- WordPress.com · · 2017-10-24 Model Question Papers. Mathematics. Time : 2½ hours. Written Exam Marks : 90 Marks. Based on Scheme of Examination as per G.O. (2D). No. 50 dated

www.surab

ooks

.com

www.surabooks.com

For Order : [email protected]: 9600175757 / 8124201001

www.Padasalai.Net www.TrbTnpsc.com

http://www.trbtnpsc.com/2017/08/11th-exam-model-question-papers-download.html

www.Padasalai.Net

www.surab

ooks

.com

Model Question Papers

MathematicsTime : 2½ hours

Written Exam Marks : 90 Marks

Based on Scheme of Examination as per G.O. (2D). No. 50 dated : 09-08-2017

Type of Questions MarksNo. of Questions

to be answeredTotal

Marks1 Mark questions 1 20 20Questions for Very Short Answers : (Total 10 questions.Out of which 1 question is compulsory).

2 7 14

Questions for Short Answers : (Total 10 questions.Out of which 1 question is compulsory).

3 7 21

Questions for Long Answers : (With sub-sections).

5 7 35

Total 90

Higher Secondary - First year

Question Paper Pattern (For Subjects without Practical Exam)

www.surabooks.com

For Order : [email protected] Ph: 9600175757 / 8124201001



www.Padasalai.Net

www.surab

ooks

.com

11thSTD.

Time : 2½ Hours Mathematics Marks : 90

Model Question PaPer

Part - I

All questions are compulsory. (20 × 1 = 20)Choose the correct answer.1. Number of elements in a matrix of order 2 × 3 is

(a) 5 (b) 2 (c) 3 (d) 62. If A is a square matrix of order 4 then |KA| is

(a) K|A| (b) K2|A| (c) K3|A| (d) K4|A|

3. If “G” is centroid of the triangle ABC and ‘O’ is any other point thenOA OB OC→ → →

+ + is equal to

(a) O→

(b) OG→

(c) 3 OG→

(d) 4 OG→

4. If a i j→ → →

= −2 and b j k→ → →

= − then the magnitude of a b→ →

− is

(a) 1 (b) 9 (c) 3 (d) 3

5. A polygon has 44 diagonals, then the number of its sides is(a) 11 (b) 7 (c) 8 (d) 12

6. If 3 71 2 2

101

xx x x x

+−( ) −( )

=−

−−

A then A is

(a) 13 (b) –13 (c) –10 (d) 107. The A.M., G.M., H.M., between two positive numbers a and b are equal then

(a) a = b (b) ab = 1 (c) a > b (d) a < b

8. If an = n2 3 –n then the third term is

(a) 19

(b) 1 (c) 13

(d) 3

9. If the pair of straight lines given by ax2 + 2hxy + by2 = 0 are perpendicular, then

(a) ab = 0 (b) a + b = 0 (c) a – b = 0 (d) a = 0

10. The radius of the circle x2 + y2 – 2x + 4y – 4 = 0 is

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

[2]

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com

+1 Std - Mathematics Sura’s Model Question PaPers 3

11. If cos θ = 0 then θ is(a) nπ (b) (2n+1) π

2 (c) –π (d) –nπ

12. If the terminal side is collinear with the initial side in the opposite direction, then the angle included is(a) 0 ° (b) 90° (c) 180° (d) 270°

13. The range of the function logex is

(a) (0, ∞) (b) (–∞, ∞) (c) (–∞, 0) (d) [0, ∞ )14. The value of [3.5] is

(a) 2 (b) 3 (c) 4 (d) 5

15. ddx xlog( ) is

(a) 12 x

(b) 12x

(c) 1

x x (d) 1

2x x

16. limx

x

x→∞+

1 3 is

(a) e (b) ex (c) e3 (d) ∞17. log x dx =∫

(a) 1xc+ (b)

log xc

( )+

2

2 (c) x log x + x + c (d) x log x – x + c

18. e x d xx2 3sin ( )∫ is

(a) e x x cx2

132 3 3 3sin cos−( ) +(2sin 3x – 3 cos 3x) + c (b) e x x c

x2

132 3 3 3sin cos−( ) + (3sin 2x – 2 cos 2x) + c

(c) e x x cx2

132 3 3 3sin cos−( ) + (2sin 3x + 3 cos 3x)+c (d) e x x c

x2

132 3 3 3sin cos−( ) + (3cos 3x + 2 sin 3x) + c

19. If two events A and B are independent then P(A/B)= ------------

(a) P(A) (b) P(A∩B) (c) P(A) = P(B) (d) P AP B

( )( )

20. X speaks truth in 95 percent of cases and Y in 80 percent of cases. The percentage of cases they likely to contradict each other in stating same fact is(a) 14% (b) 86% (c) 23% (d) 85.5%

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com

4 +1 Std - Mathematics Sura’s Model Question PaPers

Part - II

Answer any Seven questions. (7 × 2 = 14)

Question No.30 is compulsory.

