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2

1. Symbol for existantial quantifier is ____2. p∨ (q∧ r) = (p∨ q) ∧ (p∨ r) is an example

for ____ law.3. The symbol for universal quantifier is

____4. The compound statement formed by

using the connective "if and only if" iscalled ____

5. ∼ (p ⇔ q) =6. The law of ∼ (p∨ q) = (∼ p) ∧ (∼ q) is ____ 7. The law of p∨ p = p is ____8. "For all real values of x, x2 ≥0" write by

using quantifier ____9. Counter example of "all primes are odd"

is ____10. The true value of 4+3 = 7 or 5×4 = 9 is

____11. The true value of 5×4 = 20 ⇒ 5+4 = 8 is

____12. A––p°––q°––B In this series the current

flows A to B case ____13. The true value of 4+3 = 7 and 5×3 = 10 is

____14. The inverse of the statement ∼ p ⇒ ∼ q is

____15. The law of p∧ t = p is ____16. Always true statement is called ____17. An implication and its contra positive are

____ statements.18. The quantifier "for some" or "there exists

atleast one" is called the ____19. p∧∼ p is the example for ____20. In an implication p ⇒ q then p is called

____21. The inverse of the statement "All natural

numbers are even numbers" is ____22. The disjunction of the "5 is odd ; 5 is

positive" is ____23. p is a statement then the value of ∼ (∼ p) is

____24. The compound statement which uses the

connective "AND" is called ____25. (∼ p) ⇒ (∼ q) is in which statements contra

positive ____26. "In a triangle ABC, AB > AC then ∠ C >

∠ B" the statement inverse is ____27. The true value of "10+15 = 20 and 15–10

= 5" is ____28.

The current flows from A to B is ____

case.29. The symbolic form of x = –3 if and only

if x+3 = 0 is ____30. "All the students scored well in their unit

test" The above statement is an exampleof ____ quantifier.

31. The statement obtained by modifying byusing the word "not" of a given statementis called ____

32. p∧ q true value is T then p, q true valuesare ____

33. The algebraic law of p∨ (∼ p) = t is ____34. Symbolic form of "p or not p" is ____

1. A ⊆ B and B ⊆ A then ______2. A ⊂ B and n(A) = 5, n(B) = 6 then

n(A∪ B) = ______3. A ⊂ B then A ∪ B = ______4. A, B are disjoint sets then A ∩ B =

______5. A = {1, 2}, B = {4, 5}, C = {6, 7}. Then

the number of elements in A×(B∩C) is______

6. n(A) = 7, n(B) = 5 then the number ofmaximum possible elements in A∩B is______

7. A = {1, 2, 3}, B = {3, 6, 7} then n(A∩B)= ______

8. A, B are disjoint sets then A – B = ______9. A⊂ B then A – B = ______10. (A∪ B)1 = A1∩ B1 is ______ law11. (A∪ B)∪ C = A∪ (B∪ C) is ______ law12. A, B are disjoint. n(A) = 4, n(A∪ B) = 10

then n(B) = ______13. n(A) = 4, n(B) = 3, n(A∪ B) = 5. Then

n(A∩B) = ______14. A, B are two sets. A⊂ B. Then A∩B =

______15. B = {1, 8, 27, 64, 125} then write the set

- builder form ______16. A is a set then A ∪ A1 = ______

17. Power set of µ is ______18. A⊂ B, n(A) = 12, n(B) = 20. Then n

(B–A) is ______19. A∪ A1 = µ, A∩A1 = φ are the algebraic

law of ______20. The elements in the set is 4. Then the total

number of subsets in that set is ______

21. A∩B1 = ______22. A∆B = ______23. A, B are two sets. Then x∉ (A∪ B) =

______24. A is a set, then the value of (A1)1 is

______25. A is a set A∪ A = A, A∩A = A then the

algebraic law is ______26. The algebraic law of A∩(B∪ C) = (A∩B)

∪ (A∩C) is ______27. The algebraic law of A ∪ φ = A, A ∩µ =

Α is ______28. The sets which are having same cardinal

number are called ______29. The set of prime numbers in 13 and 17 is

______30. The law of A ⊂ B, B ⊂ C then A ⊂ C is

______31. In a group of 15 students 10 students are

brilliant in mathematics and 8 studentsare in social. Then the number of studentswho are brilliant in both subjects are______

32. A ∩ B = φ then B ∩ A1 = ______33. n(µ) = 10, n(A) = 6 then n(A1) = ______34. n(A) = 50, n(B) = 20 and n(A∩B) = 10

then n(A∆B) = ______

1. 'f' is bijection means it is ____2. The range of the function f(x) = 3 is ____3. A function f : A→B is said to be ____

function, if for all y∈ B their exists x∈ A,such that f(x) = y

4. If I is an identity function then f–1(4) =____

5. f(x) = 2x–3, then zero of the function is____

6. If f = {(1, 2), (2, 3), (3, 4), (4, 1)}. Thenfof = ____

7. If f(x) = 2x+3, g(x) = x–1 then gof(3) =____

8. If f = {(x, a), (y, b), (z, c)} and f–1 = g theng–1 = ____

9.

From the above figuregof = ____

10. f : A→B is said to be real valued functionif ____

11. f = {(1, 2), (2, 2), (3, 2)} then the range off is ____

12. If the function f : A→B is ____ function,then the inverse f–1 : B→A is again afunction.

13. The function f : A→R (A⊆ R) isintersecting x-axis at (a, 0). Then the zeroof the function is ____

14. The mapping f : A→{5} is defined by ∀x∈ A, f(x) = 5. Then it is ____

15.

From the above figure the zero value ofthe given function is ____

16. f : A→B is a bijective and n(A) = 4 thenn(B) = ____

17. f : A→B to be a function and if f(x1) =f(x2) ⇒ x1 = x2 then f is ____

18. f = {(x, 2008) / x∈ N} then f is ____function

19. If y = f(x) = 3x–1 then f–1(y) = ____20. f = {(4, 5), (5, 6), (7, 8)} then f–1(8) =

____21. f(x) = x then f is ____ function.22. If f(A) = B then f: A→B is a/an ____

function.23. Let f : R→R be defined by f(x) = 3x+2,

then the element of the domain of f whichhas 11 as image is ____

24. Range of a constant function is a ____ set25. f : A→B is bijective then f–1 : B→A is

____26. Let f : N→N be defined by f(x) = 12/x–3,

x≠3 then the Domain of this function is____

27. f : N→N is constant function defined byf(x) = 15 then f(10) = ____

28. The domains of f(x) and g(x) are equal.Then the functions are called ____

29. The function f : A→B is a ____ functionif there is an element C∈ B such that f(x)= C ∀ x∈ A.

30. f : A→B is a function, if A⊆ R, B⊆ R thenf is called ____

31. Let f : x→ 2x + 3, Domain of f = {x/0 ≤x ≤ 3} then the range of f = ____

32. The set builder form of R = {(1, 3), (2, 4),(3, 5)} is ____

33. If f(x) = x+1 / x–1 then f(1/2) = ____

MathematicsFUNCTIONSSETS

The law of p∧∧ t = p is?

