0 touches: MP COMBINED - 2008

(a) Only x-axis (b) Only y-axis (c) Both the axes (d) None of the axes

92. If the line hx + ky = 1 touches the circle

, then the locus of the point (h, k)

will be: MP COMBINED - 2008

(a) x2 + y2 = a2 (b) x2 + y2 = 2a2

(c) x2 + y2 = 1 (d)

93. Equation of the circle concentric to the circle x2 + y2 – x + 2y + 7 = 0 and passing through (-1, -2) will be:

MP COMBINED - 2008(a) x2 + y2 + x + 2y = 0 (b) x2 + y2 – x + 2y + 2 = 0 (c) 2(x2 + y2) – x + 2y = 0 (d) x2 + y2 – x + 2y – 2 = 0


INFOMATHS94. For the circle x2 + y2 – 4x + 2y + 6 = 0, the equation

of the diameter passing through the origin is: MP COMBINED - 2008

(a) x – 2y = 0 (b) x + 2y = 0 (c) 2x – y = 0 (d) 2x + y = 0

95. The circle x2 + y2 + 2ax – a2 = 0: (MP COMBINED – 2008)(a) touches x – axis (b) touches y – axis (c) touches both the axis (d) intersects both the axes

96. The circles x2 + y2 + 2g1x + f1y + c1 = 0 and x2 + y2 + g2x + 2f2y + c2 = 0 cut each other orthogonally, then :

(MP COMBINED – 2008)(a) 2g1g2 + 2f1f2 = c1 + c2 (b) g1g2 + f1f2 = c1 + c2 (c) g1g2 + f1f2 = 2(c1 + c2) (d) g1g2 + f1f2 + c1 + c2 = 0

97. If the straight line 3x + 4y = touches the parabola y2 = 12x then value of is

(MCA : MP COMBINED – 2008)(a) 16 (b) 9 (c) – 12 (d) – 16

98. For the parabola y2 = 14x, the tangent parallel to the line x + y + 7 = 0 is :

(MCA : MP COMBINED – 2008)(a) x + y + 14 = 0 (b) x + y + 1 = 0 (c) 2(x + y) + 7 = 0 (d) x + y = 0

99. Eccentricity of the ellipse 9x2 + 5y2 – 30y = 0 is :(MP COMBINED – 2008)

(a) 1/3 (b) 2/3 (c) 4/9 (d) 5/9

100. For the ellipse , S1 and S2 are two foci

then for any point P lying on the ellipse S1P + S2P equals:

(MCA : MP COMBINED – 2008)(a) 6 (b) 8 (c) 12 (d) 16

101. The coordinates of the foci of the hyperbola 9x2 – 16y2 = 144 are:

(MCA : MP COMBINED – 2008)(a) (0, 4) (b) ( 4, 0) (c) (0, 5) (d) ( 5, 0)

102. The lengths of transverse and conjugate axes of the hyperbola x2 - 2y2 – 2x + 8y – 1 = 0 will be respectively:

(MCA : MP COMBINED – 2008)(a) (b)

(c) (d)

103. For the given equation x2 + y2 – 4x + 6y – 12 = 0, the centre of the circle is

KARNATAKA - 2007(a) (-2, 3) (b) (-3, 2) (c) (3, - 2) (d) (2, - 3)

104. The circumference of the circle x2 + y2 + 2x + 6y – 12 = 0 is

KARNATAKA - 2007(a) 2 (b) 8 (c) 3 (d) None

105. The locus of a point which moves in a plane such that its distance from a fixed point is equal to its distance from a fixed line is.

KARNATAKA - 2007(a) Parabola (b) Hyperbola (c) Ellipse (d) Circle

106. In parabola y2 = 4kx, if the length of Latus Rectum is 2 then k is

KARNATAKA - 2007(a) +1/2 (b) –1/2 (c) 0 (d) +1/2 or – 1/2

107. The point of intersection of lines (i) x + 2y + 3 = 0 and (ii) 3x + 4y + 7 = 0 is

KARNATAKA - 2007(a) (1, 1) (b) (1, - 1) (c) (-1, 1) (d) (-1, -1)

108. The acute angle between the lines (i) 2x – y + 13 = 0 and (ii) 2x – 6y + 7 = 0

KARNATAKA - 2007(a) 0 (b) 30 (c) 45 (d) 60

109. If the points (k, - 3), (2, - 5) and (-1, -8) are collinear then K = ICET - 2007(a) 0 (b) 4 (c) – 2 (d) – 3

110. The equation of the line with slope -3/4 and y – intercept 2 is ICET - 2007(a) 3x + 4y = 8 (b) 3x + 4y + 8 = 0 (c) 4x + 3y = 2 (d) 3x + 4y = 4

111. If the lines x + 2y + 1 = 0, x + 3y + 1 = 0 and x + 4y + 1 = 0 pass through a point then a + =

ICET - 2007(a) (b) 2 (c) 1/ (d) 1/2

112. Equation of the line passing through the point (2, 3) and perpendicular to the segment joining the points (1, 2) and (-1, 5) is

ICET – 2005(a) 2x – 3y – 13 = 0 (b) 2x – 3y – 9 = 0 (c) 2x – 3y – 11 = 0 (d) 3x + 2y – 12 = 0

113. The two sides forming the right angle of the triangle whose area is 24 sq. cm. are in the ratio 3:4. Then the length of the hypotenuse (in cm) is

ICET – 2005(a) 12 (b) 10 (c) 8 (d) 5

114. The equation of the circle passing through the origin and making intercepts of 4 and 3 or OX and OY respectively is ICET – 2005(a) x2 + y2 – 3x – 4y = 0 (b) x2 + y2 + 4x + 3y = 0 (c) x2 + y2 + 3x + 4y = 0 (d) x2 + y2 – 4x – 3y = 0

115. The equation of the straight line which cuts off equal intercepts from the axis and passes through the point (1, - 2) is ICET – 2005(a) 2x + 2y + 1 = 0 (b) x + y + 1 = 0 (c) x + y – 1 = 0 (d) 2x + 2y – 1 = 0

116. If the lines 2x + 3y = 6, 8x – 9y + 4 = 0, ax + 6y = 13 are concurrent, then a = ICET – 2005(a) 3 (b) – 3 (c) – 5 (d) 5

117. The points of concurrence of medians of a triangle is ICET – 2005

(a) incentre (b) orthocenter (c) centroid (d) circumcentre

118. If (0, 0), (2, 2) and (0, a) form a right angled isosceles triangle, then a =

ICET – 2005(a) 4 (b) – 4 (c) 3 (d) – 3

119. The area of the largest rectangle, whose sides are parallel to the coordinate axes, that can be inscribed

in the ellipse IP Univ.

Paper – 2006(a) 10 (b) 20 (c) 30 (d)

(e) 120. The orthocenter of the triangle determined by the

lines 6x2 + 5xy – 6y2 – 29x + 2y + 28 = 0 and 11x – 2y – 7 = 0 is

IP Univ. Paper – 2006(a) (-4, 5) (b) (4, 4) (c) (6, 7} (d) (2, 1) (e) (-1, 3)

121. a, b, c R. if 2a + 3b + 4c = 0, then the line ax + by + c = 0 passes through the point

(a) (b)

(c) (d) (e)

122. The distance of the point (x, y) form y-axis is Karnataka PG-CET : Paper 2006

(a) x (b) y (c) |x| (d) |y|123. If the lines 4x + 3y = 1, y = x + 5 and 5y + bx = 3

are concurrent, then the value of b is Karnataka PG-CET : Paper 2006

(a) 1 (b) 3 (c) 6 (d) 0124. The system of equations x + y = 2 and 2x + 2y = 3

has Karnataka PG-CET : Paper 2006 (a) No solution (b) a unique solution (c) finitely many solutions (d) infinitely many solutions


INFOMATHS125. The radius of the circle

16x2 + 16y2 = 8x + 32y – 257 = 0 Karnataka PG-CET : Paper 2006

(a) 8 (b) 6 (c) 15 (d) None of these

126. Axis of the parabola x2 – 3y – 6x + 6 = 0 is Karnataka PG-CET : Paper 2006

(a) x = - 3 (b) y = - 1 (c) x = 3 (d) y = 1 127. The locus of a point which moves such that the

difference of its distances from two fixed points is always a constant is Karnataka PG-CET : 2006 (a) a circle (b) a straight line (c) a hyperbola (d) an ellipse

128. The Eccentricity of a rectangular hyperbola is : MP : MCA Paper – 2003

(a) (b) (c) (d) 2129. From a point (x1, y1) two tangent can be drawn on

circle x2 + y2 = a2 if: MP : MCA Paper – 2003


130. The sum of the distance of a point on the ellipse

to its foci is equal to : MP : MCA– 2003

(a) semi major axis (b) major axis (c) semi minor axis (d) minor axis

131. The foci of hyperbola 9x2 – 25y2 + 54x + 50y – 169 = 0 is

MP – 2003

(a) (-3, 1) (b)

(c) (d) None of these132. If two circles x2 + y2 + 2g1x + 2f1y + c1 = 0 & x2 + y2

+ 2g2x + 2f2y + c2 = 0 will cut each other and

satisfies the relation . Then

angle between the circles will be MP : MCA Paper – 2003

(a) π/3 (b) π/2 (c) 3π/2 (d) π/4133. Two circles x2 + y2 + 2gx + c = 0 and x2 + y2 + 2fy

+ c = 0 touch each other, then : MP :– 2003

(a) g2 + f2 = c3 (b) g2 + f2 = c (c) c(g2 + f2) = g2f2 (d) g2 + f2c = g2f2

134. S1 = x2 + y2 – 4x – 6y + 10 = 0 S2 = x2 + y2 – 2x – 2y – 4 Angle between S1 and S2 is

UPMCAT : paper – 2002 (a) 90 (b) 60 (c) 45 (d) None of these

135. The equation of line passing through the intersection of lines 5x – 6y – 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to 3x – 5y + 27 = 0 is :

UPMCAT :– 2002 (a) 5x + 3y + 10 = 0 (b) 5x + 3y + 21 = 0 (c) 5x + 3y + 18 = 0 (d) 5x + 3y + 8 = 0

136. The area of triangle formed by y = m1x + c, y = m2x + c2 and y axis is : UPMCAT : paper – 2002

(a) (b)

(c) (d)

137. Reflection of the point P(1, 2) in x + 2y + 4 = 0 is UPMCAT : paper – 2002

(a) (b)


138. The area of the region bonded by the curve y = x2 and the line y = x is UPMCAT : paper – 2002

(a) Sq U (b) Sq U

(c) Sq U (d) N.O.T.

139. If 4x2 + 9y2 + 12xy + 6x ….. + 9y – 4 = 0 represents two parallel lines then the distance between. The lines is: UPMCAT:– 2002


140. If (± 3, 0) be focus of ellipse and semi major axis is 6. Then equ. of ellipse is:

UPMCAT :– 2002

(a) (b)


141. If 2x2 – 5xy + 2y2 – 3x + 1 = 0, represents pairs of lines, then the angle between the lines is :

UPMCAT : paper – 2002 (a) tan-1 (2/3) (b) tan-1 (4/3) (c) tan-1 (3/4) (d) None of these

142. The condition that eqa. ax2 + by2 + 2gx + 2fy + 2hxy + c = 0 represents a pair of the line is

(i)

(ii) abc + 2fgh – af2 – bg2 – ch2 = 0 (iii) af + bg + ch = 0 (iv) af2 = bg2 ; h2 = ab

UPMCAT:– 2002 (a) i, ii (b) ii, iv (c) i, iv (d) i, ii and iv

143. A ellipse has , directrix is x + 6 = 0, and has a

focus at (0, 0) then the eqn. of ellipse is: UPMCAT :– 2002

(a) 3x2 + 4y2 + 12x – 36 = 0 (b) 3x2 + 4y2 – 12x + 36 = 0 (c) 3x2 + 4y2 – 12x – 36 = 0 (d) None of these

144. The eqn. of the ellipse has its centre at (1, 2), a focus at (6, 2) and passing through the point (4, 6) : UPMCAT :– 2002

(a) (b)


145. The tangents of the circle x2 + y2 = 4 at the points A and B meet at P(-4, 0). The area of the quadrilateral PAOB where O is the origin is.