21. Prove that a ba a

a aa b a b

a b a b

b b1 1

2 2

212

22

1 1 2 2

1 1 2 2

12

22

=+

+

+

+

22. If ABC and A′ B′ C′ are two triangles and G, G′ be their corresponding centroids, prove

that AA BB CC GG′ + ′ + ′ = ′→ → → →

3

23. If 10Pr = 5040, find the value of r.

24. A point moves so that it is always at a distance of 6 units from the point (1, –4). Find its locus.

25. Simplify : Cos (–870°)

26. If f, g : R→R, defined by f(x)= x + 1 and g(x) = x2 then find (fog) (3)

27. Find d ydx

2

2 if y = x3 – 6x2 + 7x + 6

28. Evaluate : cos2 x dx∫

29. Three coins are tossed once. Find the probability of getting atleast two heads.

30. Show that ee

2

211

111

131

151

1 121

141

−+

=+ +

+ +

....................

.......................

Part - III



31. Prove that the sum of the vectors directed from the vertices to the mid-point opposite sides of a triangle is zero.

32. Find the co- efficient of x5 in the expansion of xx

+

13

2

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com


33. Find 5 geometric means between 576 and 9.

34. The slope of one of the straight lines ax2 +2hxy + by2 = 0 is twice that of the other, show that 8h2 = 9ab.

35. Show that : Sin20° Sin40° Sin 80° = 38

36. Let f : R→R be defined by f (x) = 3x + 2 find f –1 and show that fof –1 = f –1of = 1.

37. Evaluate : Limx

x xx→ −

+ − −0 1

1 1sin

38. Integrate : 3 4 3 7x x dx+( ) +∫

39. Two cards are drawn from a pack of 52 cards in succession. Find the probability that both are kings when,

(i) The first drawn card is replaced

(ii) The card is not replaced.

40. Find K so that A2 = KA – 2I where A = 3 24 2

−−

Part - IV

Answer all the question. (7 × 5 = 35)

41. Using factor theorem prove that

(b + c)2 a2 a2

b2 (c + a)2 b2 = 2abc (a + b + c)3

c2 c2 (a + b)2

(OR)

Examine whether the vectors i j k i j k i k→ → → → → → → →

+ + − − +3 2 7 5, and are coplanar.

42. If A + B = 45° , show that (1 + tanA) (1 + tanB) = 2 and hence deduce the value of tan 22 12

°

(OR)

State and prove Napier’s formulae.

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com


43. Prove by Mathematical Induction

12 + 22 + 32 +................................+ n2 = n n n+( ) +( )1 2 16

,for all n∈N

(OR)

If a, b, c are in H.P. Prove that b ab a

b cb c

+−

++−

= 2

44. Find the equation of the circle passing through the points (1,1), (2,–1) and (3,2).

(OR) Find the co-ordinates of orthocentre of the triangle formed by the straight lines

x – y – 5 = 0, 2x – y – 8 = 0 and 3x – y – 9 = 0

45. If y = cos (sinx), Prove that d ydx

x dydx

y x2

22 0+ + =tan cos

(OR)

For ∆ xa < 1 and for any rational index n, prove that lim

x a

n nnx a

x ana a

→

−−−

= ≠( )1 0

46. Evaluate the definite integral as limit of sum 12 2 5x dx+( )∫

(OR)

Evaluate 3 1

2 32

x

x xdx+

+ +∫

47. If x is real, prove that the range of f xx xx x

( ) =− ++ +

2

22 42 4

is between 13

3,

(OR)

In a bolt factory machines A1, A2, A3 manufacture respectively 25%, 35% and 40% of the total output of these 5, 4, 2 percent are defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine A2?

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com

11thSTD.