STATEMENTS

FUNCTIONS (MAPPINGS)

SETS

Answers:1. ∃ ; 2. Distributive ; 3. ∀ ; 4. Bi-implication ; 5. p⇔(∼ q) or (∼ p)⇔q ; 6. DeMorgan's law ; 7. Idempotent ; 8. ∃ x∈ R,x≥0 ; 9. 2 ; 10. T (True) ; 11. F (False) ; 12.p∧ q ; 13. False ; 14. p⇒ q ; 15. Identity law;16. Tautology; 17. Equivalent; 18.Existential quantifier; 19. Contradiction;20. Hypothesis ; 21. All natural numbersare odd numbers; 22. (5 is odd) ∨ (5 ispositive) ; 23. p ; 24. Conjunction ; 25.q⇒ p ; 26. In a triangle ABC, AB < AC then∠ C < ∠ B ; 27. False ; 28. p∨ q ; 29. x = –3⇔ x+3 = 0 ; 30. Universal quantifier ; 31.Negation statement ; 32. True ; 33.Complement law ; 34. p∨ (∼ p)

Answers:1. A= B ; 2. 6 ; 3. B ; 4. φ ; 5. 0 ; 6. 5 ; 7. 1; 8. A ; 9. B ; 10. De Morgan's ; 11.Associative ; 12. 6 ; 13. 2 ; 14. A ; 15. B ={x/x = n3, n ∈ N and n ≤ 5}; 16. µ ; 17. φ ;18. 8 ; 19. Complement ; 20. 24 or 32 ; 21.A–B ; 22. (A–B) ∪ (B–A) ; 23. x ∉ A ∩ x∉ B ; 24. A ; 25. Idempotent ; 26.Distributive ; 27. Identity ; 28. Equivalencerelation ; 29. Null Set (φ) ; 30. Transitive ;31. 3 ; 32. B ; 33. 4 ; 34. 50

K.UmaMaheshwar ReddySr. Teacher, A.P.R.S.

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34. Every identity function is ____ function.35. f = {(1, 2), (2, 3), (3, 4)} ; g = {(2, 5), (3,

6), (4, 7)} then fog = ____36. The graph of a relation is a function if no

line parallel to y-axis cut the graph ____37. f(x) = 2x, g(x) = x–1, h(x) = x+1 then

[ho(gof)] (2) = ____38. f = {(x, 3) / x∈ N} then f is ____ function.39. Let I : B→B then I(x) = x then the

function is called ____40. If f : x→ log2

x then f (16) = ____41. y = sinx function range is ____42. f : A→B is bijection, n(A) = 4. Then n(B)

= ____43. f = {(1, 3), (2, 5)}, g = {(1, 6), (2, 10)}

then f + g = ____44. If f–1(y) = y–3 then f(x) = ____

1. Inequation having solution "–3≤x≤4" is______

2. Remainder where ax + b divides f(x) is______

3. If the sum of the co-efficients of apolynomial is zero, then ______ is afactor to it.

4. Sum of the roots of 6x2–5 = 0 is ______5. The discriminant of the quadratic

equation 2x2–7x+3 = 0 is ______6. The rationalising factor of a1/3+b1/3 is

______7. The graph of y = mx2 (m > 0) is

symmetric about ______ axis.8. Sum of the binominal co - efficients of

the expansion of (x/y + y/x)4 is ______9. If nC8 = nC7 then n = ______10. If x + 1 is a factor of ax2+bx+c then the

condition is ______11. The solution of x2–x (α+β) +αβ>0

______ between α and β12. If there is no common point for the graph

y = x2 and y = 4x – 5 then the equation______ does not have real roots.

13. If the number of terms in a binominalexpansion is 4 the exponent of thebinominal is ______

14. If 2 is a root of the equation x2–px+q = 0and p2 = 4q then the other root is ______

15. If x2–5x+4 < 0 then x lies between______

16. (a1/3+b1/3) (a2/3–a1/3b1/3+b2/3). = ______17. If f(b/a)=0 then the factor of f(x) is

______18. The number of terms of the expansion

(1+x)n+1 is 6 then n = ______19. If the roots of the equation px2+qx+r = 0

are equal then ______20. If x2–x–2<0, then the value of x is

______21. The last term in the expansion of (x+2/x)5

is ______22. If (x–y) is a factor of xn–yn , then 'n' is

______23. Middle term in the expansion of (x/y +

y/x)8 is ______24. The graph of x = my2 (m>0) lies in

______ quadrants.

25. If .Then x = ______

26. The nature of the roots of 4x2–5x+4 = 0 is______

27. The product of the roots of √3x2+9x+6√3= 0 is ______

28. The graph y = mx2 (m > 0) lies in ______quadrants.

29. x = my2 (m < 0) parabola lies in ______quadrants.

30. 8C2+8C4= ______31. The equation whose roots are √3+1 and

√3–1 is ______32. The constant term in the expansion of

(5/√x+6√x)20 is ______33. If (x–α) (x–β) <0 then x lies between

______34. If the roots of 2x2+Kx+2 = 0 are equal

then K value is ______35. If (x+y) is a factor of xn + yn then the

condition is ______36. (x–2) is the factor of the function f(x)

then f(2) = ______37. The equation whose roots 2, –5 are

______38. "The sum of the co-efficients of even

powers of 'x' is equal to sum of the co-efficients of odd powers of x'' then thefactor of f(x) is ______

39. If x4–2x3+3x2–mx+5 is divisible byx–3then the value of m is ______

40. The solution set of the inequation x2–6 x+8 > 0 is ______

41. The other name of the pascal's triangle is______

42. The exponent of the binomial is 4 then

the co-efficients of the expansions are______

43. If one root of ax2+bx+c=0 is five timesthe other root then the condition is______

44. The (r+1)th term of (1+x)n is ______45. The sum of the co-efficients of (x+y)7

expansion is ______46. The discriminant of px2–10x+8 is 4 then

p = ______47. If the roots of x2–7x–8 = 0 are p, q then

p2+q2 = ______48. Which is the maximum value of K if the

roots of Kx2+10x+4 = 0 are real andunequal ______

49. If (x+1) is a factor ofax5+bx4+cx3+dx2+ex+f then thecondition is ______

50. If 2x+1 = 4x+1 then x = ______51. If 30C2r+3=30C3r+3 then r value is ______52. If α, β are the roots of x2–px+q = 0 then

the value of α/β + β/α = ______53. The standard form of second degree

homogeneous equation in two variables xand y is ______

54. Which term is independent of 'x' in theexpansion of (x+1/x)8 is ______

55. ______ is a factor of 32n+7 for all n∈ N56. f(x,y) is algebraic function in x and y. If

f(x, y) = f(y, x) then f(x, y) is ______

57. If f(x, y, z) = f(y, z, x) = f(z, x, y) then f(x,y, z) is ______ expression.

58. The sum of the roots of the quadraticequation is 7 and their product is 12 thenthe equation is ______

59. If x+1/x = 3 then x2+1/x2 = ______60. If nC2=21 then n value is = ______61. If 2x4–7x2+ax+b is divisible by x–3 then

the relation between a and b are ______62. The first term of (5/√x+6√x)20 is ______63. (2, K) is the point on the parabola y =