KIITEE - 2008(a) 4 (b) (c) (d) None

146. The x2 + y2 + 2x = 0, R touches the parabola y2

= 4x externally. Then KIITEE - 2008

(a) > 1 (b) < 0 (c) > 0 (d) None

147. A point P on the ellipse has the

eccentric angle . The sum of the distance of P

from the two foci is. KIITEE - 2008

(a) 10 (b) 6 (c) 5 (d) 3


INFOMATHS148. For the hyperbola which of the

following remains constant when varies? MCA : KIITEE - 2008

(a) directrix (b) eccentricity (c) abscissae of foci (d) abscissae of vertices

149. The sum of the intercepts made on the axes of co-ordinates by any tangent to the curve is equal to KIITEE - 2008(a) 4 (b) 8 (c) 2 (d) None

150. If the focus and directrix of a parabola are (-sin , cos ) and x cos + y sin = p respectively, then length of the latus rectum will be:

(MP COMBINED – 2008)(a) 2p (b) 4p (c) p2 (d) p(cos – sin )

151. The distance between the two focii of a hyperbola H is 12. The distance between the two directories of hyperbola H is 3. The acute angle between the asymptotes of H in degrees is

IP Univ. Paper – 2006(a) 30 (b) 40 (c) 45 (d) 60 (e) 70

152. L1 || L2. Slope of L1 = 9. Also L3 || L4. Slope of L4

. All these lines touch the ellipse

. The area of the parallelogram

determine by these lines is IP University : Paper - 2006

(a) 21 (b) 28 (c) 40 (d) 56 (e) 60

153. If P, Q, R, S are four distinct collinear points such

that , then, the value of is

IP University : Paper - 2006

(a) (b)

(c) (d) (e) N.O.T.

154. P moves on the line y = 3x + 10. Q moves on the parabola y2 = 24x. The shortest value of the segment PQ is IP University - 2006

(a) (b) (c) (d) (e) 6

155. The line 2x + y – 1 = 0 cuts the curve 5x2 + xy – y2 – 3x – y + 1 = 0 at P and Q. O is the origin. The acute angle between the lines OP and OQ is

IP University - 2006

(a) (b) (c) (d) (e)

156. The limiting points of the system of coaxial circles of which two members are x2 + y2 + 2x + 4y + 7 = 0 and x2 + y2 + 5x + y + 4 = 0 is:

MP : MCA Paper – 2003 (a) (-2, 1) and (0, - 3) (b) (2, 1) and (0, 3) (c) (4, 1) and (0, 6) (d) None of these

157. The length of common chord of the circles (x – a)2 + y2 = a2 and x2 + (y – b)2 = b2 is :

MP : MCA Paper – 2003

(a) (b)


158. An arch way is in the shape of a semi ellipse. The road level being the major axis. If the breadth of the road is 30 metres and the height of the arch is 6m at

a distance of 2 metre from the side, then find the greatest height of the arch.

MP : MCA Paper – 2003

(a) m (b) m

(c) m (d) m

159. The locus midpoint of a chord of the circle x2 + y2 = 4, which subtend angle 90 at the centre.

UPMCAT : paper – 2002 (a) x + y + 3 = 0 (b) x2 + y2 = 0 (c) x + y + 2 = 0 (d) x2 + y2 = 2

FUNCTIONS

1. is a real-valued function

in the domain :PU CHD-2012

(A) (–, – 1] [3, ) (B) (–, – 1] (2, 3](C) [– 1, 2) [3, ) (D) [– 1, 2]

2. If X = {a, b, c, d} then no. of 1–1. Then number of functions from X X are

Pune-2012(a) 64 (b) 13 (c) 24 (d) 16

3. If R+ is set of all real +ve nos. then F: R+ R+ be defined by f(x) = 3x. Then f(x) is

Pune-2012(a) neither one-one nor onto (b) one-one and onto (c) one-one but not onto (d) onto but not one-one

4. If f :R R, where .

Then fofPune-2012

(a) 1 (b) - 1 (c) (d) 05. If the function f: [1, ∞) → [1, ∞) is defined by f(x) =

2x(x−1) , then f −1(x) isKIIT-2010, NIMCET-2011

(a) (b)

(c) (d) not defined

6. Let the function f (x) = x2 from the set of integers to the set of integers. Then :

PU CHD-2011(A) f is one-one and onto (B) f is one-one but not onto(C) f is not one-one but onto (D) f is neither one-one nor onto

7. The value of P and Q for which the identity f(x+1) - f (x) = 8x + 3 is satisfied, where f (x) = Px2 + Qx + R, are :

PU CHD-2011(A) P = 2, Q = 1 (B) P = 4, Q = –1(C) P = –1, Q = 4 (D) P = –1, Q = 1

8. Let , then f(x) =

PU CHD-2011 (A) x2 (B) x2 – 1 (C) x2 – 2 (D) x2 + 29. The range of the function f(x) = 1/(2 – cos3x) =

PU CHD-2011

(A) (B)

(C) (d)


INFOMATHS10. If f = {(1, 1), (2, 3), (0, - 1), (-1, -3)} be a function

described by the formula f(x) = ax + b for some integers a, b, then the value of a, b is

BHU-2011(a) a = - 1, b = 3 (b) a = 3, b = 1 (c) a = - 1, b = 2 (d) a = 2, b = - 1

11. Set A has 3 elements and set B has 4 elements. The number or injection that can be defined from A to B is

NIMCET-2010(a) 144 (b) 12 (c) 24 (d) 64

12. Let A and B be sets and the cardinality of B is 6. The number of one-to-one functions from A to B is 360. Then the cardinality of A is (Hyderabad Central University – 2009)(a) 5 (b) 6 (c) 4 (d) Can’t be determined

13. Suppose that g(x) = and f{g(x)} = then f(x) is

KIITEE-2010(a) 1 + 2x2 (b) 2 + x2 (c) 1 + x (d) 2 + x

14. If for x R, then f(2010) is

KIITEE-2010(a) 1 (b) 2 (c) 3 (d) 4

15. The function is KIITEE-2010

(a) neither an even nor an odd function(b) an even function (c) an odd function (d) a periodic function

16. The domain of is KIITEE-

2010(a) [1, 9] (b) [-, 9] (c) [-9, 1] (d) [-9, -1]

17. A function f from the set of natural numbers to

integers defined by if

is : KIITEE-2010

(a) one-one but not onto (b) onto but not one-one (c) one-one and onto both (d) neither one-one nor onto

18. For real x, let f(x) = x3 + 5x + 1, then KIITEE-2010(a) f is onto R but not one-one (b) f is one-one and onto R (c) f is neither one-one nor onto R (d) f is one-one but not onto R

19. Let f(x) = [x2 - 3] where [ ] denotes the greatest integer function. Then, the number of points in the interval (1, 2) where the function is discontinuous is

(MCA : NIMCET – 2009)(a) 4 (b) 2 (c) 6 (d) None of these

20. Let f(x) = - log2x + 3 and a[1, 4] the f(a) is equal to (MCA : KIITEE - 2009)

(a) [1, 3] (b) [2, 4] (c) [1, 2] (d) [1, 9]

21. The function is

(MCA : KIITEE - 2009)(a) periodic (b) odd (c) even (d) neither odd or even

22. Which of the function is periodic?(MCA : KIITEE - 2009)

(a) f(x) = x cos x (b) f(x) = sin (1/x) (c)(d) f(x) = {x}, the fractional part of x

23. The function f : R R given by f(x) = 3.2 sin x is

(MCA : KIITEE - 2009)(a) one – one (b) onto (c) bijective (d) None of these

24. The domain of the function is (MCA : KIITEE - 2009)

(a) [1/2, 3/2] (b) (1/2, 3/2) (c) [1/2, ) (d) (-, 3/2]

25. The period of the function f(x) = cosec23x + cot 4x is (MCA : KIITEE - 2009)

(a) (b) /8 (c) /4 (d) /326. Let f : R R be a function defined by

then (MCA : KIITEE - 2009)

(a) f is both one – one and onto (b) f is one – one but not onto (c) f is onto but not one – one (d) f is neither one – one nor onto

27. The domain of is

(MCA : KIITEE - 2009)(a) R ~ {1, 2} (b) (-, 2)(c) (-, 1) (2, ) (d) (1, )

28. If f(x – 1) = 2 x2 – 3x + 1 then f(x + 1) is given by (MCA : KIITEE - 2009)

(a) 2x2 + 5x + 1 (b) 2x2 + 5x + 3 (c) 2x2 + 3x + 5 (d) 2x2 + x + 4

29. If y = log3 x and F = {3, 27}. Then the set onto which the set F is mapped contains

(MCA : KIITEE - 2009)

(a) {0, 3} (b) {1, 3} (c) {0, 1} (d) {0, 2}

30. If f : [1, ) [2, ) is given by then

f – 1(x) equals to (MCA : KIITEE - 2009)

(a) (b)

(c) (d)

31. If then f(x + y) is

equal to (KIITEE – 2009)(a) f(x) f(y) (b) f(x) + f(y) (c) f(x) – f(y) (d) None of these

32. Let for all real x and y. If

f’(0) exists and equals – 1 and f(0) = 1, then, f(2) is Hyderabad Central Univ. – 2009

(a) -1 (b) 2 (c) 0 (d) 133. If f(x) = sin (log x), then, the value of

f(xy) + f(x/y) – 2f(x) cos log (y) is Hyderabad Central Univ. – 2009

(a) 0 (b) – 1 (c) 1 (d) – 2

34. Consider the function on R.

Let x1 and x2 be two real values such that f(x1) = f(x2). Then x1 – x2 is always of the form

Hyderabad Central Univ. – 2009(a) n : n Z (b) 2n : n Z

(c) (d)

35. If f(x) + f(1 – x) = 2, then the value of


INFOMATHS is

MCA : NIMCET - 2008(a) 2000 (b) 2001 (c) 1999 (d) 1998

36. If f(x) is a polynomial satisfying

and f(3) = 28, then f(4)

is given by NIMCET - 2008(a) 63 (b) 65 (c) 67 (d) 68

37. The number of functions f from the set A = {0, 1, 2} in to the set B = {0, 1, 2, 3, 4, 5, 6, 7} such that f(i) f(j) for i < j and ij A is.