Time : 2.30 Hours Mathematics Marks : 90

sura’s Model Question PaPer - 1Based on Scheme of Examination as per G.O. (2D). No. 50 dated : 09-08-2017

Part - I

All questions are compulsory. (20 × 1 = 20)Choose the correct answer.

1. If A B=

=−

− −−

a b cx y zp q r

q b yp a xr c z

, then

(a) |A| = |B| (b) |A| = –|B|

(c) |A| = 2|B| (d) A is invertible

2. The determinant ∆ =+

++

a x ab acab b x bcac bc c x

2

2

2

is divisible by

(a) x2 (b) x3 (c) 0 (d) none of these

3. The position vector of the mid-point of the vector joining the points (2, 3, 4) and (4, 1, –2) is

(a) 3 2i j k→

−→

+→

(b) 2 3 4i j k→

+→

+→

(c) 6 4 2i j k→

+→

+→

(d) 3 2i j k→

+→

+→

4. The following diagram represents vectors (a) co-terminus (b) co-initial

0

(c) collinear (d) none of these

5. If the co-efficients of rth and (r + 1)th terms is the expansion of (3 + 7x)29 are equal, their r =(a) 29 (b) 21 (c) 3 (d) 7

6. The number of five-digit telephone numbers having atleast one of their digits repeated is

(a) 90,000 (b) 1,00,000 (c) 30,240 (d) 69,760

[7]

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com


7. If b + c , c + a , a + b are in H.P., then ab c

bc a

cc a+ + +

, , are in

(a) A.P (b) G.P (c) H.P (d) None

8. If ( 1 + x2 ) 2 (1 + x ) n = a0 + a1 x + a2 x2 + ...... and if a0 , a1 , a2 are in A.P. then n =

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

9. The lines x – 2y – 6 = 0, 3x + y – 4 = 0 and λx + 4y + λ2 = 0 are concurrent of

(a) λ = 2, 4 (b) λ = –3, 1 (c) λ = 4, 1 (d) λ = –4, 2

10. The centres of the circles x2 + y2 = 1, x2 + y2 + 4x + 8y – 1 = 0 and x2 + y2 – 6x – 12y + 1 = 0 are

(a) equal (b) lies on X-axis (c) Collinear (d) lies on Y-axis

11. If tan α = 56

and tanβ = 111

then

(a) α + β = π6

(b) α + β = π4

(c) α + β = π3

d) None of these

12. Which is greater ? sin 1980° or cos 1980°

(a) sin 1980 (b) cos 1980 (c) equal d) 0°

13. Which of the following function is an odd function ?

(a) f(x) = cos x (b) 2

2 xy −= (c) 4

2x xy −= (d) sin x

14. The solution of 5x – 1 < 15 is

(a) x < 3.2 (b) x = 3.2 (c) x > 3.2 (d) none of these

15. If x2 + y2 = 2 and y11 = Ay3 then A =

(a) 0 (b) 2 (c) –2 (d) None of these

16. The function y = sin (log x) + cos (log x) satisfies the equation.

a) x2 y11 + xy1 + 2y = 0 b) x2 y11 + y1 = 0 c) y1 + 2x = 0 d) y111= 0.

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com


17. If dxe e

ex xx

2 21 2

+=−

−∫ A tan then A is

(a) 2 (b) 2 (c) 12

(d) 12

18. The anti - derivative of every odd function is a ________ function

(a) odd (b) even

(c) neither odd nor even (d) none

19. For two events A and B if P(A) = P(A/B) = 14

and P(B/A) = 12

then A and B are

(a) mutually exclusive (b) dependent(c) independent (d) exhaustive

20. If P(A ∪ B) = P(A ∩ B) then the relation between P(A) and P(B) is

(a) P(A) = P(B) (b) P(A) < P(B) (c) P(A) = 0 (d) P(A) = 1

Part - II



21. What is Triangular matrix?

22. If x yz w

=

4 31 5

, then find the values of x, y.

23. What is negative vector?

24. A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?

25. Evaluate 8P3.

26. If the point P(5t − 4, t + 1) lies on the line 7x − 4y + 1 = 0, find the co-ordinates of P.

27. What is locus?

28. 34π into degrees.

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com


29. Find A × B and B × A if A = {1, 2}, B = {a, b}.

30. An experiment has the four possible mutually exclusive outcomes A, B, C and D. Check

whether the following assignments of probability are permissible. P(A) = 0.37.