2x2–3 then K = ______64. The arrangement of Binominal co-

efficient was in the form of a diagramcalled Meru-prastara provided by ______

65. The two factors of x3+3x2–x–3 are (x–1),(x+1) then the other factor is ______

1. If ISO profit line coincides with a side ofpolygon, then it has ____ solutions.

2. In linear programming, the expressionwhich is to be minimised or maximised iscalled ____

3. If the profit line moves away from theorigin, then the values of the objectivefunction f is ____

4. The minimum value of f = x+y based onthe conditions x+y ≥ 6, 2x+y ≥ 8, x ≥ 0and y ≥ 0 is ____

5. y = x passes through ____

6. Given then the value of P

at the point (0, 12) is ____

7. "The value of x+y should not be less than15". This can be written as ____

8. Any point (x, y) in the feasible regiongives a solution to LPP is called ____

9. In a linear programming, the function f =ax+by is called ____

10. The line x = K is ____ axis.11. The point (–2, –4) lies on ____ quadrant.12. The slope of x-axis is ____13. Q1, Q2 are two quadrants then Q1 ∩ Q2 =

____14. The knowledge of Linear Programming

help to solve the problems in ____ sector.15. "The Maximum or Minimum value of f

occurs on atleast one of the vertices of thefeasible region". This is the statement ofthe ____ theorem of LinearProgramming.

16. The solution set of constraints of a Linear

1 3P x y

4 2= +

x 1 3+ =

MathematicsLINEAR PROGRAMMINGPOLYNOMIALS

POLYNOMIALS

Answers:1. Injection, surjection ; 2. {3} ; 3.Surjection ; 4. 3 ; 5. 3/2 ; 6. {(1, 3), (2, 4),(3, 1), (4, 2)}; 7. 8 ; 8. {(x, a), (y, b), (z, c)}; 9. {(1, 7), (2, 6)} ; 10. B⊆ R ; 11. {2}; 12.Bijection ; 13. a ; 14. Constant ; 15. ±2; 16.4 ; 17. Injection function ; 18. Constantfunction ; 19. y+1 / 3 ; 20. 7 ; 21. Identityfunction ; 22. Surjection ; 23. 3; 24. One-element ; 25. Inverse function ; 26. N–{3}; 27. 15 ; 28. Equal functions ; 29.Constant; 30. Real function ; 31. {5, 7, 9} ;32. R = {(x, y) / y = x+2} ; 33. 3 ; 34.Bijection function ; 35. Not Define ; 36.One ; 37. 4; 38. Constant ; 39. Identityfunction ; 40. 4 ; 41. {0, 1} ; 42. 4 ; 43. {(1,9), (2, 15)}; 44. x+3

Answers:1. x2 – x – 12 ≤ 0 ; 2. f(–b / a) ; 3. x – 1 ; 4.0 ; 5. 25 ; 6. a2/3 – a1/3 b1/3 + b2/3 ; 7. y-axis ;8. 16 ; 9. 15 ; 10. a + c = b ; 11. does not ;12. x2 – 4x + 5 = 0 ; 13. 5 ; 14. 2 ; 15. 1 and4 ; 16. a+b ; 17. ax – b ; 18. 4 ; 19. q2 = 4pr;20. lies between –1 and 2 ; 21. 32 / x5 ; 22.Even Number ; 23. 6th term ; 24. Q1 and Q4

; 25. 8 ; 26.Complex numbers ; 27. 6 ; 28.Q1 and Q2 ; 29. Q2 and Q4 ; 30. 98 ; 31. x2

– 2√3x + 2 = 0 ; 32. 20C10 . 510 . 610 ; 33.

lies between α and β ; 34. ±4 ; 35. n is odd; 36. 0; 37. (x–2) (x+5) =0 or x2+3x–10 = 0; 38. x + 1; 39. 23 ; 40. x < 2 or x > 4 ; 41.Arithmetic Triangle ; 42. 1, 4, 6, 4, 1; 43.5b2 = 36ac; 44. ncr x

r; 45. 27 ; 46. 3 ; 47. 65; 48. 6 ; 49. a + c + e = b + d + f ; 50. –1;51. 5 ; 52. p2 – 2q / q ; 53. ax2 + bxy + cy2 ;54. 8C4 ; 55. 8 ; 56. Symmetric expression;57. Cyclic ; 58. x2 – 7x + 12 = 0 ; 59. 7 ; 60.7 ; 61. 3a + b + 27 = 0 ; 62. 520 / x10 ; 63. 5; 64. Pingala; 65. (x + 3).

Sum of the roots of 6x2–5 = 0 is?

LINEAR PROGRAMMING


4

MathematicsPROGRESSIONSREAL NUMBERS

Programming problem is a convex setcalled ____

17. The solution set of x≥y, x≤y is ____18. The function f = ax+by which is to be

____ is called L.P.P.19. Any line belonging to the system of

parallel lines given by the objectivefunction for various values of theobjective function f is called ____ line.

20. If the line segment joining any two pointsin a set lines entirely in a set then it iscalled ____

21. The slope of y-axis is ____22. A set of points which satisfy all the

constraints of a L.P.P. is called ____23. If the point (–3, –2) lies on 3x–5y+k > 0

then the Minimum Value of k is ____24. If the point (2, 3) lies on x–3y+p < 0 then

the Maximum Value of p is ____25.

The graph that represents ____inequation.

26. The polygonal region which is theintersection of finite number of closedhalf planes is called ____

27. ISO-profit lines are ____28. The line divides the plane into ____ point

of sets.29. The line x–y = 0 is passing through ____30. If c < 0 then ax+by+c < 0 represents the

region ____31. The point of intersection of x = 2 and y =

–1 is ____32. If none of the feasible solution Maximises

or Minimises the objective function, thenthe problem has ____

33. The solution of x≥0, y≥0, 2x+3y ≤6 lies is____ quadrant.

1. ax–1 = bc; by–1 = ca; cz–1=ab thenxy+yz+zx = ______

2. x3/2 = 0.027 then the value of x is ______

3. The value of = ______

4. If a+b+c= 0 then a3+b3+c3 = ______

5. = ______

6. ∑n = 10 then ∑n3 value = ______

7. x = 256 then value = ______8. The value of (xp–q)r.(xq–r)p. (xr–p)q. is

______9. If (x2/3)P = x2 then P value is ______

10. = ______

11. The value of (32)–4/5 = ______12. The product of x3/5.x4/3.x–2/5 = ______

13. if x > 0, then then x value is______

14. |x| < a, if a > 0 then the solution set x is______

15. |6–9x| = 0 then x value is ______

16. = ______

17. ∑n = 66 then n value is ______

18. f(x) = 3√x then = ______

19. =______

20. value ______

21. a≠0 and p+q+r = 0 then a3p+3q+3r = ______

22. = ______

23. The limiting position of a secant of acircle is ______

24. (64)x = 2√2 then x value ______25. ax=b, by=c, cz = a then the value of xyz

is______26. If x = –8 then |x – 1| = ______27. The modulus of a real number is never