NIMCET - 2008(a) 8C3 (b) 8C3 + 2(8C2) (c) 10C3 (d) None

38. The range of the function f(x) = 7-xPx-3 is MCA : KIITEE – 2008

(a) {1, 2, 3, 4} (b) {1, 2, 3} (c) {1, 2, 3, 4, 5} (d) {3, 4, 5, 6}

39. Let A = {x|-1 < x < 1} = B. If f: A B be bijective then f(x) could be defined as

MCA : KIITEE – 2008 (a) |x| (b) sin x (c) x|x| (d) None

40. Let f : R R be a mapping such that

then the property of the function f is. MCA : KIITEE – 2008

(a) one – one (b) one – many (c) many – one (d) onto

41. If f(x) = x2 + 4 and g(x) = x3 – 3 then the degree of the polynomial f[g(x)]

ICET - 2007(a) 6 (b) 5 (c) 3 (d) 3

42. If f(x) = 2x2 + 5x + 1 and g(x) = x – 4 then { R : g (f()) = 0} =

ICET - 2007(a) {-1/2, 3} (b) {-1/2, -3} (c) {1/2, - 3}(d) {1/2, 3}

43. If f : |R | R and g : |R R| are defined by f(x) = x - (x) and g(x) = (x) for each x in |R where (x) is the greatest integer not exceeding x, then, the range of gof is. ICET – 2005(a) (b) (0) (c) Z (d) |R

44. The number of injections of the set {1, 2, 3} into the set {1, 2, 3, 4, 5, 6} is

ICET – 2005(a) 10 (b) 30 (c) 60 (d) 120

45. The number of mappings from {a, b, c} to {x, y} is PUNE - 2007(a) 3 (b) 6 (c) 8 (d) 9

46. If f = {(6, 2), (5, 1)}, g = {2, 6), (1, 5)} then f o g = PUNE - 2007(a) {(6, 6) (5, 5)} (b) (2, 2) (1, 1) (c) {(6, 7) (2, 6) (5, 1) (1, 5} (d) None of these

47. If (x + 2y, x – 2y) = xy then f(x, y) is equal to (KIITEE - 2009)

(a) (b)

(c) (d)

48. The function f and g are given by f(x) = (x), the fractional part of x and g(x) = 1/2 sin[x], where [x] denotes the integral part of x, then the rage of (g o f) is (MCA : KIITEE - 2009)(a) [-1, 1] (b) {-1, 1}(c) {0} (d) {0, 1}

49. The least period of the function f(x) = [x] + [x + 1/3] + [x + 2/3] – 3x + 10 where [x] denotes the greatest integer x is KIITEE – 2008 (a) 2/3 (b) 1 (c) 1/3 (d) 1/2

LIMITS & CONTINUITY

1. The value of is :

PU CHD-2012(A) 1 (B) –1 (C) (D)

Does not exist

2. If f (1) = 2 f '(1) = 1 then

Pune-2012(a) – 1 (b) 0 (c) 1 (d) 2

3. F(x) = x + |x|. Then F(x) is continuous for ………….Pune-2012

(a) x = 0 only (b) for all x R (c) for all x R except x = 0 (d) None of these

4. What is the value of a for which

is continuous?

NIMCET-2012(a) π (b) π /2 (c) 2/ π (d) 0

5. is equal to : BHU-2012

(a) 0 (b) 1 (c) e (d) 1/e6. The function f(x) defined by

, then:

BHU-2012(a) f(x) is continuous at x = 0 (b) f(x) has discontinuity of first kind at x = 0 (c) f(x) has discontinuity of second kind at x = 0 (d) f(x) has removable discontinuity at x = 0

7. Let f(x) be the function defined on the interval (0, 1) by

then f is continuous at HCU-2011

(a) no point in (0, 1)(b) at exactly 2 points in (0, 1) (c) at exactly one point in (0, 1) (d) at more than 2 points in (0, 1)

8. Suppose f(x) = [x2] – [x]2 where [x] denotes the largest integer x. Then which of the following statements is true?

HCU-2011(a) f(x) ≥ 0 x R(b) f(x) can be discontinuous at points other than the integral values of x (c) f(x) is a monotonically increasing function (d) f(x) 0 everywhere, except on the interval [0, 1]

9. equals to

NIMCET-2011(a) 0 (b) 1 (c) –1 (d) none of

these

10. Let f (2) = 4 and f´ (2) = 1. Then

is given by :PU CHD-2011

(A) 2 (B) –2 (C) –4 (D) 3


INFOMATHS

11. If

Then, f (x) is BHU-2011

(a) continuous at (b) continuous at x = 1

(c) continuous at x = 0 (d) discontinuous at x = 0

12. The value of is equal to

BHU-2011(a) + 1 (b) - 1 (c) (d) 3

13. If f(1) = 1, f ' (1) = 2, then

KIITEE-2010(a) (b) 4 (c) 1 (d) 1/2 (e) None of these

14. The integer n for which

is a finite non – zero

number is MCA : NIMCET - 2008

(a) 1 (b) 2 (c) 3 (d) 4

15. If when [.] denotes the

greatest integer function then is equal to KIITEE - 2008(a) 0 (b) 1 (c) – 1 (d) None

16. ICET - 2007

(a) – 1 (b) 0- (c) 1 (d) 2

17. ICET

- 2007(a) 0 (b) 1 (c) 3/5 (d) 9/25

18. ICET –

2005(a) 1 (b) 2 (c) 0 (d) 3

19. ICET –

2005(a) 1/2 (b) 1/3 (c) 1/4 (d) 1/12

20. is

IP Univ. Paper – 2006 (a) 1/4 (b) 2/4 (c) 3/4 (d) 1 (e) 5/4

21.

UPMCAT : Paper - 2002

(a) Does not exist at x = 1 (b) 1/2 (c) – 1 (d) 1

22. f = R R is given by f(x) = x2 + 6x + 2 if x is rational and f(x) = x2 + 5x – 4 otherwise. F is continuous at IP Univ. Paper – 2006 (a) x = R (b) for no x R (c) for only one value of x. (d) for two values of x

DERIVATIVES

1. If y = logex and n is positive integer, then is

equal toPU CHD-2012

(A) (B) (n – 1)x–n

(C) (n – 1) ! x–n (D) (–1)n – 1 (n – 1)! x–n

2. F(x) = xn then the value of

is Pune-2012

(a) 2n (b) 2n-1 (c) 0 (d) 1

3. 0 < x < 1 then at is.

Pune-2012(a) e (b) 4e (c) 3e (d) 2e

4. log(x + y) – 2xy = 0 then y'(0) isPune-2012

(a) 1 (b) – 1 (c) 2 (d) 05. If f(x) is twice differentiable function. Then

f '(x) = g(x), f '(x) = -f (x). if h(x) = f(x)2 + g(x)2,h(1) = 8, h(0) = 2 then h(2) =

Pune-2012(a) 1 (b) 2 (c) 3 (d) None of these

6. f (x) = x|x| and g(x) = sin x then Pune-2012

(a) gof(x) differential and its derivative is continuous (b) fog(x) is twice diff. at x = 0 (c) fog(x) is not differentiable(d) None of these

7. If f(a + b) = f(a) × f(b) for all a and b and f(5) = 2, f'(0) = 3, then f'(5) is

NIMCET-2012(a) 2 (b) 4 (c) 6 (d) 8

8. The derivative of w.r.t.

is : BHU-2012

(a) – 1 (b) 0 (c) 1/x (d) x

9. If , then is :

NIT-2008, BHU-2012

(a) 1 (b) 0 (c) (d)

10. Let f1(x) = ex, f2(x) = , f3(x) = , …. and in general fn+1(x) = for any n 1. For any fixed

value of n, the value of is

HCU-2011(a) fn(x) (b) fn(x) fn-1(x) fn-2(x) …. f2(x) f1(x) (c) fn(x) fn-1 (x) (d) fn(x) fn-1(x)fn-2(x) …. f2(x) f1(x) ex

11. Let f : [0, 1] [0, 1] be a function that is twice differentiable in its domain, then the equation f(x) = x has

HCU-2011(a) no solution (b) exactly one solution


INFOMATHS(c) at least one solution(d) not enough data to say about number of solution

12. Find

NIMCET-2011

(a) (b)

(c) (d) none of these

13. Let f(x) = where p is

constant. Then f ′′′ (0) =PU CHD-2011

(A) P (B) P + P2 (C) p + p3 (D) Independent of p14. The differential coefficient of xx is

BHU-2011

(a) xx logx (b)

(c) xx(logx + 1) (d) x xx – 1 15. Let f(a) = g(a) = k and their nth derivatives f " (a),

g" (a) exist and are not equal for some n.

If

then the value of k is KIITEE-2010

(a) 4 (b) 2 (c) 1 (d) 0

16. If x = a sin, y = b cos, then is KIITEE-2010

(a) (b)

(c) (d)

17. The derivative of f(x) = 3|2 + x| at the point x0 = - 3 is KIITEE-2010(a) 3 (b) – 3 (c) 0 (d) does not exist

18. Let y be an implicit function of x defined by x2x – 2xx cot y – 1 = 0 then y' (1) equals

KIITEE-2010(a) 1 (b) log2 (c) – log2 (d) – 1

19. If and f(0) = 0 then f’(0) is

Hyderabad Central Univ. – 2009(a) 0 (b) 1 (c) e (d) None of these

20. If f(0) = f '(0) = 0 and f "(x) = tan2x then f(x) is Hyderabad Central Univ. – 2009

(a) (b)

(c) (d) None of the

above21. If they y’(0) is equal to

KIITEE – 2008(a) 1/2 (b) e2 (c) 0 (d) 3/2

22. If and f(0) = 0 then f’(0) is KIITEE – 2008

(a) 1 (b) 0 (c) e (d) None

23. If then equals: (MP COMBINED

– 2008)

(a) (b)

(c) (d) (log x) x(log x-1)

24. If then equals: MP COMB. – 2008

(a) (b) (c) (d)

25. If then ICET -

2007(a) x – 1 (b) x + 1 (c) 2x – 1 (d) 2x + 1

26. If xy = ex-y, then, ICET –

2005

(a) (b)

(c) (d)

27. If y = 4x3 – 3x2 + 2x – 1, then at is

ICET – 2005(a) 0 (b) 1 (c) 2 (d) 3

28. If then MP–

2004

(a) (b)

(c) (d)

29. If then is equal to :

MP– 2004

(a) (b)


30. The value of differential coefficient of

with respect to x at x = 2 is : MP Paper – 2004

(a) 1/2 (b) -1/5 (c) -1/2 (d) 1/3

31. Differential coefficient of is :

MP– 2004

(a) (b)

(c) (d) None of the above


INFOMATHS32. f(x) = |x|, at x = 0 UPMCAT

Paper – 2002 (a) is derivable (b) not derivable (c) either may follow (d) None of these

33. If y = f(x) is an odd and differentiable function defined on (- , ) such that f'(3) = - 2, then f’(-3) equals to (NIMCET – 2009)(a) 4 (b) 2 (c) –2 (d) 0

APPLICATION OF DERIVATIVES 1. A particle moves on a coordinate axis with a velocity

of v(t) = t2 - 2t m/sec at time t. The distance (in m) travelled by the particle in 3 seconds if it has started from rest is

HCU-2012(a) 3 (b) 0 (c) 8/3 (d) 4

2. F:R R is defined

if F has local min. at x = - 1 then the value of k is Pune-2012

(a) 1 (b) 0 (c) (d) – 1

3. In the Interval [0, 1] function x2 – x + 1 is Pune-2012

(a) increasing (b) decreasing (c) neither increasing nor decreasing(d) None of these

4. Normal to the curve y = x3 – 3x + 2 at the point (2, 4) is

NIMCET-2012(a) 9x – y – 14 = 0 (b) x – 9y + 40 = 0 (c) x + 9y – 38 = 0 (d) -9x + y + 22 = 0

5. The function xx decreases in the interval NIMCET-2012

(a) (0, e) (b) (0, 1) (c) (d) None of these

6. The condition that the curve ax2 + by2 = 1 and a'x2

+ b'y2 = 1 should intersect orthogonally is that : BHU-2012

(a) a + b = a' + b' (b) a – b = a' – b'

(c) (d)

7. If x and y be two real variable, such that x > 0 and xy = 1, then the minimum value of x + y is :

BHU-2012(a) 1 (b) – 1 (c) 2 (d) – 2

8. The maximum value of is :

BHU-2012(a) 1 (b) 2/e (c) e (d) 1/e

9. The minimum value of px + qy when xy = r2 isNIMCET-2011

(a) (b) (c) (d)10. If f (x) = x5 - 20x3 + 240x, then f (x) satisfies which

of the following?PU CHD-2011

(A) It is monotonically decreasing only in (0, ∞)(B) It is monotonically decreasing every where(C) It is monotonically increasing every where(D) It is monotonically increasing only in (–∞, 0)