Part - III



31. If A = 2 14 2

,−

B =

4 21 4

,−

C =

− −

2 31 2 find each of the following –2A + (B + C)

32. Solve for xx

xif

57

1 21 1

0+−

−= .

33. Find the magnitude and direction cosines of 2 7i j k→

−→

+→

.

34. A person wants to buy one fountain pen, one ball pen and one pencil from a stationery shop. If there are 10 fountain pen varieties, 12 ball pen varieties and 5 pencil varieties, in how many ways can he select these articles?

35. In how many ways can an examine answer a set of 5 true / false type questions?

36. Write the first five terms of the sequence given by : a1 = a2 = 2, an = a n – 1 – 1 , n > 2.

37. Determine the equation of the straight line passing through (–1, 2) and having slope 27

.

38. Identify the name of the function, the domain, Co-domain, independent variable, dependent variable and range if f : R → R defined by y = f (x) = x2.

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com


39. If A and B are two independent events such that P(A) = 0.5 and P(A ∪ B) = 0.8. Find P(B).

40. The difference between two positive numbers is 18 and 4 times their G.M is equal to 5 times their H.M. Find the numbers.

Part - IV

Answer all the question. (7 × 5 = 35)

41. If A = 1 84 3

, B =

1 37 4

, C =

−−

4 63 5

Prove that (i) AB ≠ BA (ii) A(B + C) = AB + AC

(OR)

Solve : X + 2Y = 4 68 10−

, X – Y =

1 02 2− −

42. Show that the points with position vectors a b c→

−→

+→

2 3 , −→

+→

+→

2 3 2a b c and −→

+→

8 13a b

are collinear.

(OR)

How many three digit odd numbers can be formed by using the digits 4, 5, 6, 7, 8, 9 if

(i) the repetition of digits is not allowed? (ii) the repetition of digits is allowed?

43. Find the sum 101th terms to 200th terms of the series 1

21n

n=

∞

∑

(OR)

Resolve into partial fractions 3 7

3 22

xx x

+− +

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com


44. Find the locus of the point which is equidistant from (− 1, 1) and (4, − 2).

(OR)

Write the first 5 terms of each of the following sequences.

(i) an = (–1)n–1 5n+1 (ii) an = n n2 5

4

+( )

45. Find the values of

(i) cos (135°) (ii) sin (240°) (iii) sec (225°) (iv) cos(–150°) (v) cot (315°)

(OR)

If x is real, prove that xx x2 5 9− +

lies between −111 and 1.

46. Evaluate the left and right limits of f (x) =x

x

3 273

−−

at x = 3. Does the limit of f (x) as x → 3

exist ? Justify your answer.(OR)

13 + 23 + 33 + … + n3 = n n2 2( +1)

4.

47. Prove that (1 + cot A + tan A ) (sin A – cos A) = secA

cosec A

cosec A

sec A2 2−

(OR)

A die is thrown twice. Let A be the event. “First die shows 4’ and B be the event, ‘second die shows 4’. Find P(A ∪ B).

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com

[13]

11thSTD.



Part - I


1. Let A and B the 3 × 3 matrices. Then AB = 0 implies

(a) A = 0 or B = 0 (b) |A| = 0 and |B| = 0

(c) either |A| = 0 or |B| = 0 (d) A = 0 and B = 0

2. If a, b, c are all different from zero, and ∆ =+

++

= + +1 1 1

1 1 11 1 1

0 1 1 1a

bc

a b c, then is

(a) abc (b) 1 1 1a b c

⋅ ⋅ (c) –a –b –c (d) –1

3. The scalars in the following is ____________

(a) work done (b) force

(c) velocity (d) work done and distance

4. The vector in the direction of −→

+→

+→

i j k2 2 is

(a) −→

−→

+→

i j k2 2 (b) −→

+→

−→

i j k2 2

(c) −→

+→

+→

2 4 4i j k (d) +→

+→

−→

2 4 4i j k

5. The number of squares which we can form on a chessboard is

(a) 64 (b) 160 (c) 224 (d) 204

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com


6. If m + n P2 = 90 and m – n P2 = 30 then (m, n) is

(a) (7, 3) (b) (16, 8) (c) (9, 2) (d) (8, 2)

7. The sum to n term of the series 12

34

78

1516

+ + + + …… is

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

8. The 10th term of the series given as t n n nrr

n= + +

=∑ 1

61 2

1( ) ( ) for all n ≥ 1 is

(a) 1320 (b) 121 (c) 220 (d) 120

9. The points A(2a, 4a), B(2a, 6a) and C(2a + 3a , 5a) are the vertices of a _________ triangle.

(a) isosceles acute angle (b) equilateral

(c) isosceles obtuse angle (d) right angle

10. The equation ax2 + by2 + cx + ay = 0 represents a pair of straight lines if

(a) a + b = 0 (b) b + c = 0 (c) a + c = 0 (d) ab = 0.