______28. The solution set of |x| ≤ a is ______

29. = ______

30. If 5x –√5 = 15 – √5 then x2 value is______

31. The solution set of |x|>a is ______32. Rationalising factor of √3 + 7 is ______

33. a2/3 [a1/3 (a1/4)4] = ______

34. = ______

35. =

36. numbers, which number is

greatest ______

37. The rationalising factor of is______

38. = ______

39. Value of (0.001)1/3______

40. If 2x = 3y = 12z then = ______

41. a1/3+b1/3+c1/3 = 0 then (a+b+c)3 = ______42. If xx√x = (x√x)x then x = ______43. If 64x = 2√2 then the value of x ______44. If ax = by = cz, and abc = 1 then

xy+yz+zx = ______

45. If a1/x = b1/y = c1/z and b2 = ac then(x+z)/2y = ______

46. 1/a + 1/b = 12, 1/a – 1/b = 6 then the valueof a is ______

1. If there are 'n' Arithmetic Means betweena and b then d = ____

2. If arithmetic mean and geometric mean oftwo numbers are 16 and 8 then theirharmonic mean is ____

3. If x, y, z are in Harmonic Progression theny = ____

4. If the first and 4th terms of a G.P. are 1and 27 respectively then the commonratio r = ____

5. Geometric mean of 5 and 125 is ____6. If TanA, TanB, TanC are in A.P., then

CotA, CotB, CotC are in ____progression.

7. Sum of the n terms of the series 1, 4, 9,16, ......... is ____

8. Harmonic mean of 3 and 5 is ____9. If a, b, c are in A.P., then 1/a, 1/b, 1/c are

in ____ progression.10. The 'n'th term of the series a, ar, ar2, ar3,

......... is ____11. 'n'th term of the progression 8, 16, 32, 64,

........ is ____12. The common ratio of the G.P., 1/2, –1/4,

1/8, –1/16, ......... is ____13. 3/2, 3/4, 3/8, ......... progression, the 10th

term is ____14. Sum of the first 'n' natural numbers is

____15. The 7th term of the progression 1, –1/2,

1/4, ........ is ____16. The nth term in an A.P. is 2n+5 then the

common difference 'd' is ____17. The Harmonic mean between 1/a, and 1/b

is ____18. If |r| < 1, then the sum to infinite terms of

the series a+ar+ar2+ ......... is ____19. The nth term of G.P. is tn = 5 (0.3)n–1 then

the common ratio is ____ 20. In a G.P., a = 2, S= 6 then r = ____ 21. The relation between A.M, G.M. and H.M

is ____22. If there are 'n' Geometric means between

a and b then the common ratio is ____23. If 7 times the 7th term = 11 times the 11th

term, then 18th term is equal to ____24. The A.M of 4 and 20 is ____25. ____ term in A.P., 10, 8, 6, ............. is

–22.26. a, b are positive, then A.M, G.M, H.M, are

in ____ progressions.27. If 5 Arithmetic means are between a and

b. what is the common difference is ____28. –2/7, x, –7/2 are in G.P. then x value is

____29. The 'n'th term of the series 2.5 + 4.7 + 6.9

+........ is ____30. In an A.P, the sum of three terms is 39

then the middle term is ____31. In an A.P, the first term is a, common

difference d then the 15th term in H.P., is____

32. The number of 9 multiples in between 1and 1000 is ____

33. In an G.P, the first term is 50, 4th term is1350 then 5th term is ____

34. p/q form of is ____

35. If a, b, c are in Arithmetic progressionthen Ka, Kb, Kc are ____ progression.

36. The nth term of 1+(1+3) + (1+3+5)+........is ____

37. a–2d, a–d, a, a+d, a+2d are in ____progression.

1.56

Z(x 2y)

xy

+

3

2x 2

x 2x 2Lt

2x 3x 5→−

− ++ +

3 35 3−

( ) 332 23 and 3

5 5

3 3x a

x aLt

x a

− −

→

−−

x 4

x 12Lt

4→

+

215 59 27

×

2x 1

3Lt 4

x→−−

a 2 ab b

a b

− +−

2

x 0

x 5xLt

x→

+

x 9Lt f (x)→

x

2x 3Lt

3x 5→∞

++

xx x x=

m m

n nx a

x aLt

x a→

−−

x

n n

x a

x aLt

x a→

−−

x

1Lt

x→∞

The Slope of Y-Axis is...?REAL NUMBERS

PROGRESSIONSAnswers:1. Infinite; 2. Objective function ; 3.Increase ; 4. 6 ; 5. Origin ; 6. 18 ; 7. x+y ≥15 ; 8. Feasible point ; 9. Objectivefunction or profit function ; 10. y-axis ; 11.Q3 ; 12. 0 ; 13. φ ; 14. Business, Transport,Industry etc., ; 15. Fundamental Theorem ;16. Feasible region ; 17. x = y ; 18.Minimum or Maximum ; 19. ISO profitline ; 20. Convex set ; 21. Undefined ; 22.Feasible region ; 23. 0 ; 24. 6; 25.3x–4y+12 > 0 ; 26. Polyhedral set ; 27.Parallel ; 28. 3 ; 29. Origin ; 30. Below theorigin ; 31. (2, –1) ; 32. No solution ; 33. Q1

B(–4,0)

(0,3)AY

X

Answers:1. xyz ; 2. 0.09 ; 3. 0 ; 4. 3 abc ; 5. n an–1 ; 6.100 ; 7. 4 ; 8. 1 ; 9. 3 ; 10. m/n a m–n ; 11.1/16 ; 12. x ; 13. 2/3 ; 14. –a<x<a ; 15. 2/3; 16. 2/3 ; 17. 11 ; 18. 9 ; 19. 5 ; 20. √a + √b; 21. 1 ; 22. 1 ; 23. Tangent Line ; 24. 1/4 ;25. 1 ; 26. 9 ; 27. Negative ; 28. –a ≤ x ≤ a; 29. 9 ; 30. 9 ; 31. x < –a or x > a ; 32. √3 – 7 ; 33. a2 ; 34. 1 ;35. –5/3 a–8 or –5/3a8 ; 36.

37. ; 38. –2/7 ;

39. 0.1 or 1/10; 40. 1; 41. 27 abc ; 42. 9/4;43. 1/4; 44. 0; 45. 1; 46. 1/9

3 3 325 15 9+ +

323


5

38. g1,g2 are the two geometric means between

a and b the common ratio of G.P. is ____

39. The nth term of A.P. is 3n+1 then the sumof n terms is ____

40. The sum of three terms in A.P. is 21 andtheir product is 315 then the terms are____

41. K+2, 4K–6, 3K–2 are in A.P. then thevalue of K is ____

42. The 12th term of an A.P., x, 4x/3, 5x/3,.............. is ____

43. The reciprocals of A.P., is ____progression.

44. x–3b, x+b, x+5b are in Arithmetic progre-ssion then common difference is ____

45. 1+x, 6, 9 are in G.P. then value of x is____

46. The sum of the first 'n' natural numbers is15 and the sum of cubes of first 'n' naturalnumbers is ____

47. The relation between Σn, Σn3 is ____48. a, b, c are in G.P. then log a, log b, log c

are in ____49. If a, b, c, d, ............. are in Geometric

progression then aK, bK, cK, dK......... arein ____ progression.