11. If for every real number x, then the

minimum value of f :PU CHD-2011

(A) does not exist because f is bounded (B) is not attained even though f is bounded(C) is equal to 1 (D) is equal to –1

12. If f be the quadratic function defined on [a, b] by f (x) = αx2 + βx + , α ≠ 0, then the real ‘c’

guaranteed by the Langrange’s mean value theorem is equal to :

PU CHD-2011

(A) (b)

(c) (d) 13. The volume of a right circular cylinder of height h

and radius of base r is BHU-2011

(a) (b)

(c) (d)

14. The function f(x) = 8x5 – 15x4 + 10x2 has no extreme value at

BHU-2011

(a) (b)

(c) x = 1 (d) x = – 1 15. The normal to the curve

x = a(cos + sin ), y = a (sin - cos )at any point is such that it

BHU-2011(a) passes through the origin(b) makes a constant angle with the x-axis (c) makes a constant angle with the y-axis(d) is at constant distance from the origin

16. The length of the normal at the point (2, 4) to the parabola y2 = 8x is

BHU-2011(a) (b) 4 (c) (d)

17. The equation of tangent to the curve y2 = 2x3 – x2 + 3 at the point (1, 4) is

BHU-2011(a) y = 2x (b) x = 2y – 7 (c) y = 4x (d) x = 4y

18. If f(x) satisfies the conditions of Rolle’s theorem is [1, 2] and f(x) is continuous in [1, 2] then

is equal to KIITEE-2010

(a) 3 (b) 0 (c) 1 (d) 2

19. The function has a local minimum at

KIITEE-2010(a) x = - 2 (b) x = 0 (c) x = 1 (d) x = 2

20. Angle between the tangents to the curve f = x2 – 5x + 6 at the points (2, 0) and (3, 0) is

KIITEE-2010

(a) (b) (c) (d)

21. For the function the number c satisfying the mean value theorem is c = 1, then b is

(MCA : KIITEE – 2009)(a) 0 (b) 4 (c) 2 (d) 3

22. The maximum value of the function y = x(x – 1)2, 0 x 2 is (MCA : KIITEE – 2009)

(a) (b) (c) (d)

23. The sum of two non zero numbers is 8. the minimum value of the sum of their reciprocal is

(KIITEE – 2009)(a) 1/4 (b) 1/8 (c) 1/2 (d) None of these

24. If f(x) = a loge|x| + bx2 + x has the extrema at x = 1 and x = 3 then

NIT-2010, HYDERABAD CENTRAL UNIVERSITY - 2009

(a) (b)


INFOMATHS(c) (d) None of the

above 25. The function f(x) = 2 sin x + sin 2x, x [0, 2] has

absolute maximum and minimum at NIMCET – 2008


26. Equation of the tangent to the curve y = be-x/a at the point where it crosses y – axis is :

(MCA : MP COMBINED – 2008)(a) bx + ay = ab (b) ax + by = ab (c) bx + ay = - ab (d) ax + by = - ab

27. The points on the circle x2 + y2 – 2x – 4y + 1 = 0 where the tangents are parallel to x-axis, will be:

(MCA : MP COMBINED – 2008)(a) (3, 2), (-1, 2) (b) (-1, 2), (1, 0) (c) (1, 2), (1, 0) (d) (1, 0), (1, 4)

28. The normal to curve y2 = 4ax passing through (a, 2a) is: (MP COMBINED – 2008)(a) x + y = a (b) x + y = 3a (c) x – y = a (d) y = 2a

29. sin x (1 + cos x) is a maximum when x equals : BHU-2011, (MCA : MP COMBINED – 2008)

(a) /6 (b) /4 (c) /3 (d) /230. For positive values of x, the minimum value of xx will

be: (MP COMBINED – 2008)

(a) ee (b) (c) (d)

31. The points situated on x2 = 2y and nearest to (0, 5) are:

(MP COMBINED – 2008)(a) (0, 0) (b) ( 2, 2) (c) (d)

32. P(x) is a real polynomial of degree three. P(x) = 0 has a double root at x = 2. It has a relative extremum at x = 1. The remaining root of P(x) = 0 is

IP Univ. paper – 2006(a) 4/5 (b) 3/4 (c) 2/3 (d) 1/2 (e) N.O.T

33. If y2 = 8(x + 2) Equ. of tangent at (-1, 3) is : UPMCAT– 2002(a) y = 2x – 5 (b) y = x + 3 (c) y = x + 5 (d) None of these

34. A cubic f(x) vanishes at x = - 2 and has relative minimum / maximum at x = - 1 and x = 1/3. If

, the cubic f(x) is HYDERABAD

CENTRAL UNIVERSITY - 2009(a) x3 + x2 + x + 6 (b) x3 – x2 – x + 10(c) x3 + x2 + x + 2 (d) x3 + x2 – x + 2

35. If has the extremums at x = 1 and x = 3 then KIITEE - 2008

(a) (b)

(c) (d) None

36. Let f(x) = cosx + 10x + 3x2 + x3 if -2 x 3, the absolute minimum value of f(x) is KIITEE - 2008(a) 0 (b) – 15 (c) 3 – 2 (d) None

37. A function y = f(x) has a second derivative f”(x) = 6(x – 1). If its graph passes through the point (2, 1) and at that point the tangent to the graph is y = 3x – 5, then the function is KIITEE - 2008(a) (x – 1)3 (b) (x + 1)2 (c) (x – 1)2 (d) (x + 1)2

MATRICES 1. Let A be an n n non-singular matrix over ℂ where

n 3 is an odd integer. Let a ℝ. Then the equation

det(aA) - a det(A) = 0 holds forHCU-2012

(a) All values of a(b) No value of a(c) Only two distinct values of a(d) Only three distinct values of a

2. How many matrices of the form

are orthogonal, where x, y, z, s and t are real numbers.

HCU-2012 (a) 1 (b) 2 (c) 0 (d) infinity

3. Let A be an n n-skew symmetric matrix with a11, a22, ….. ann as diagonal entries. Then which of the following is correct?

HCU-2012(a) a11a22 … ann = a11 + a22 + …. + ann (b) a11a22 … ann = (a11 + a22 + …. + ann)2

(c) a11a22 + … + ann = (a11 + a22 + …. + ann)3

(d) all of the above 4. Consider the system of equations

8x + 7y + z = 11 x + 6y + 7z = 27 13x – 4y – 19z = - 20 How many solutions does this system have?

HCU-2012 (a) Single (b) Finite (c) Zero (d) Infinite

5. If A is a 3 × 3 matrix such that :

and then the product

is

PU CHD-2012

(A) (B) (C) (D)

6. Consider the following system of linear equations over the real numbers, where x, y and z are variables and b is a real constant :x + y + z = 0x + 2y + 3z = 0x + 3y + bz = 0Which of the following statements are true?I. There exists a value of b for which the system

has no solution.II. There exists a value of b for which the system

has exactly one solution.III. There exists a value of b for which the system

has more than one solution.PU CHD-2012

(A) I and II only (B) I and III only(C) II and III only (D) I, II and III

7. The only integral root of the equation

is :

PU CHD-2012(A) y = 0 (B) y = 1 (C) y = 2 (D) y = 3

8. Let N be the set of all 3 3 symmetric matrices. All of whose entries are zero or 1 (Five zero and four 1). Then the no. of matrices in N is

Pune-2012


INFOMATHS(a) 12 (b) 6 (c) 9 (d) 3

9. If M & N are square matrices of order "n".Then (M – N)2 =

Pune-2012(a) M2 – 2MN + N2 (b) M2 – N2 (c) M2 – 2NM + N2 (d) M2 – MN – NM + N2

10. M and N are symmetric matrices of same order then MN – NM is a matrix which is

Pune-2012(a) null (b) symmetric (c) skew-symmetric (d) unit

11. the M50 is equal to

Pune-2012

(a) (b)

(c) (d)

12. If matrix is singular the =

Pune-2012(a) – 2 (b) 4 (c) 2 (d) – 4

13. The number of values of k for which the system of equations (k + 1) x + 8y = 4k and kx + (k + 3)y = 3k – 1 has infinitely many solutions is

NIMCET-2012(a) 0 (b) 1 (c) 2 (d) infinite

14. If is the cube root of unity, then the system of equations x + 2y +z = 0, x + y + 2z = 0 and 2x + y + z = 0 is

NIMCET-2012(a) consistent and has unique solution (b) Consistent and has more than one solution (c) Inconsistent (d) None of these

15. The value of k for which the set of equations 3x + ky – 2z = 0, x + ky + 3z = 0 and 2x + 3y – 4z = 0 has a non-trial solution, is

NIMCET-2012

(a) (b) (c) (d)

16. If then An for any natural number n is

NIMCET-2012

(a) (b)


17. If is cube root of unity, then the value of

determinant is equal to :

BHU-2012(a) – 1 (b) 1 (c) 0 (d) 2

18. If the matrices and ,

then AB is equal to : BHU-2012

(a) (b)

(c) (d)

19. If A is a 2 2 real matrix such that A – 3I and A – 4I are not invertible, then A2 is

HCU-2011(a) 12A – 7I (b) 7A – 12I (c) 7A + 10I (d) 12I

20. If A and B are 3 3 matrices with |A| = 4 and |B| = 3, which of the following is generally false?

HCU-2011(a) 3|B| = 9 (b) |2A| = 32(c) |AB| = 12 (d) |A + B| = 7

21. The n n matrix P is idempotent if P2 = P and orthogonal if P'P = I. Which of the following is false?

HCU-2011(a) If P and Q are idempotent n n matrices and PQ= QP = 0, then P + Q is idempotent (b) If P is idempotent then – P is idempotent (c) If P and Q are orthogonal n n matrices then PQ is orthogonal

(d)

22. Let

be a 3 3 matrix. Let x and y be the values such that matrix A is singular. What is x + y?

HCU-2011(a) 0 (b) 3 (c) 1/2 (d) 2

23. If A and B are two square matrices such that B = − A−1BA, then (A + B)2 =

NIMCET-2011(a) 0 (b) A2 + 2AB + B2 (c) A2 + B2 (d) A + B

24. Consider the system of linear equations3x1 + 7x2 + x3 = 2x1 + 2x2 + x3 = 32x1 + 3x2 + 4x3 = 13The system has

NIMCET-2011(a) infinitely many solutions (b) exactly 3

solutions(c) a unique solution (d) no solution

25. If , then A is

BHU-2011(a) symmetric matrix (b) a skew-symmetric matrix (c) a singular matrix (d) non-singular matrix

26. If , then AB is equal to

BHU-2011

(a) (b)

(c) (d)


INFOMATHS

27. If , where x, y, z are unequal and

non-zero real numbers, then xyz is equal to BHU-2011

(a) 1 (b) 2 (c) – 1 (d) – 2 28. The system of equations

ax + y + z = - 1 x + ay + y = - 1 x + y + az = - 1 has not solution if is KIITEE-2010(a) 1 (b) Not – 2 (c) either – 2 or 1 (d) – 2 (e) None of these(e) None of these

29. Matrix is invertible for

KIITEE-2010(a) k = 1 (b) k = - 1 (c) all real k (d) None of these(e) None of these

30. The matrix is

KIITEE-2010(a) unitary (b) orthogonal (c) nilpotent (d) involutory (e) None of these

31. If is a cube root of unity, then a root of the

following equation is

KIITEE-2010(a) x = 1 (b) x = (c) x = 2 (d) x = 0

32. If A is a singular matrix, then A. adj A is KIITEE-2010

(a) a scalar matrix (b) a zero matrix (c) an identity matrix (d) an orthogonal matrix