11. The general solution of the equation tan2 x = cos2x –1 is

(a) nπ3

(b) nπ (c) nπ + π4

(d) nπ – π4

, n∈Z

12. The smallest value of θ which satisfies the equation tan θ = – cot 500° is

(a) 10° (b) 40 (c) 50 (d) 100

13. If f:R→R is defined by f(x) = x2+1, the value of f –1(17) is

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

14. Which of the following function is an even function ?

(a) f(x) = x2 + 7 (b) f(x) = x + 2 (c) f(x) = x7 + 2x5 (d) f(x) = 5+x

15. The function y = ( x 2 + 1)50 should be differentiated ______ times to result in a polynomial of the 30th degree.

(a) 50 (b) 100 (c) 70 (d) 30

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com


16. If x = log t and y = t2 – 1 then y11 (1) at t = 1 is.

(a) 2 (b) 4 (c) 3 (d) None of these

17. e dxx2∫ is

(a) 2 2ex

(b) ex2 (c) e dx

x2 (d) 1

22ex

18. e dxe

x

x1 2+∫ is

(a) log ( )1 2+ e x (b) tan− ( )1 ex

(c) tan− ( )1 2e x (d) tan− ( ) +1 2e cx

19. If A and B are two mutually exclusive even then

(a) P(A) = P(B) (b) P(A) ≠ P(B)

(c) P(A) < P(B) (d) P(A ∩ B) = 0

20. A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is

(a) 125

(b) 225 (c)

325

(d) 2425

Part - II

Answer any Seven questions.

Question No.30 is Compulsory. (7 × 2 = 14)

21. What is Negative of matrices.

22. Find the value of the determinant 2 6 45 15 10

1 3 2− − − without usual expansion.

23. Write any two types of vectors name.

24. Find the magnitude and direction cosines of 2 7i j k→

−→

+→

.

25. In a class there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent a competition. In how many ways can the teacher make this selection?

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com


26. What is a sequence.

27. Find the indicated terms of the following sequences whose nth term is an = 2 + 1n

; a5, a7.

28. Determine the equation of the straight line passing through (–1, 2) and having slope 27

.

29. Find the quadrants in which the terminal sides of the following angles be –300°.

30. Find A × B and B × A if A = {1, 2}, B = {a, b}.

Part - III



31. Find the matrix C if A = 3 72 5

, B =

−−

3 24 1 and 5C + 2B = A.

32. Find the components along the co-ordinates of the position vector of p(–4, 3).

33. Find the unit vectors parallel to the sum of 3 5 8i j k→

−→

+→

and −→

−→

2 2j k ..

34. How many 4-digit numbers are there?

35. Prove that the sum of n arithmetic means between two numbers is n times the single A.M. between them.

36. IA point moves so that it is always at a distance of 6 units from the point (1, − 4). Find its locus.

37. Simplify: cot ( ) sin ( ) sec ( )

tan ( ) sec ( ) cos ( )90 180 360

180 90− + −

+ − +θ θ θ

θ θ θ.

38. Solve : x2 ≤ 9

39. Integrate : 1

2sin x .

40. The probability of an event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive events, then find the probability of neither A nor B occurring.

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com


Part - IV

Answer all the questions. (7 × 5 = 35)

41. If A = 3 24 2

−−

find k so that A2 =kA – 2I.

(OR) In a triangle ABC, if D and E are the mid-points of sides AB and AC respectively, show

that BE DC BC→

+→

=→3

2.

42. x x

x x

2

2

+ +1+ 2 +1

(OR)

If the A.M. between two numbers is 1, prove that their H.M is the square of their G.M.

43. Find ‘a’ so that the straight lines x − 6y + a = 0, 2x + 3y + 4 = 0 and x + 4y + 1 = 0 may be concurrent.

(OR)

If a cosA = b cosB then show that the triangle is either an isosceles triangle or right angled triangle?