50. The sum of 'r' terms of the series (a–1) +(a–2) + (a–3) +........ is ____

51. The cotangent of π/3, π/4, π/6 are in ____progression.

52. Σn = 55 then n value is ____53. In A.P. the first term is a, last term is l then

Sn = ____54. The Geometric mean of x1, x2, x3, x4 is

____

1. ∆ABC ∼ ∆ DEF, if ∠ A = 50°, then ∠ E +∠ F = ______

2. If two circles touch externally, thennumber of their common tangents is______

3. If a line divides any two sides of a trianglein the same ratio then the line is ______ tothe third side.

4. The point which is equidistance from thevertices of a triangle ______

5. The length of the direct common tangentto externally touching circles whose radiiare 5cm and 6cm is ______

6. The vertical angle bisector of ∠ X of the∆XYZ , intersects the side YZ at p, then______

7. If ABCD is cyclic quadrilateral with ∠ C= 120° then ∠ A = ______

8. The point of intersection of angle bisectorof a triangle is ______

9. The number of circles drawn throughthree non - collinear point is ______

10. The diagonal of a square is ______ timesto its side.

11. If ∆ABC ∼ ∆ PQR then =______

12. Angle in the same segment are ______13. The distance between the centres of two

circle is 'd'. If the radii are r1 and r2 thenthe length of transverse common tangentis ______

14. The angle in the major segment of a circleis ______

15. If two circles of radii 3cm and 5cm touchinternally, then the distance between theircentres is ______ cm.

16. In ∆ABC, ∠ B = 90°, ∠ CAB = 30° andAC = 10, then BC = ______

17.

In the adjacent figure is a tangent tothe circle at A ∠ CAX= 80° and AB = AC then ∠ ABC = ______

18. The ratio of corresponding sides of twosimilar triangles is 3:4 then the ratio oftheir areas is ______

19. The height of an equilateral triangle withside 2√3 is ______

20. Opposite angles of a cyclic quadrilateralare ______

21. If the two circles touches externally withradii are 6 cm and 7 cm. Then distancebetween their centers is______

22.

'O' is the centre of the circle, If ∠ BOA=140° and ∠ COA = 100° then ∠ BAC =______

23. ∆ABC ∼ ∆ PQR, AB = 3.6, PQ = 2.4, AC= 8.1cm then PR = ______

24. Angle in semi circle is ______25. If a Rhombus is cyclic then it is ______26. Two circles touch internally, then the

number of their common tangents are______

27. The point of concurrence of the mediansof a triangle ______

28. The perpendicular bisectors of the sidesof a triangle is ______

29. In a triangle, a line dividing the two sidesin the same ratio is ______ to the thirdside.

30. The bisector of the vertical angle of atriangle divides the base in the ratio of theother ______ sides.

31. If R, r are radii of the circles and d is thedistance between the centres of twocircles. If R = r + R then the two circles is______

32. The angle between a line drawn throughthe end point of a radius and its tangent tothe circle is ______

33. A line drawn through the end point ofradius and perpendicular to it is ______ tothe circle.

34. The number of tangents drawn from anexternal point to a circle is ______

35. In ∆ABC ∠ A = 90° AD ⊥ BC then AD2 =______

36. If an arc subtends an angle of 80° at thecentre, its corresponding are subtends anangle of ______ at the circumference.

37. The number of tangents drawn to the non- intersecting and non - touching circle is______

38. The length of the tangent drawn to a circlewith radius 'r' from a point 'p' which is 'd'cm away from the centre is ______

39. In ∆ABC , the circle drawn asdiameter passes through A then thetriangle ABC is ______

40.

'O' is the centre of the circle if ∠ AOC =130° then ∠ B = ______

41. If is a secant to a circle

intersecting the circle at A and B and PTis a tangent segment then PT2 = ______

42. If R, r are the radii of the circles. 'd' is thedistance between the centres of twocircles and if R + r < d then the two circlesare ______

43. If x,y,z are the midpoints of AB, BC and

CA respectively then the ratio of ∆XYZ :∆ABC = ______

44. The line which intersects a circle in twodistinct points is called a ______ of thecircle.

45. The number of common tangents drawnto the concentric circles is ______

46. The number of circles drawn throughthree non - collinear points is ______

47.

In this circle the chords AB and CDintersects at E. AE = 8, EB = 6, CE = 4then ED = ______

48. In ∆ABC, the bisector of ∠ A meets BC atD and BD = 6cm, DC = 8 cm then theratio of AB:AC = ______

49. The Indian mathematician who provedpythagorean theorem is ______

PAB

BC

XY��

AB: AC

GEOMETRY

Answers:1. 130°; 2. 3 ; 3. Parallel; 4. Circum center; 5. 2√30cm ;

6. ; 7. 60° ;

8. Incenter of the circle ; 9. 1 ;

10. √2 ; 11. ; 12. equal ;

13. ; 14. acute angle ;

15. 2 cm ; 16. 5 cm ; 17. 80° ; 18. 9: 16 ;19. 3 ; 20. Supplementary ; 21. 13 cm ; 22.60° ; 23. 5.4 ; 24. 90° or Right angle ; 25.Squire ; 26. 1 ; 27. Centroid ; 28. CircumCenter ; 29. Parallel ; 30. 2 Sides ; 31.Externally ; 32. 90° ; 33. Tangent ; 34. 2 ;35. BD.DC ; 36. 280° ; 37. 4 ; 38. ;

39. equilateral Triangle ; 40. 115° ; 41.PA.PB ; 42. Do not intersect circles ; 43.1:4 ; 44. Secant line ; 45. 0 ; 46. 1; 47. 12;48. 3:4 ; 49. Bhaskaracharya

2 2d r−

( )221 2d r r− +

PQ;PR

XY YP

XZ ZP=

MathematicsGEOMETRYPAPER - II

The relation between ΣΣn, ΣΣn3 is?

Answers:1. b–a / n+1 ; 2. 4 ; 3. 2xz / x+z ; 4. 3 ; 5.25 ; 6. Harmonic Progression ; 7. n(n+1)(2n+1) / 6 ; 8. 15/4 ; 9. HarmonicProgression ; 10. arn–1 ; 11. 2r+2 or 8×2r–1 ;12. –1/2 ; 13. 3/1024 ; 14. 5050 ; 15. 1/64 ;16. 2 ; 17. 2/a+b ; 18. a/1–r ; 19. 0.3 ; 20.2/3 ; 21. A.M ≥ G.M ≥ H.M. or (G.M.)2 =A.M × H.M ; 22. (b/a)1/n+1 ; 23. 0 ; 24. 12 ;25. 20 ; 26. G.P. ; 27. q–p/6 ; 28. ±1 ; 29.2n(2n+3) or 4n2 + 6n ; 30. 13 ; 31. 1/a+14d;32. 111 ; 33. 4050 ; 34. 155/99 ; 35.Geometric Progression ; 36. n(n+1)(2n+1) /6 ; 37. Arithmetic Progression ; 38. (b/a)1/3;39. n(3n+5) / 2 ; 40. 5, 7, 9 ; 41. 3 ; 42.14x/3 ; 43. Harmonic Progression ; 44. 4b ;45. 2 ; 46. 225 ; 47. Σn3 = (Σn)2 ; 48. A.P. ;49. G.P. ; 50. r/2 [2a–r–1] ; 51. G.P. ; 52. 10;53. n/2(a + l) ; 54. (x1 . x2 . x3 . x4)