33. If then A4 + A3 – A2 = PGCET-

2010(a) 0 (b) 1 (c) A (d) None of these

34. The value of the determinant is

PGCET-2010(a) 100 (b) 202 (c) 303 (d) 0

35. The inverse of the matrix

(PGCET– 2009)

(a) (b)

(c) A itself (d) N.O.T

36. If then A2 – 5A + 7l is

(PGCET– 2009)

(a) (b)

(c) (d) N.O.T

37. If a + b + c 0, then the system of equations (b + c) (y + z) – ax = b – c (c + a) (z + x) – by = c – a (a + b) (x + y) – cz = a – b has

(NIMCET – 2009)(a) a unique solution (b) no solution(c) infinite number of solutions(d) finitely many solutions

38. If , then I + A + A2 + …. equals to

(NIMCET – 2009)

(a) (b)

(c) (d)

39. If A is a 3 3 matrix with det (A) = 3, then det (adj A) is

(NIMCET – 2009)(a) 3 (b) 9 (c) 27 (d) 6

40. Let . If A2 – 2A + I = B,

then value of b is (Note that I is identity matrix of order 2)

(MCA : KIITEE - 2009)(a) 1 (b) 3 (c) –1 (d) 2

41. The value of the determinant

is

(MCA : KIITEE - 2009)(a) 0 (b) 80 (c) –(6!) (d) N.O.T

42. The sum of two non integral roots of

is (MCA :

KIITEE - 2009)(a) 5 (b) –18 (c) –5 (d) N.O.T

43. If A = then A-1 is equal to

(KIITEE - 2009)(a) AT (b) adj A (c) A (d) N.O.T

44. If A= then the value of |adj A| is

equal to (KIITEE - 2009)

(a) 5 (b) 1 (c) 0 (d) N.O.T45. It is given that square matrix A is orthogonal and

also that det A is not equal to 1. Then, HYDERABAD CENTRAL UNIVERSITY - 2009

(a) |A| is zero (b) |A| > 1 (c) |A| cannot be determined (d) None of the above


INFOMATHS46. If and then A8

equals to HYDERABAD CENTRAL UNIVERSITY - 2009

(a) 64 B (b) 128 B (c) -128 B (d) -64 B47. If A is a 3 3 matrix and A’ A = I and |A| = 1 then

the value of |(A – 1)| = HYDERABAD CENTRAL UNIVERSITY - 2009(a) 1 (b) – 1 (c) 0 (d) N.O.T

48. If a, b, c are the roots of x3 + px2 + q = 0, then

HYDERABAD CENTRAL

UNIVERSITY - 2009(a) p (b) p2 (c) p3 (d) q

49. The following system of equations 6x + 5y + 4z = 0 3x + 2y + 2z = 0 12x + 9y + 8z = 0 has

HYDERABAD CENTRAL UNIVERSITY - 2009(a) no solutions (b) a unique solution (c) more than one but finite number of solution(d) infinite solutions

50. Let be a 2 2 matrix such that A3 = 0.

The sum of all the elements of A2 is HYDERABAD CENTRAL UNIVERSITY - 2009

(a) 0 (b) a + b + c + d (c) a2 + b2 + c2 + d2 (d) a3 + b3 + c3 + d3

51. ax + 4y + z = 0, bx + 3y + z = 0, cx + 2y + z = 0 can be a system of equation with nontrivial solutions if a, b, c are in KIITEE–2008(a) HP (b) AP (c) GP (d) None

52. The system of equations 2x + 3y = 8, 7x – 5y = - 3 and 4x – 6y + = 0 is solvable when is

KIITEE – 2008(a) – 6 (b) – 8 (c) 6 (d) 8

53. For and

KIITEE – 2008(a) AB exists (b) A + B exists (c) BA exists (d) None

54. If then A-1 exists of

KIITEE – 2008(a) = 4 (b) 8 (c) 4 (d) None

55. If then A2 is equal to

KIITEE – 2008(a) A (b) AT (c) I (d) None

56. If then x y is equal to

KIITEE – 2008(a) – 5 (b) 5 (c) 4 (d) 6

57. The value of the determinant : will be

negative when MP COMBINED - 2008

(a) a, b, c are positive (b) a, b, c are negative (c) (a + b + c) < 0 (d) (a + b + c) > 0

58. The value of the determinant

is MP COMBINED -

2008(a) (a + b + c) (b) (a + b + c)3

(c) a2 + b2 + c2 – ab – bc – ca (d) a3 + b3 + c3 – 3abc

59. The value of the determinant : is

MP COMBINED - 2008(a) 0 (b) 1(c) (a + b + c) (d) (1 + a + b + c)

60. If one root of the equation :

is -9, then other roots are:

MP COMBINED - 2008(a) -2, - 7 (b) 2, 7 (c) -2, 7 (d) 2, - 7

61. If then a and b will

be equal to : MP COMBINED - 2008

(a) (b) a = - 3, b = 4

(c) a = 1, b = 1 (d) a = 4, b = - 3

62. If and then the

value of |AB| will be MP COMBINED - 2008(a) 4 (b) 8 (c) 16 (d) 32

63. If then its inverse matrix M-1 will

be: MP COMBINED - 2008

(a) (b)

(c) (d)


INFOMATHS64. The value of the given determinant is

KARNATAKA - 2007(a) 1 (b) 0 (c) 2 (d) 3

65. If , then An = ICET – 2005

(a) (b)

(c) (d)

66. If the matrix is invertible, then K

ICET – 2005(a) 2 (b) – 5 (c) 10 (d) 5

67. If , then which of the following is true?

Pune– 2007(a) A2 – 4 A + I = O (b) A2 + 4A + I = O (c) (A – 4I) (A + I) = O (d) (A + 4I) (A – I) = O

68. A is a square matrix of order 3; then which of the following is not true? |A| means determinant

Pune– 2007(a) | A + A’| = |A| + |A’| (b) |A * A| = |A| |A| (c) |kA| = k3 |A| where k is a constant.(d) |-A| = - |A|

69. If then A2 is

Pune– 2007(a) null matrix (b) unit matrix (c) A (d) –A

70. If AB is a zero matrix, then Pune– 2007

(a) A = O or B = O (b) A = O and B = O (c) It is not necessary that either A or B should be O. (d) N.O.T

71. If A is a square matrix of order 3 and entries of A are positive integers then |A| is

Karnataka PG-CET– 2006(a) Different from zero (b) 0(c) Positive (d) an arbitrary integer

72. If AB = A and BA = B then B2 is equal to Karnataka PG-CET– 2006

(a) A (b) B (c) I (d) 0

73. The value of is Karnataka PG-

CET– 2006(a) 20 (b) – 2 (c) 0 (d) 5

74. what will be the value of A?

MP– 2004

(a) (b)

(c) (d) None

75. Matrix multiplication is not : MP– 2004

(a) commutative (b) associative (c) distributive (d) Both commutative & associative

76. The matrix is : MP–

2004(a) orthogonal (b) unitary (c) singular (d) None of the above

77. MP–

2004(a) (x + y + z)2 (b) 3xyz (c) 1 (d) N.O.T


MP– 2004(a) 0 (b) 1(c) – a – b – c (d) (a + b + c)2

79. A and B are two matrices where A is a non singular matrix. If AB = 0 then :

MP– 2004(a) B is singular (b) B is non singular (c) B is 0 (d) A is 0

80. The roots of the equation are

UPMCAT - 2002(a) 0, 0, 3 (b) 0, 0, - 3 (c) 0, - 3 (d) 0, 3

81. If , then x is equal to :

UPMCAT - 2002(a) – 1 (b) 1 (c) 0 (d) N.O.T

82. If then (A – 2I) (A – 3I) : UPMCAT

- 2002(a) Identity Matrix (b) Null Matrix (c) NiL potent Matrix (d) N.O.T

83. The eigen vectors of a real symmetric matrix corresponding to different eigen values are

HYDERABAD CENTRAL UNIVERSITY - 2009(a) Singular (b) Orthogonal (c) Non-singular (d) None of the above

84. P, Q are 3 3 matrices. X is 3 1 matrix. PX = 0 has infinitely many solutions, QX = 0 has a unique solution. T be the solution set of P(QX) = 0. S be the solution set of Q(PX) = 0. Then

IP Univ.– 2006(a) both T and S are infinite sets. (b) only T is an infinite1 set. (c) only S is infinite set. (d) both T and S are finite sets. (e) exactly one of S, T is an infinite set.

85. and then

IP Univ.– 2006(a) PQ QP

(b)

(c)


INFOMATHS(d) PQ = O for some x, y R (e) None of these

86. All the matrices in this equation are of order 3 3. A1 = P-1 BP, A2 = P-1B2P, |B| = 3. The value of |A1

2 + A2| is

IP Univ.– 2006(a) 36 (b) 48 (c) 60 (d) 72

87. If A is a square matrix then A + A| is Karnataka PG-CET– 2006

(a) Unit matrix (b) Null Matrix (c) A (d) Symmetric matrix

52. The following system of linear equations 3x + 2y + z = 3 2x + y + z = 0 6x + 2y + 4z = 6 has

HCU-2006(a) an infinitely many solutions (b) no solution(c) the solution lies on the intersection of the

planes x = 2 and y = - 2 (d) The solution lies on the plane x + z = 1 (e) None of the above

INDEFINITE INTEGRAL


BHU-2012

(a) (b) (x – 1)2ex

(c) (x + 1)ex (d) ex


BHU-2012

(a) (b)

(c) (d)

3. The value of is BHU-2011

(a) x (log x + 1) (b) x (logx – 1)(c) log x (x + log x) (d) x (x – log x)

4. is equal to (MCA : KIITEE

– 2009)

(a) (b)

(c) ex tan x + k (d)

5. equals: (a) ex (sin x – cos x) + C (b) ex (cos x – sin x) + C

(MCA : MP COMBINED – 2008)

(c)

(d)

6. is equal to : UPMCAT–

2002

(a) (b)


7. If

then values of and are: (MP COMBINED – 2008)

(a) = 0, = 1 (b) = 1,

(c) = - 1, (d) = 1,

DEFINITE INTEGRAL

1. The value of the integral

NIMCET-2010 (a) 1 (b) 1/2 (c) 3/2 (d) 2

2. The value of the integral

NIMCET-2010

(a) log 2 (b) log 3 (c) (d)

3. log 10 xdx is NIMCET-2010

(a) (x – 1) loge x + c (b) loge 10.x loge

(c) log10 e. x loge + c (d)

4. If I1 =

NIMCET-2010 (a) I3 =I4 (b) I3 > I4 (c) I2 > I1 (d) I1 > I2

5. The area between the curves y = 2 – x2 and y = x2 is NIMCET-2010

(a) 8/3 (b) 4/3 (c) 2/3 (d) 5/3

6. The value of is

KIITEE-2010(a) 0 (b) 1 (c) /4 (d) /2

7. In then equals KIITEE-2010

(a) 1/2 (b) 1 (c) (d) 0

8. The solution of the differential equation

satisfying the condition y(1) = 1 is KIITEE-2010

(a) y = In x + x (b) y = x In x + x2 (c) y = xe(x-1) (d) y = x In x + x

9. The value of is (NIMCET

– 2009)

(a) (b) (c) (d)

10. The smaller of the areas bound by y = 2 – x and x2 + y2 = 4 is

(NIMCET – 2009)(a) - 1 (b) - 2 (c) 2 - 1 (d) 2 - 2

11. The value of is NIMCET –

2008(a) 0 (b) 1 (c) /4 (d) /2


INFOMATHS12. equals: (MP

COMBINED – 2008)

(a) 1 (b) 1/2 (c) 0 (d)

13. dx equals :

(MCA : MP COMBINED – 2008)(a) 0 (b) 1 (c) a (d) 2a

14. The area enclosed between the curves y = x and y2

= 16x is: (MCA : MP COMBINED – 2008)

(a) sq. unit (b) sq. unit

(c) sq. unit (d) sq. unit

15. equals: (MP COMBINED

– 2008)(a) 0 (b) 1/2 (c) 1 (d) 2

16. equals IP Univ.–

2006(a) (b) (c) (d)


MP– 2004(a) 0 (b) 1 (c) 4(3 – e) (d) None

18. The area bounded by the curve y = sin x between x = 0 and x = 2 is :

MP– 2004(a) 2 (b) 4 (c) 4 (d) 14


MP– 2004(a) 0 (b) 1 (c) – 1 (d) 2

20. The area of the plane bounded by the curves , x [0, 1], y = x2, x [1, 2] and y = - x2 +

2x + 4, x [0, 2] is NIMCET–2008

(a) 10/7 (b) 19/3 (c) 3/5 (d) 4/3

21. equals

IP Univ.– 2006(a) 0 (b) 1 (c) 2 (d) 3 (e) 4

22. Assume that p is a polynomial function on the set of real numbers. If p(0) = p(2) = 3 and p'(0) = p'(2) = –

1, then

PU CHD-2012(A) – 3 (B) – 2 (C) – 1 (D) 2

23. If f is a continuous function on the set of real numbers and if a, b are real numbers, which of the following must be true ?