44. Draw the graph of the function f (x) = x2.

(OR)

Let f be defined by f (x)

x x

x x x

= 2, if 0 1

2 3 + 32

, if 1 < 2

2

2

≤ ≤

− ≤

45. An integer is chosen at random from the first fifty positive integers. What is the probability that the integer chosen is a prime or multiple of 4?

(OR)

(i) Express the following as functions of A sec A −

32π

(ii) Integrate : 1

2 + 7 + 132x x

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com


46. The probability that a girl will get an admission in IIT is 0.16, the probability that she will get an admission in Government Medical College is 0.24, and the probability that she will get both is 0.11. Find the probability that (i) She will get atleast one of the two seats (ii) She will get only one of the two seats.

(OR)

Evaluate :

(i) limx

xx→

−−1

3 11

(ii) lim ( )x

xx→

+ −0

41 1

47. Given A = 1 2 31 3 4

2 0 1−

−

B = 2 0 12 1 21 1 1

− −−

C = 1 1 12 1 21 1 1

−−

−

verify the following results :

(i) AB π BA (ii) (AB) C = A (BC)

(OR)

If the 5th and 12th terms of a H.P are 12 and 5 respectively, find the 15th term.

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com

11thSTD.



Part - I


1. If x x xx x xx x x

ax bx cx d

2

2

2

3 2

5 3 2 5 33 4 6 1 9

7 6 9 14 6 21

− + −+ + +− + −

= + + + , then

(a) a = b = c = 1 (b) a = b = c = 0 (c) a = 2, b = 3, c = 1 (d) none of these

2. If a, b and c are non-zero real numbers, then ∆ =+++

=b c bc b cc a ca c aa b ab a b

2 2

2 2

2 2

(a) abc (b) a2 b2 c2 (c) ab + bc + ca (d) 0

3. The vectors among the following measures will be____________

(a) 10 kg (b) 40º (c) 40 watt (d) 20 m/sec2

4. Represent the diagram in vector form 60°

NP

W

S

E35 km

0(a) 35 km 60° north of east (b) 60 km 35° north of east

(c) 35 km 60° east of north (d) none of these

5. The number of ways in which 7 distinct toys can be distributed among 3 children is

(a) 37 (b) 73 (c) 7C3 (d) 7P3

6. If a polygon has 54 diagonals, then the number of its sides is

(a) 12 (b) 11 (c) 10 (d) 9

[19]

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com


7. The number of divisions of 1029, 1547 and 122 are in

(a) A.P (b) G.P (c) H.P (d) None of these

8. tan 70° , tan 50° , + tan 20° and tan 20° are in

(a) A.P (b) G.P (c) H.P (d) None of these

9. The circles x2 + y2 + 2x – 2y + 1 = 0 and x2 + y2 – 2x – 2y + 1 = 0.

(a) touch each other externally (b) touch each other internally

(c) intersect on the Y-axis (d) intersect on the X-axis

10. The equation 3x2 + 2hxy + 3y2 = 0 represents a pair of straight lines passing through the origin. The two lines are

(a) real and different if h2 > 3 (b) real and different if h2 > 9

(c) real and coincident if h2 = 3 (d) imaginary if h2 < 9.

11. If 21

sincos sin

αα α+ +

= y then 11

− ++

cos sinsinα α

α=

(a) 1y

(b) y (c) 1 – y (d) y.

12. If A lies in the II quadrant and 3 tanA+ 4 = 0, then 2 cotA – 5 cosA + sinA =

(a) −5310 (b)

2310

(c) 3710

(d) 7

10

13. The domain of the function f(x) 1 6− + −x x is (a) [1, ∞) (b) (–∞, 6) (c) [1,6] (d) none of these

14. Let f: R→R defined by f(x) = 6x+11, then fof (3) is

(a) 77 (b) 36 (c) 108 (d) 185

15. The value of yn (1) if x3 – 2x2y2 + 5x + y – 5 = 0 when y (1) = 1 is equal to

(a) 227

(b) −7 2128

(c) 8 (d) −8 2227

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com


16. The derivative of an even derivable function is always an ______ function.

(a) odd (b) even (c) constant (d) linear

17. 3 2cos sinx x−( )∫ dx is ________ + c

(a) 3 sin x – 2 cos x (b) 3 sin x + 2 cos x

(c) – 3 sin x – 2 cos x (d) – 3 sin x + 2 cos x

18. If the velocity of the moving particle is constant, its path is a

(a) straight line (b) parabola (c) circle (d) curve

19. If A and B are two events, the probability that exactly one of them occurs is given by

(a) P(A) + P(B) – P(A ∪ B) (b) P(A ∩ B ) + P( A ∩ B)