1/4

C

AX80°

Y

B

C

A

°O B

A

O

B

C

A

D

BC

E64 8

130°


6

MathematicsTRIGONOMETRYANALYTICAL GEOMETRY

1. The slope of the straight line joining thepoints (3, –1), (5, 3) is ____

2. The equation of the line passing through(1, 2) and is parallel to 2x–3y+8 = 0 is____

3. The equation of a straight line that makesintercepts of 5 and 3 units respectively onx-axis and y-axis is ____

4. Equation of the line whose slope is 5 andy-intercept is –3 is ____

5. The centroid of the triangle, whose sidesare given by x = 0, y = 0 and x+y = 6 is____

6. Distance between the points (a Cosθ, 0),(0, a Sinθ) is ____

7. The line x = my+c, cuts the y-axis at ____point.

8. The angle between the lines x–2 = 0, y+3= 0 is ____

9. The slope of a straight line which isperpendicular to x–2y+5 = 0 is ____

10. The lines y = 2x–3, y = 2x+1 are ____11. The points (P, 2), (–3, 4), (7, –1) are

collinear then P = ____12. The equation of y-axis is ____13. The slope of a line making an angle 45°

with the positive direction x-axis is ____14. The distance from origin to the given

point (a, b) is ____15. If the slope of a line joining the points (3,

2) and (4, k) is 2 then k = ____16. The slope of the line perpendicular to

3x+4y = 10 is ____17. If ax+by+c = 0 represents a straight line

then condition is ____18. The distance between the points (0, 1)

and (8, k) is 10 then k value is ____19. The centroid of the triangle with vertices

(–1, 0), (5, –2) and (8, 2) is ____20. The area of the triangle with vertices (0,

0), (0, 2) and (1, 0) is ____21. y = mx line as known as ____ form.22. The line x = 3y+1 cuts x-axis at ____23. The slope of the line ax+by+c = 0 is ____24. Slope-point form of a line is ____25. The intercepts form of a line is ____26. Area of a triangle whose vertices are (x1,

y1), (x2, y2) and (x3, y3) is ____27. The sum of the intercepts made by 3x+4y

= 12 on the axis is ____28. Slope of the line y = 5 is ____29. Who has introduced analytical geometry

is ____

30. If two straight lines are parallel, theirslopes are ____

31. The slope of x/a + y/b = 1 is ____32. x-intercept of the line zx–y+7 = 0 is ____33. Three points are in the straight line then

the points are called ____34. The slope of ax+7y = 0 is 2 then a value

is ____35. The centroid of the triangle whose

vertices are (x1, y1), (x2, y2), (x3, y3) is____

36. The mid point of the line join of (Sin2α,Sec2α) and (Cos2α, – Tan2α) is ____

37. Two lines are perpendicular then theproduct of the slopes = ____

38. The slope of the line parallel to y-axis is____

39. The equation of a straight line passing(x1, y1) and (x2, y2) is ____

40. One end of the diameter of a circle is (–3,4) and the center is (0, 0) then the otherend point of the diameter is ____

41. The equation of a straight line passingthrough the origin and slope 2/3 is ____

42. The line y = x makes the angle with x-axis is ____

43. If the slope of the line is 2/5 then slope ofthe line perpendicular to the above line is____

44. The equation of the straight line passingthrough (2, –3) and equal intercepts withthe axis is ____

45. The line √3x – y + 50 makes an angle ofx-axis is ____

46. ____ diagram is formed the vertices of (0,0), (5, 0), (5, 5) and (0, 5)

47. The centroid divides the median in theratio ____

48. The peremeter of the vertices of thetriangle (0, 0), (4, 0), (0, 3) is ____

49. (9, 3) and (1, –1) are the end points of thediameter of the circle then the center is____

50. Equation of a straight line parallel to x-axis and it makes an intercept 4 units ony-axis is ____

1. Tan230 + Tan260° = ______2. If (Secθ + Tanθ) = m the value of (Secθ –

Tanθ) = ______3. Eliminate 'θ' from x = 2sinθ; y = 2cosθ

then ______4. If Tan(A+B) = √3, Tan A = 1 then ∠ B =

______5. If a wheel makes 360 revolutions in one

minute, then through how many radiansdoes it turn in one second is ______

6. Eliminate 'θ' from x = a Secθ, y = b Tanθthen ______

7. A minute hand of a clock is 3 cm. long,the distance moved in 20 minutes is______

8. The value of Sinθ interms of Sec θ is______

9. One radian is equal to ______ degrees.10. Eliminate θ from x = Cosecθ + Cotθ, y =

Cosecθ – Cotθ is ______11. If Cosθ = √3/2 then the value of Sinθ

______12. The value of Tan250 – Sec250 = ______13. The circular measure of 72° = ______14. Sin225 + Cos225 = ______15. The value of Cosθ . Tanθ = ______16. If Sinθ = Cos2θ then Cotθ value ______17. If x = Secθ + Tanθ, y = Secθ – Tanθ then

xy = ______18. The sexagesimal measure of πc/6 is

______19. The value of Cos(π/3) = ______20. Cos (A+B) = ______21. Sin 90° + Cos 0° +√2Sin45° = ______22. If Sinθ = 5/13 than Cos(90–θ) = ______

23. = ______

24. value = ______

25. = ______

26. The value of (Sinθ + Cosθ)2 + (Sinθ –Cosθ)2 = ______

27. One degree is equal to ______ radians28. If 8Tanθ = 15 then Cotθ = ______29. Cos2A is equal to ______30. The radius of a circle is 14 cms. The

angle subtented by an arc of the circle atthe centre 45°. Then the length of the arcis ______

31. The centesimal measure of 150° is______

32. The centesimal measure of 5πc/2 is______

33. The circular measure of 30g is ______34. The sexagesimal measure 150g of is

______35. Secθ (1–Sinθ) (Secθ + Tanθ) value is

______36. (1–Cosθ) (1+Cosθ) (1+Cot2θ)= ______37. If Tanθ = 1 then Cos2θ – Sin2θ = ______

38. The value of = ______

39. The Range of Sinθ is ______40. The Minimum value of Cosθ is ______41. Cos1°.Cos2°.Cos3°....... Cos17° =

______42. The value of Sin 420° = ______43. The value of Tan 30°, Tan 45°, Tan 60°

are in ______ progression.44. Cot π/20. Cot 3π/20. Cot 5π/20.

Cot7π/20.Cot 9π/20 = ______45. The value of Sin0°.Sin1°.Sin2° .........