I.

II.

III.

PU CHD-2012(A) I only (B) II only

(C) II and III only (D) I, II and III24. The area of the region bounded by the curves y = |x

– 1| and y = 3 – |x| isPU CHD-2012

(A) 2 sq units (B) 3 sq units(C) 4 sq units (D) 6 sq units

25. Area between curve y = 1 - |x| and X-axis Pune-2012

(a) 1 sq. unit (b) 1/2 sq. units (c) 2 sq units (d) 3 sq. units

26. If F(x) is continuous such that area bounded by curve y = F(x) and X – axis gives x = a and x = 0 is

. Then the value of is

Pune-2012

(a) (b) (c) (d)

27. The value of

is

NIMCET-2012(a) 0 (b) π (c) 2 (d) /2

28. If and

then

NIMCET-2012(a) I1 = I2 (b) I2 > I1 (c) I3 > I4 (d) I4 > I3

29. The value of integral is

NIMCET-2012(a) π (b) /2 (c) /3 (d) 0

30. The value of is

NIMCET-2012(a) /4 (b) /2 (c) 1 (d) None of these


BHU-2012(a) 0 (b) x/4 (c) x/2 (d)

32. For a >1, the value of is

HCU-2011

(a) 2 (b) (c) (d) 0

33. Evaluate

HCU-2011

(a) - (b) (c) (d)

34. Consider the region bounded by the graphs y = ex, y = 0, x =1 and x = t, where t < 1.The area of this region is atmost

HCU-2011(a) unbounded (b) e(c) 0 (d) 1n

35. If ‘a’ is a positive integer, then the number of values satisfying

isNIMCET-2011

(a) only one (b) two (c) three (d) four36 INFOMATHS/MCA/MATHS/OLD QUESTIONS

INFOMATHS36. If then f'(x) is

NIMCET-2011

(a) cos x + x sin x (b) x sin x (c) x cos x (d)

37.

[no correct answer was given in choices, correct answer should be π/2 ]

NIMCET-2011

(a) (b) π (c) (d) 38. If the area bounded by y = x2 and y = x is A sq.

units then the area bounded by y = x2 and y = 1 isNIMCET-2011

(a) 2A + 1 sq. units (b) 2A sq. units (c) 2A + 2 sq. units (d) A + 2 sq. units

39. The value of a < b is :

PU CHD-2011(A) b – a (B) a – b (C) b + a (D) |b|–|a|

40.

PU CHD-2011 (A) 1 (B) 3/2 (C) 2 (D) 5/2

41. The value of is

BHU-2011

(a) (b)

(c) (d)

42. The value of

BHU-2011

(a) (b) (c) (d)

DIFFERENTIAL EQUATIONS

1. Solution of the equation is

(MP COMBINED – 2008)(a) (x + a) (1 – ay) = cy (b) (x + a) (1 + ay) = cy (c) (1 + ax) (1 + y) = cy (d) (1 – ax) (1 + y) = cy

2. If and it is known that for x = 1, y = 1; if

x = - 1, then the value of y will be: (MP COMBINED – 2008)(a) e2 (b) e (c) 1 (d) – 1


is:

(MCA : MP COMBINED – 2008)(a) 4x + y + 1 = tan (2x + c) (b) 4x + y + 1 = 2 tan (2x + c) (c) 2(4x + y + 1) = tan (2x + c) (d) tan (4x + y + 1) = 2x + c

4. The solution of the equation is :

(MP COMBINED – 2008)(a) (b) (c) (d)

5. The solution of the equation :

(MP COMBINED – 2008)(a) x = y(y2 + c) (b) xy = y2 + c (c) y = x(y2 + c) (d) x + y3 = c

6. Integrating factor of is : MP–

2004(a) x2 (b) 1/x (c) – 1/x (d) 1/y

7. The solution of the differential equation y(2x + y2)dx + x(x + 3y2)dy = 0, is IP Univ.– 2006 (a) x2y + 2xy3 = c (b) 2x2y xy3 = c (c) xy + xy3 = c (d) x2y + xy3 = c. (E) x2y + xy2, = c

8. If the solution of the differential equation

is x + y – 1 = Ceu, then the value of

u is: (MP COMBINED – 2008)(a) x + y (b) xy (c) x – y (d) x + y + 1


is:

(MP COMBINED–2008)(a) (b)

(c) (d)

68. The general solution of the differential equation

HCU-2011(a) y2 = (ln |x| + C)x (b) y = (ln |x| + C)x(c) y2 = (ln |x| + C) (d) y = (ln |x| + C)x2

75. The differential equation, whose solutions are all the circles in a plane, is given by

HCU-2011(a) (1 + y')2 y'" – 3y'y"2 = 0 (b) xy' + y = 0 (c) (1 + y')2y'" + 3'y"2 = 0 (d) yy" + y'2 + 1 = 0

40. Solution of the differential equation

is :PU CHD-2012

(A) x(y + cos x) = sin x + C (B) x(y – cos x) = sin x + C

(C) x(y + cos x) = cos x + C (D) x(y – cos x) = cos x + C7. Curve of D.E. xy' = 2y, passing through (1, 2) is also

passing through Pune-2012

(a) (1, 2) (b) (4, 24) (c) (24, 4) (d) (4, 8)17. Solution of D.E. 9yy' + 4x = 0 is

Pune-2012

(a) (b)

(c) (d)

24. Solution of D.E. xdy – ydx = 0 is a Pune-2012

(a) circle (b) parabola (c) straight line (d) Hyperbola

31. D.E. determines a family of circle with

Pune-2012(a) fixed radii and center at (0, 1) (b) fixed radii and center at (0, - 1) (c) fixed radius 1 and variable center along X-axis


INFOMATHS(d) fixed radius 1 and variable center along Y-axis.

44. The differential equation y = px + f(p) is called of : BHU-2012

(a) Clairaut’s form (b) Newtonian form (c) Bernoulli’s form (d) None of these

45. Which of the following differential equation is linear? BHU-2012

(a) (b)

(c)

(d)

46. Which of the following differential equations can be reduced to homogenous form?

BHU-2012(a)

(b)

(c) (4x + 6y + 5)dx = (2x + 3y + 4)dy (d) (1 + y2) dx + (x – siny)dy = 0

102. Solution of the differential equation is

BHU-2011(a) (b)

(c) (d) 105. The degree of the differential equation

is

BHU-2011(a) 3 (b) 4 (c) 5 (d) 6

COMPLEX NUMBERS 1. Let 1 be a cube root of unity and i = the value

of the determinant is

NIMCET-2010 (a) 0 (b) (c) 2 (d) 1 +2

2. The value of X4 + 9X3 +35X2 – X + 4 for X = - 5+ 2 is NIMCET-2010

(a) 0 (b) -160 (c) 160 (d) -164

3. If and then z lies on KIITEE-2010(a) an ellipse (b) a circle (c) a straight line (d) a parabola

4. If z1 and z2 are two complex numbers such that |z1 + z2| = |z1| + |z2| then arg z1 – arg z2 is equal to”

KIITEE-2010

(a) (b) - (c) 0 (d) 5. If |Z + 4| 3 then the maximum value of |z + 1| is

KIITEE-2010(a) 4 (b) 10 (c) 6 (d) 0

6. The conjugate of a complex number is , then that complex number is KIITEE-2010

(a) (b) (c) (d)

7. If z2 + z + 1 = 0, where z is a complex number, then

the value of

is KIITEE-2010

(a) 54 (b) 6 (c) 12 (d) 18

8. The value of is PGCET-2010(a) 2 (b) 3 + i (c) 1 (d) – 1

9. The number of solution to the equation is (KIITEE - 2009)

(a) 2 (b) 3 (c) 4 (d) 110. The area of the triangle whose vertices are I, a, b

where and a, b are the nonreal cube roots of unity, is

(MCA : KIITEE – 2009)

(a) (b) (c) 0 (d) 11. If Z2 is purely imaginary when Z is a complex

number of constant modules then the number of possible values of Z is KIITEE–2009(a) 4 (b) infinite (c) 2 (d) 1

12. If w is an imaginary cube root of unity then (1 + w – w2)7 equals to (KIITEE – 2009)(a) 128 w (b) 128 w2 (c) – 128w (d) –128w2

13. The smallest positive integer n, for which

is

(KIITEE - 2009)(a) 8 (b) 12 (c) 16 (d) None of these

14. Let and be the roots of the equation x2 + x + 1 = 0. The equation whose roots are 19 and 7 is

NIMCET – 2008(a) x2 – x – 1 = 0 (b) x2 + x – 1 = 0 (c) x2 – x + 1 = 0 (d) x2 + x + 1 = 0

15. The equation |Z + i| - |Z – i| = k represents a hyperbola if

KIITEE – 2008(a) 0 < k < 2 (b) – 2 < k < 2 (c) k > 2 (d) None

16. is purely real then the non zero real value of x is KIITEE – 2008(a) (b) 2 (c) 1 (d) – 1

17. The fourth roots of unity are given as z1, z2, z3 and z4. The value of is

KIITEE–2008(a) i (b) 1 (c) -i (d) 0

18. If then the value of is : MP–

2004(a) /4 (b) /3 (c) /2 (d) /6

19. The fourth roots of unity are :. UPMCAAT - 2002

(a) 1, 1, 1, 1 (b) 1, -1, 1, -1 (c) 1, 1, i, i (d) -1, 1, -i, i

20. The radius of a circle given by the equation is KIITEE –

2008(a) 5/2 (b) (c) 5 (d) None

21. If |Z - i| 2 and Z0 = 5 + 3i then the maximum value of |iZ + Z0| is KIITEE – 2008(a) (b) (c) 7 (d) 4


INFOMATHS22. If z is different from i and |z| = 1 then is

KIITEE – 2008(a) purely imaginary (b) purely real (c) non real with equal real and imaginary parts (d) None

23. If and then

is equal to KIITEE -

2008(a) 1 (b) i (c) -i (d) 0

24. For complex number z, 0 ≤ arg z < 2 . S is IP Univ.–

2006(a) /3 (b) /4 (c) /5 (d) /6

(e) /725. Let A be the set of all complex numbers that lie on

the circle whose radius is 2 and centre lies at the origin. Then

B = {1 + 5z|z A}describes HCU-2012(a) a circle of radius 5 centred at (-1, 0) (b) a straight line (c) a circle of radius with centre at (-1, 0). (d) a circle of radius 10 centred at (-1, 0)

26. Consider a set of real numbers T = {t1, t2, ….,} defined as

. This set is

HCU-2012(a) an unbounded infinite set (b) an infinite bounded set (c) a finite set with |T| > 319 (d) a finite set with |T| < 10