(c) P( A B∪ ) (d) P(A’ ∩ B’)

20. One card is drawn at randon from a well shuffled pack of 52 cards. Let A denote the event “the card drawn is a king or a queen” and B be the event “the card drawn in a queen or a jack”. Then A and B are

(a) independent (b) not independent

(c) mutually exclusive (d) equally likely

Part - II

Answer any Seven questions.

Question No.30 is Compulsory. (7 × 2 = 14)

21. What is magnitude of a vector?

22. Find a unit vector in the direction of i j→

+→

3 .

23. In a class there are 15 boys and 20 girls. The teacher wants to select a boy and a girl to represent the class in a function. In how many ways can the teacher make this selection?

24. Find the single A.M. between –5 and –3.

25. Determine the equation of this straight line whose slope is 2 and Y - intercept is 7.

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com


26. Find the distance between the parallel lines 2x + 3y – 6 = 0 and 2x + 3y + 7 = 0.

27. Simplify - tan 735°

28. What is linear function?

29. For the functions f, g as defined in (1) define - fg(x)

30. Differentiate the following functions with respect to - x. ex cosx.

Part - III



32. Find the values of x, y, z if x x yx z y w a

32 3

0 73 2

−+ −

=

−

.

33. Find the unit vectors parallel to the vector −→

+→

3 4i j .

34. Twelve students compete in a race. In how many ways first three prizes be given?

35. Write the first 5 terms of each of the following sequences. - an = –11 n + 10.

36. Determine the equation of the line with slope 3 and y-intercept 4.

37. If A, B, C, D are angles of a cyclic quadrilateral, prove that cos A + cos B + cos C + cos D = 0

38. Prove the following: sin4 A– cos4 A = 1 – 2 cos2 A.

39. Show that the function y = x2 is not one-to-one.

40. 1+sin 2x dx∫

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com


Part - IV

Answer all the questions. (7 × 5 = 35)

41. Find the value of x y [ ] .2 31 23 0 3

0xx

−

=

(OR)

Prove that 111

a ab bc c

= (a - b) (b - c) (c - a) (a+b+c)

3

3

3

.

42. Prove using vectors, the mid-points of two opposite sides of a quadrilateral and the mid-points of the diagonal are the vertices of a parallelogram.

(OR)

How many different numbers of six digits can be formed from the digits 2, 3, 0, 7, 9, 5 when repetition of digits is not allowed?

43. Find the nth partial sum of the series 1

31n

n=

∞

∑

(OR)

Find the locus of the point which is equidistant from (− 1, 1) and (4, − 2).

44. Prove that tan sectan sec

sincos

θ θθ θ

θθ

+ −− +

= +11

1

(OR)

A father ‛d’ has three sons a,b,c. By assuming sons as a set A and father as a singleton set B, show that

(i) the relation ‘is a son of’ is a function from A→B and (ii) the relation ‘is a father of’ from B→A is not a function.

www.surabooks.com




www.Padasalai.Net

www.surab

ooks

.com


45. If f (x) = x3 – 8x + 10, find f ′(x) and hence find f ′(2) and f ′(10)

(OR)

Prove that sec2 A + cosec2 A = sec2 A • cosce2 A.

46 A factory has two Machines-I and II. Machine-I produces 25% of items and Machine-II produces 75% of the items of the total output. Further 3% of the items produced by Machine-I are defective whereas 4% produced by Machine-II are defective. If an item is drawn at random what is the probability that it is defective?

(OR)

How many arrangements can be made with the letters of the word ‘MATHEMATICS’?

47 Compute limsinsin

, .x

xx→

≠0

0βα

α

(OR)

For ∆

<x

a1 and for any rational index, n, lim ( )

x a

n nnx a

x ana a

→−−

−= ≠1 0

www.surabooks.com




www.Padasalai.Net

Documents

- WordPress.com · · 2017-10-24 Model Question Papers. Mathematics. Time : 2½ hours. Written Exam Marks : 90 Marks. Based on Scheme of Examination as per G.O. (2D). No. 50 dated