27. If 1, , 2 be the cube roots of unity, then value of (1 + – 2)7 + (1 – + 2)7 is :

PU CHD-2012(A) – 128 (B) 128 (C) 64 (D) – 64

28. If and z = x + iy then the equation z2 = has

PU CHD-2012(A) No solution (B) 2 solutions(C) 4 solutions (D) An infinite number of

solutions

29. The value of complex number is :

BHU-2012

(a) 2 (b) - 2 (c) (d)

30. If 1, , 2, ……, n-1 are nth roots of unity, then (1 - ) (1 - 2) ….. (1 - n-1) is equal to

BHU-2011(a) n2 (b) 0 (c) 1 (d) n

31. The value of is

BHU-2011(a) 1 (b) 2 (c) 2i (d) – 2i

VECTORS 1. If C is the middle point of AB and P is any point

outside AB, then NIMCET-2010(a) + = (b) + =2(c) + + = (d) + +2 =

2. Let , and be three non zero vectors, no two of which are collinear and the vector + is collinear with ,while + is collinear with then + +

, is equal to NIMCET-2010 (a) (b) (c) (d) none of these

3. The position vector of A, B, C and D are then the

angle between and is NIMCET-2010 (a) 0 (b) /4 (c) /2 (d)

4. A vector has components 2p and 1 with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the counterclockwise sense. If, with respect to the new system, has components p + 1 and 1, then

NIMCET-2010

(a) p = 0 (b) p = 1 or p =

(c) p = -1 or p = (d) p = 1 or p = -1

5. The value of ‘a’ for which the system of equations a3 x + (a + 1 )3 y + (a + 2)3 z = 0ax + (a + 1) y + (a + 2) z = 0x + y + z = 0has a non zero solution, is NIMCET-2010 (a) 1 (b) 0 (c) -1 (d) N.O.T

6. The vectors and are equal in length and taken pairwise make equal angles. If

make an obtuse angle with

the base vector i, then is equal to NIMCET-2010

(a) (b)

(c) (d)

7. The average marks per student in a class of 30 students were 45. On rechecking it was found that marks had been entered wrongly in two cases. After correction these marks were increased by 24 and 34 in the two cases. The corrected average marks per student are

NIMCET-2010 (a) 75 (b) 60 (c) 56 (d)

47 8. If are non-coplanar unit vectors such that

, then the angle between

the vectors and is KIITEE-2010

(a) (b) (c) (d)

9. If and , where

, then KIITEE-2010(a) 2 + 22 (b) = + 1 (c) = = (d) None of these

10. If 3P and 4P are the resultants of a force 5P, then the angle between 3P and 5P is KIITEE-2010


INFOMATHS(a) (b)

(c) 90 (d) None of these11. Area of the parallelogram whose adjacent sides are i

+ j – k and 2i – j + k is (PGCET– 2009)(a) (b) (c) (d)

12. The vector is to be written as the sum of a vector parallel to and a vector

perpendicular to , then is (NIMCET – 2009)

(a) (b)


13. If and are unit perpendicular vectors, then

NIMCET – 2009(a) 9 (b) 4 (c) 8 (d) 6

14. If are non-coplanar unit vectors such that

, then the angle between and

is (NIMCET – 2009)

(a) (b) (c) (d)

15. is equal to KIITEE – 2009

(a) (b) 0


16. The value of x for which the volume of parallelepiped formed by the vectors I + xj + k, j + xk and xi + k is minimum is

HYDERABAD CENTRAL UNIVERSITY - 2009

(a) – 3 (b) (c) (d)

17. If and is a vector

satisfying and then HYDERABAD CENTRAL UNIVERSITY - 2009

(a) 0 (b) 3/4 (c) 30/4 (d)

18. The value of for which the volume of parallelepiped formed by the vectors and

is minimum is given by NIMCET - 2008

(a) -3 (b) 3 (c) (d)

19. The value of such that the four points whose position vectors are

and NIMCET - 2008

(a) – 6 (b) 4 (c) 5 (d) 8

20. If then the

angle between and is NIMCET - 2008(a) /6 (b) 2/3 (c) 5/3 (d) /4

21. Let be three vectors such that = 4

then is equal to KIITEE – 2008(a) 64 (b) 16 (c) 8 (d) None

22. The volume of the tetrahedron whose vertices are P(k, k, k), Q(k + 1, k + 6, k + 36), R(k, k + 2, k + 5), S(k, k, k + 6) is IP Univ.– 2006(a) 1 (b) 2 (c) 4 (d) 6 (e) 36

23. If the vectors and are orthogonal, then the value of is

Karnataka PG-CET– 2006(a) 12 (b) 10 (c) 5 (d) – 5

24. If

Then area of ponallelogram is equal to :UPMCAT– 2002

(a) 0sq units (b) 42sq units (c) 49 sq units (d) N.O.T.

25. If ;

are the adjacent sides of a ||gm then ||gm is a: UPMCAT– 2002

(a) rectangle (b) square (c) rthombus (d) None of these

26. If

and then

is HYDERABAD CENTRAL UNIVERSITY - 2009

(a) 6 (b) 9 (c) 1 (d) 027. Let and are three non-zero vectors, no two

of which are collinear. If is collinear with

and is collinear , then is HYDERABAD CENTRAL UNIVERSITY - 2009

(a) (b) parallel to

(c) parallel to (d) parallel to

28. Let and If is a vector

such that and the

angle between and is 300, then

is equal to NIMCET - 2008

(a) 2/3 (b) 3/2 (c) 2 (d) 329. The projection of a line segment on the axes of

reference are, 3, 4 & 12 respectively. The length of the line segment is

KIITEE – 2008

(a) 13 (b) 5 (c) (d) 19

30. The vertices of a triangle ABC are A (-1, 0, 2), B(1, 2, 0) and C(2, 3, 4). The moment of a force of magnitude10 acting at A along AB about C is

KIITEE – 2008


INFOMATHS(a) (b) (c) (d) None

31. The coplanar points A, B, C, D are (2 – x, 2, 2), (2, 2 – y, 2), (2, 2, 2 – z) and (1, 1, 1) respectively. Then one the following is true, find it

KIITEE – 2008

(a)

(b) x + y + z = 1

(c) (d) None

32. Let be three unit vectors of which and

are non – parallel. Let the angle between and

be and that between and be . If

then. KIITEE – 2008

(a) (b)

(c) (d) None

33. p, q, r are mutually perpendicular unit vectors. d is also a unit vector. If d = u1p + v1q + w1r and d = u2(q r) + v2 (r q) + w2 (p q), then the maximum value of (u1 – u2)2 + (v1 – v2)2 + (w1 – w2)2 equals

IP Univ.– 2006(a) 0 (b) 1 (c) 2 (d) 3 (e) 4

34. Suppose A = i – j – k, B = i – j + k and C = - i + j + k, where i, j, k are unit vectors. Pick the odd one out among the following:

HCU-2012(a) A (B C) (b) (A B) C (c) A C (d) A B

35. Consider the following equalities formed for any three vectors A, B and C.

HCU-2012I. (A B)C = A(B C)II. (A B) C = A (B C) III. A (B C) = (A B) C IV. A (B + C) = (A B) + (A C) (a) Only I is true (b) I, III and IV are true (c) Only I and IV are true (d) All are true

36. A line makes angles , , and with the four diagonals of a cube. Then the sum cos2 +cos2 +cos2 + cos2is

HCU-2011(a) 4/3 (b) 0 (c) 1/3 (d) 1

37. Let A = 2i – 3j + k and B = - i + 2j + k be two vectors. The vector perpendicular to both A and B having length 10 is

HCU-2011

(a) (b)

(c) Both A and B (d) None of the above

38. If and and , then

the angle between and is HCU-2011

(a) (b) (c) (d)

39. If the vectors and are mutually perpendicular, then the value of x is

NIMCET-2012

(a) – 2 (b) 2 (c) 4 (d) – 4 40. The equation of the plane passing through the point

(1, 2, 3) and having the vector as its normal, is

NIMCET-2012(a) 2x – y + 3z + 7 = 0 (b) 3x – y + 2z + 7 = 0 (c) 3x – y + 2z = 7 (d) 3x + y + 2z = 7

41. If , , , , then angle

between the vector and is NIMCET-2012

(a) /2 (b) /3 (c) /4 (d) /642. If (0 ≤ ≤ π) is the angle between the vectors

and , then equals

NIMCET-2012(a) -cot (b) tan (c) -tan (d) cot

43. If and are unit vectors such that

, then the value of is NIMCET-2012

(a) (b) (c) (d)

44. If are non-coplanar vectors and is a real number, then the vectors and

are non-coplanar for NIMCET-2012

(a) All values of (b) All except one value of (c) All except two values of (d) No value of

45. If a, b and c are unit coplanar vectors, then the scalar triple product [2a – b, 2b – c, 2c – a] =

NIMCET-2011(a) 0 (b) 1 (c) (d)

46. Let and . Suppose

that the angel between and is acute and the

angle between and the positive direction of the y-

axis lies between and π, then the set of all

possible values of x isNIMCET-2011

(a) {1, 2} (b) {–2, –3} (c) {x : x < 0} (d) {x : x > 0}

47. Let and . If is a unit vector, then the maximum value of the scalar triple product is

NIMCET-2011(a) –1 (b) (c) (d)

48. If θ is the angle between a and b and |a×b| = |a.b|, then θ is equal to:

NIMCET-2011(a) 0 (b) π (c) π/2 (d) π/4

49. ABCD is a parallelogram with AC and BD as diagonals. Then is equal to:

NIMCET-2011(a) (b) (c) (d)

50. The vector 2i + j – k is perpendicular to i – 4j + k, if is equal to


INFOMATHSBHU-2011

(a) 0 (b) – 1 (c) – 2 (d) – 3 51. If |a| = |b|, then (a + b) . (a – b) is

BHU-2011(a) positive (b) negative (c) unity (d) zero

52. If A = 2i + 2j – k, B = 6i – 3j + 2k, then A B will be given by

BHU-2011(a) 2i – 2j – k (b) 6i – 3j + 2k (c) I – 10j – 18 k (d) i + j + k

53. If the position vectors of three points are a – 2b + 3c, 2a + 3b – 4c, - 7b + 10c, then the three points are

BHU-2011(a) collinear (b) coplanar (c) non-coplanar (d) None of these

54. If a = 4i + 2j – 5k, b = - 12i – 6j + 15k, then the vectors a, b are

BHU-2011(a) parallel (b) non-parallel (c) orthogonal (d) non-coplanar

55. If is the angle between vectors a and b, then |a b| = |a . b| when is equal to

BHU-2011(a) 0 (b) 45 (c) 135 (d) 180

56. If [abc] is the scalar triple product of three vectors a, b and c, then [abc] is equal to

BHU-2011(a) [bac] (b) [cba] (c) [bca] (d) [acb]

57. If be the angle between the vectors 4(i – k) and i +j + k, then is

BHU-2011

(a) (b) (c) (d)

58. a b = 0 implies only BHU-2011

(a) a = 0 (b) b = 0 (c) = 90(d) either a = 0 or b = 0 or = 90

59. If a and b are two unit vectors and is the angle between them. Then, a + b is a unit vector, if

BHU-2011

(a) (b)

(c) (d)

60. If two vectors a and b are parallel and have equal magnitudes, then

BHU-2011(a) they are not equal (b) they may or may not be equal (c) they have the same sense of direction (d) they do not have the same direction

61. Let ABCD be a parallelogram. If a, b, c be the position vectors of A, B, C respectively with reference to the origin 0, then the position vector of D with reference to 0 is

BHU-2011(a) a + b + c (b) b + c – a (c) c + a – b (d) a + b – c

62. If a and b represent two adjacent sides AB and BC respectively of a parallelogram ABCD, then its diagonals AC and DB are equal to

BHU-2011(a) a + b and a – b (b) a – b and a + b (c) a + 2b and a – 2b (d) 2a + b and 2a – b

63. Let the vectors a, b, c be the position vectors of the vertices P, Q, R of a triangle respectively. Which of the following represents the area of the triangle?

BHU-2011

(a) (b)

(c) (d)

THREE DIMENSIONAL GEOMETRY 1. The image of the point (-1, 3, 4) in the plane x – 2y

= 0 is KIITEE-2010

(a) (b) (15, 11, 4)

(c) (d) (8, 4, 4)

2. The length of the perpendicular from (1, 0, 2) on the

line is KIITEE-

2010

(a) (b) (c) (d)

3. If A = (5, -1, 1), B = (7, -4, 7), C = (1, - 6, 10), D = (-1, -3, 4) then ABCD is a (MCA : KIITEE – 2009)

(a) square (b) rectangle (c) rhombus (d) None of these

4. The points A = (1, 2, -1), B = (2, 5, -2), C = (4, 4, -3) and D = (3, 1, -2) are (MCA : KIITEE – 2009)(a) vertices of a square (b) vertices of a rectangle (c) collinear (d) vertices of a rhombus

5. If (1, -1, 0), (-2, 1, 8) and (-1, 2, 7) are three consecutive vertices of a parallelogram then the fourth vertex is (KIITEE – 2009)(a) (0, -2, 1) (b) (1, 0, -1) (c) (1, -2, 0) (d) (2, 0, -1)

6. The points (0, 0, 0), (0, 2, 0), (1, 0, 0), (0, 0, 4) are KIITEE – 2008

(a) vertices of a rectangle (b) on a sphere (c) vertices of a parallelogram (d) coplanar

7. Find the point at which the line joining the points A (3, 1,-2) and B(-2, 7, -4) intersects the XY-plane.

HCU-2012(a) (5, -6, 0) (b) (8, -5, 0)(c) (1, 8, 0) (d) (4, -5, 0)

8. If x + y + z = 0 and x3 + y3 + z3 – kxyz = 0, then only one of the following is true. Which one is it?

HCU-2012(a) k = 3 whatever be x, y and z(b) k = 0 whatever be x, y and z.(c) k = + 1 or -1 or 0(d) If none of x, y, z is zero, then k = 3

9. Consider the lines given by (x = a1z + b1, y = c1z + d1) and (x = a2z + b2, y = c2z + d2). The condition by which these lines would be perpendicular is given by

HCU-2011(a) a1c1 – a2c2 + 1 = 0 (b) a1c1 + a2c2 – 1 = 0 (c) a1a2 – c1c2 = 1 (d) a1a2 + c1c2 + 1= 0

10. The image P' of the point P(p, q, r) in the plane 2x + y + z = 6

HCU-2011(a) (p, q, - r)

(b)

(c)


INFOMATHS(d)

11. The image of the line from the point P given in Question 37 and it’s reflection P' about the plane 2x + y + z = 6 is given by

HCU-2011

(a)

(b)

(c)

(d)

12. If h is height and r1, r2 are the radii of the end of the frustum of a cone, then the volume of the frustum is

BHU-2012

(a) (b)

(c) (d)

13. If r is a radius and k is thickness of a frustum of a sphere, then its curved surface of frustum is :

BHU-2012

(a) (b) (c) (d)

14. The area of the triangle having vertices (1, 2, 3) and (-1, 2, 3) is :

BHU-2012

(a) (b)

(c) (d)

15. The point of intersection of the line and the plane

is :

BHU-2012(a) (b)

(c) (d) 16. The straight line through the point (-1, 3, 3) pointing

in the direction of the vector (1, 2, 3) hits the xy plane at the point

HCU-2011(a) (2, - 1, 0) (b) (-2, 1, 0) (c) (1, 3, 0) (d) never

ANSWERS (OLD QUESTIONS-CW1)SETS & RELATIONS

1 2 3 4 5 6 7 8 9 10C A D B C A C C C C11 12 13 1

4 15 16

17

18

19 20

D A A A AC B B B D D21 22 23 2

4 25 26

27

28

29 30

C C D B D A B B C C31 32 33 3

4 35 36

37

A A C D D B D

THEORY OF EQUATIONS1 2 3 4 5 6 7 8 9 10A A C B B A C D C11 12 1

3 14 15 16 17 18 19 20C A B A B A C C B D21 22 2

3 24 25 26 27 28 29 30

C B A D D C B ABCD B D

31 32 33 34 35 36 37 38 39 40

A B C D C B B C A BC41 42 4

3 44 45 46 47 48 49 50CD B C B B D ABC

D B B A

51 52 53 54 55 56

A D C D A B

SEQUENCE & SERIES1 2 3 4 5 6 7 8 9 1

0A A B D C B B A A D11

12

13

14

15

16

17

18

19

20

B B B A A A B A C B21

22

23

24

25

26

27

28

29

30

B C C C B C A B C B31

A

BINOMIAL1 2 3 4 5 6 7 8 9 1

0A B C A A C B A B A11

12

13

14

15

16

17

18

19

20

B A C B C B A D B A21

22

23

24

25

26

27

28

29

30

C B B A B C A A C B31

32

33

34

35

36

37

38

39

40

A A D A A C B A B A41

42

43

44

45

46

47

48

49

A C B B D C C B C

EXPONENTIAL & LOGARITHMIC SERIES1 2 3 4 5 6 7C D C B A A D

PERMUTATIONS & COMBINATIONS1 2 3 4 5 6 7 8 9 1

0C A C C B A A A D C11

12

13 14 15

16

17

18

19

20

C B D A A B C C D A21

22

23 24 25

26

27

28

29

30

C A A C D C A C C C31

32

33 34 35

36

37

38

39

40

B C D C C A C B D B41

42

43 44 45

46

47

48

49

50

B A D D B B D D D C

TRIGONOMETRY1 2 3 4 5 6 7 8 9 10C A C D A A D A B D

11 12 13 14 15 16 17 18 19 20A B A D D C B A D D21 22 23 24 25 26 27 28 29 30


INFOMATHSB C D A * A B C C C

31 32 33 34 35 36 37 38 39 40D D C D A B C C A C41 42 43 44 45 46 47 48 49 50D A D A C B A A A C

51 52 53 54 55 56 57 58 59 60A D C B D A C C B D

61 62 63 64 65 66 67 68 69 70D B D B C B D C C A71 72 73 74 75 76 77 78 79 80A D C C A B A D C C81 82 83 84 85 86 87 88 89 90B D C D B B B C B C91 92 93 94 95 96 97 98 99 10

0A C A B B B A C A D101

102

103 104

105

106

107

108

109

110

A C B D C C A D A C111

112

A B

PROBABILITY1 2 3 4 5 6 7 8 9 10D - - B C D B A D A11 12 13 14 15 16 17 18 19 20D A A D B + - - - C21 22 23 24 25 26 27 28 29 30A B D - C - B D D D

31 32 33 34 35 36 37 38 39 40A B C A A C C D D C41 42 43 44 45 46 47 48 49 50A D D C B A B C A C

51 52 53 54 55 56 57 58 59 60B D C C A C C A B B61 62 63 64 65 66 67 68 69 70D D A B A B D B B B71 72 73 74 75 76 77 78C D D A A D D C

TWO DIMENSIONAL GEOMETRY1 2 3 4 5 6 7 8 9 10- - - - A D D C D D

11 12 13 14 15 16 17 18 19 20A - A C D C B A A B21 22 23 24 25 26 27 28 29 30C A D A C D B A D B31 32 33 34 35 36 37 38 39 40- - B D D A B C B A

41 42 43 44 45 46 47 48 49 50C B B D A A B B B D51 52 53 54 55 56 57 58 59 60A D D B B C D B B C61 62 63 64 65 66 67 68 69 70C B D B A A C A D N71 72 73 74 75 76 77 78 79 80C A B D C D C A B D81 82 83 84 85 86 87 88 89 90A D C A C A A A C D91 92 93 94 95 96 97 98 99 10

0C A D B D A D C B D101

102

103

104

105

106

107

108

109

110

D A D D A D D C B A111

112

113

114

115

116

117

118

119

120

B A B D B D C A C D121

122

123

124

125

126

127

128

129

130

E C C A D C C B A B131

132

133

134

135

136

137

138

139

140

B B C D D A B C C C141

142

143

144

145

146

147

148

149

150

B D C B C C A C A A151

152

153

154

155

156

157

158

159

D E A E E D C B D

FUNCTIONS1 2 3 4 5 6 7 8 9 1

0

C C C B B D B C B D11

12

13

14

15

16

17

18

19

20

C C B A C A C B B A21

22

23

24

25

26

27

28

29

30

D D D A A D A B B B31

32

33

34

35

36

37

38

39

40

A A A A A B C B C C41

42

43

44

45

46

47

48

49

A C B D C B A C C

LIMITS AND CONTINUITY1 2 3 4 5 6 7 8 9 1

0D C B C C A A A B A11

12

13

14

15

16

17

18

19

20

D A E C D B B B D C21

22

D C

DERIVATIVES1 2 3 4 5 6 7 8 9 1

0D C A A D A C B B B11

12

13

14

15

16

17

18

19

20

A D D C C D B D D A21

22

23

24

25

26

27

28

29

30

C B C B C C C C D B31

32

33

C B C

APPLICATION OF DERIVATIVES1 2 3 4 5 6 7 8 9 10B D C C C D C D A C11 12 13 14 15 16 17 18 19 20D A A B

dD A B B D A

21 22 23 24 25 26 27 28 29 30B D C C A A D B C B31 32 33 34 35 36 37C D D D D B A

MATRICES1 2 3 4 5 6 7 8 9 1

0- - - - B C B A D C11

12

13

14

15

16

17

18

19

20

D B B B D B C B - -21

22

23

24

25

26

27

28

29

30

- - C D D B C D C C31

32

33

34

35

36

37

38

39

40

D B C D C D C - B B41

42

43

44

45

46

47

48

49

50

D C B B - B C C D A51

52

53

54

55

56

57

58

59

60

B D C B C A D D A B61

62

63

64

65

66

67

68

69

70

B C C A C D A A B C71

72

73

74

75

76

77

78

79

80

D C B C A A D D A B81

82

83

84

85

86

87

C B B A B D D

INDEFINITE INTEGRATION1 2 3 4 5 6 7A B B D C A C

DEFINITE INTEGRAL 11 1 3 1 2 1 1 1 1 41


INFOMATHS6 9 8 9 1 3 4 8

B D C A A C D D * A31 4

142

17

20

26

27

31

32

108

- - - D B - A D C C110

1 2 3 4 5 6 7 8 9

A C - C D A D B D B10 1

112

13

14

15

16

17

18

19

B C C A D D C C C B20 2

1B C

(D.E.) DIFFERENTIAL EQUATION1 2 3 4 5 6 7 8 9A D B B A B C B

COMPLEX NUMBER1 2 3 4 5 6 7 8 9 1

0A B C C C C C C C D11

12

13

14

15

16

17

18

19

20

A D D D B A D C D B21

22

23

24

C A D AVECTORS

1 2 3 4 5 6 7 8 9 10

B D D - C C D B D C11

12

13

14

15

16

17

18

19

20

C D C B B B D C B C21

22

23

24

25

26

27

28

29

30

B B C C A B A B A D31

32

33

C A A

THREE DIMENSIONAL-OLD QUESTIONS1 2 3 4 5 6B A D B D B


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QUINTESSENCE: - Infomathsinfomathsonline.com/Que_papers/All Chapters 1-20-Old Questions.doc · Web view... the intersection of any two of the subsets ... 3y = 5 and 3x – 4y = 7