Sin90° = ______46. If Sin70° = Cos θ then θ = ______47. Sin31°Cos59° + Cos31°Sin59° = ______48. Angle of elevation of the top of the

electric pole from man 40 mts from itsfoot is 60°. Then the height of the pole is______

49. Tan 1°. Tan 2°. Tan 3° ....... Tan89° =______

50. The value of Sec (270-θ) = ______

2Cosec 1

Cosec

θ −θ

4 4

2 2

Sin A Cos A

Sin A Cos A

−−

Sin18

Cos72

°°

2 2 2Sin Cos Tanθ + θ + θ

The value of Sinθθ interms of Secθθ is?

TRIGONOMETRY

Answers:1. 2 ; 2. 2x–3y+4 = 0 ; 3. x/5 + y/3 = 1 ; 4.5x–y–3 = 0 ; 5. (3, 3) ; 6. a ; 7. (0, –c/m) ;8. 90° ; 9. –2 ; 10. Parallel ; 11. 1 ;

12. x = 0 ; 13. 1 ; 14. ;

15. 4; 16. 4/3; 17. |a| + |b| ≠ 0; 18. 7; 19. (4,0) ; 20. 1 sq. unit ; 21. Slope ; 22. (1, 0); 23.–a/b ; 24. y–y1=m(x–x1); 25. x/a + y/b = 1;

26. ;

27. 7 ; 28. 0 ; 29. Rene Decarde; 30. Parallel; 31. –3/2 ; 32. –7/2 ; 33.Collinear ; 34. –14 ;

35. ;

36. (1/2, 1/2) ; 37. –1 ; 38. Not define ; 39.(y – y1) (x1– x2) = (x – x1) (y1 – y2) ; 40. (3,–4) ; 41. 2x–3y = 0 ; 42. 45° ; 43. –5/2 ; 44.x+y–1 = 0 ; 45. 60° ; 46. Square ; 47. 2:1 ;48. 12 ; 49. (5, 1) ; 50. y = 4

1 2 3 1 2x x x y y y3,

3 3

+ + + +

( ) ( ) ( )1 2 3 2 3 1 3 1 2

1x y y x y y x y y

2− + − + −

2 2a b+

ANALYTICAL GEOMETRY


7

1. The average of 2, 3, 4 and x is 4. Thevalue of x is ____

2. The formula for finding out A.M. bydeviation Method is ____

3. The median of 10, 12, 13, 15, 17 is ____4. The median of x/5, x, x/4, x/2 and x/3 is 8

then the value of x is ____5. The mode of 4, 5, 6, 7, 8, 9, 6, 7, 6, 5, 10

is ____6. The class interval of the frequency

distribution having the classes 10–20,20–30, 30–40 is ____

7. Class middle value is used in ____8. If arithmetic mean is 48.5, median is

46.25 a data, then mode is ____9. In finding mode, ∆2 = ____10. The median of natural numbers from 1 to

9 is ____11. The mid value of the class 40–50 is ____12. If the mean of 10 observations is 7 and

the mean of 15 observations is 12, thenthe mean of total observations is ____

13. The value of ∆1 while calculating themode in delta method is ____

14. The observation which occurs frequentlyin a data is ____

15. The formula to the empirical relationamong mean, median and mode of agiven data is ____

16. In a histogram, the breadths of therectangles represent the ____

17. The range of the first 9 natural numbers is____

18. The mean of the first 'n' natural numbersis ____

19. The class interval of the class 10–19 is____

20. The median of scores x1, x2, 2x1 is 6 and

x1 < 2x1 < x2 then x1 = ____21. In the classes 1–5, 6–10, 11–15, ........the

upper limit of the class 1–5 is ____22. In a data the A.M. is 39 and mode is 34.5

then median = ____23. In the data sum of 15 observations is 420

then the mean is ____24. The range of 20, 18, 37, 42, 3, 12, 15, 26

is ____25. For the construction of a frequency

polygon ____ and frequencies are takeninto consideration.

26. Formula for finding the mode of groupeddata is ____

27. In a frequency distribution the mid valueof class is 35 and the lower boundary is30. Then its upper boundary is ____

28. If a data have two modes, then its is called____

29. The lower limit of the class 10–19 is ____30. Formula for finding mean by deviation

method is ____31. Formula for finding the median of

grouped data is ____32. Father of statistics is ____33. The difference between two consecutive

lower limits of the classes is ____34. A histogram consists of ____35. Central tendency value is based on all

observations of the data36. The formula for mean of grouped data is

____37. The greater than cumulative frequency of

a class is 83 and that of the next class is73 then the frequency of that class is ____

38. Mean = where A is called

____39. The most reliable measure of mean,

median and mode is ____

40. The cumulative frequencies are used tomeasure the ____

41. The range of first 'n' natural numbers____

42. The mean of 11 observations is 10.5. If anobservation is deleted then the mean ofthe remaining observations ____

43. The mean of the squires of first 'n' naturalnumbers is ____

44. ____ is not affected by the extremevalues.

45. The mode of 4, 8, 9, P, 7, 6, 4, 2 is 9 thenthe value of P is ____

1. A square Matrix whose determinant is zero is called ______

2. In a Matrix, if the rows and columns areinterchanged then the Matrix obtained iscalled ______ of the given Matrix.

3. If then AB =

______

4. If then |A| = ______

5. If = 0 then d =______

6. If has no Multiplicative

inverse then a = ______

7. If then A–1 =

______

8. If = (1, 2) then the order of

A is ______

9. Ifthen A+B

= ______ 10. The Matrix is introduced by ______

11. The product=______

12. The determinate of the singular Matrix is______

13. Ifthen x = ______

14. If and ad = bc then

A is ______ Matrix.15. The element of the second row and third

columns of

is ______

16. Order of matrix A is 3×4, order of MatrixB is 5 × 3 then the order of BA is ______

17. The determinate of the Matrix

is ______

18. If then a = ______

19. A, B are two Matrices then (AB)T =______

20. If

is a scalar Matrix, then λ = ______ 21. While solving the equation 3x+4y = 8 and

x – 6y = 10 by Cramer's method, theMatrix B1 = ______

22. A, B are two Matrices then (AB)–1 =______

23. If then A + AT= ______

24. A is square Matrix and A = AT then A iscalled ______ Matrix.

25. The product is ______

26. If then |A| =

______ 27. The Multiplicative unit matrix of order

3×3 is ______ 28. The inverse of the Identify Matrix is

______ 29. If AB = I then 'B' is called ______ of 'A' 30. If A is a square Matrix, A.A–1. A–1A =

______

31. If the T = ______

32. If X + 2I = then Matrix X =

______

3 1

1 2

−

T

4 3 4 3

2 16 2 2

− − =

Cos SinA

Sin Cos

θ − θ = θ θ

( )1 2 32

3

4

1 3A

5 6

=

4 0P

0

= λ

a 3 2 7

1 2 1 0

− =

Sec Tan

Tan Sec

θ θ θ θ

1 8 5

2 3 4

2 7 0

− −

a bA

c d

=

2 0

5 1

= −

x y x y

2x 3y 2x 3y

+ − + −

( )x ya

b

1 3 1 2A ,B

2 1 3 0

= = − −

1 1A

0 2

×

1 4A

0 1

= −

2a 5

6 3

−

d 2 5

4 2

−−

4 3A

2 1

= −

1 0 0 1A ,B

0 1 1 0

= =

fxA C

N

Σ+ ×

STATISTICS

Answers:

1. 7 ; 2. ; 3. 13 ;

4. 24 ; 5. 6 ; 6. 10 ; 7. Mean ; 8. 41.75 ; 9.f–f2 ; 10. 5 ; 11. 45 ; 12. 7 ; 13. f–f1 ; 14.Mode ; 15. Mode = 3 Median–2 Mean ; 16.Length of the class interval ; 17. 8 ; 18.n+1/2 ; 19. 10 ; 20. 3 ; 21. 5.5 ; 22. 38.5 ;23. 28 ; 24. 39 ; 25. Mid value of the class;

26. ; 27. 40 ;

28. Bimodal ; 29. 9.5 ;

30. ; 31. ;

32. R. A. Fisher ; 33. Class-interval ; 34.Rectangles ; 35. Mean ; 36. Σιx/n ; 37. 11 ;38. Expected mean ; 39. Mean; 40. Median;41. n–1 ; 42. 10.65 ; 43. (n+1) (2n+1) / 6 ;44. Median ; 45. 9

N F2L Cf

−+ ×i if x

A CN

Σ+ ×

1

1 2

CL

∆+∆ + ∆

fdA C

N

Σ+ ×Answers:

1. 10/3 ; 2. 1/m ; 3. x2 + y2 = 4 ; 4. 15° ; 5.12πc ; 6. b2x2 – a2y2 = a2b2 ; 7. 44/7 cm ;

8. ;

9. (57.3)° or 57°16' ; 10. xy = 1 ; 11. 1/2 ;12. – 1 ; 13. 2πc/5 ; 14. 1 ; 15. Sinθ ;

16. ; 17. 1 ; 18. 30° ; 19. 1/2 ;

20. CosACosB – SinASinB ; 21. 3 ; 22.5/13 ; 23. Secθ ; 24. 1 ; 25. 1 ; 26. 2 ; 27.0.01745c ; 28. 8/15 ; 29. Cos2A – Sin2A ;30. 11 cm ; 31. 500g/3 ; 32. 500g ; 33. 27° ;34. 5πc/6 ; 35. 1 ; 36. 1 ; 37. 0 ; 38. Cos θ ;39. [–1, 1] ; 40. – 1 ; 41. 0 ; 42. √3/2 ; 43.G.P. ; 44. 1 ; 45. 0 ; 46. 20° ; 47. 1 ; 48.40√3 m.; 49. 1 ; 50. – Cosecθ

1

3

Sec 1

Sec

θ −θ

MATRICES

MathematicsMATRICESSTATISTICS

Who is the Father of Statistics?


8

MathematicsWEIGHTAGE ANALYSISCOMPUTING

33. If and A = B

then the value of x + y is =______ 34. A is a Matrix then (A–1)–1 = ______ 35. If A is a Matrix then AT = – A then the

Matrix is called ______

36. If and P+R = I then

Matrix R = ______ 37. A and B are two Matrices. The product

AB is defined ______

38. If A is Matrix, A + B = 0 when 0 is a nullMatrix. Then B is called ______ of A.

39. 2x+3y–4 = 0, 5x–7y+8=0 express theabove equations in Matrix equation formAX = B then Matrix B = ______

40. If and A+B = Athen A

Matrix is ______ 41. If A,B,C are three Matrices A(B+C) = AB

+ AC is ______ law42. A is a Matrix if AX = B then X = ______

43. If then AB =

______

44. then A = ______

45. K is a Scalar, A is a Matrix then (KA)T =______

46. Additive inverse Matrix is ______ Matrix

47. then the order ofB Matrix is ______

48. Ifthen B2 = ______

49. Ifthen

3A+2B = _____50. If A is a Matrix then A.A–1 = ______

1. ____ is used to make a diagrammaticrepresentation of an algorithm.

2. The Rhombus shaped box is used in aflow chart for ____

3. The second generation computers ____were used.

4. An example for input unit is ____5. Large scale circuits are used in ____

generation computers.6. Father of the computers is ____7. The language known to computers is

called ____8. A language used in computers is ____9. Expand C.P.U. is ____10. To express the algorithm in a language

understandable by a computer is called____

11. All parts of a computer are controlled by____

12. The present day computers are make as____ generation computers.

13. The set of instructions of solving aproblem by a particular method, writtenin a language understands by a computeris called ____

14. Small translators are used in ____generation of computers.

15. A component of hardware is ____16. Input, output, CPU are ____ of the

computer.17. "Vacuum tubes" are used in ____

generation computers.18. All the parts of a computer are controlled

by ____19. Large amount of information is stored in

____ unit of a computer.20. Electronic circuits are used in ____

generation of computers.21. The number of major parts in a computer

is ____

22. The systematic step by step procedure ofsolving a problem is called ____

23. All arithmetic operations are performedin ____ of computer.

24. ____ unit is received the result by C.P.U.

25. BASIC stands for ____ 26. Yes/No box in flow chart is ____ 27. Present computers are called ____ 28. ____ is used entry/exist from another part

of the flow chart.29. A set of instruction which leads to a step

by step procedure for solving a problemon a computer called an ____

30. The example of output is____ 31. In a flow chart, a rectangular box is used

for ____ 32. Shape box is used for ____ 33. A.L.U. means ____

2 4 4 3A ,B

6 5 5 7

− = = −

xX

y

=

3 8 7A ,B ,

6 1 31

= = −

( ) ( )1 2 3 B 3 4× =

( )1 1A 1 2

0 2

=

( ) xA a b ;B

y

= =

5 6A

7 8

=

3 5P

4 2

− = −

2 4 y xA ;B

6 5 6 5

= =

The Number of Major Parts in Computer?

COMPUTING

Answers:1. Singular Matrix ; 2. Transpose Matrix ;

3. ; 4. 10 ; 5. – 8 ; 6. 5 ;

7.;8. 1 × 2 ; 9. ;

10. J.J.Sylvester ; 11. ;

12. Zero ; 13. 1 ; 14. Singular ; 15. 4 ;16. 5 × 4 ; 17. 1 ; 18. – 2 ; 19. BTAT ;

20. 4; 21. ; 22. B–1A–1

23. ; 24. Symmetric Matrix ;

25. ; 26. 1 ;

27. ; 28. Unit Matrix ;

29. Inverse Matrix ; 30. I ; 31. 4 ;

32. ; 33. 6 ; 34. A ;

35. Skew Symmetric Matrix ;

36. ;

37. Number of Columns of the Matrix A isequal to the number of rows of the MatrixB ; 38. Additive Inverse ;

39. ; 40. Null Matrix

41.Distributive law ; 42. A–1B; 43. (ax+by);

44. ; 45. KAT

46. Null Matrix ; 47. 2×3 ;

48. ; 49. ; 50. I14 6

8 29

−

3 7

6 31

11

2

4

8

−

4 5

4 3

− −

1 1

1 0

−

1 0 0

0 1 0

0 0 1

2 4 6

3 6 9

4 8 12

2 8

8 12

8 4

10 6

−

ax ay

bx by

2 5

1 1

− −

1 4

0 1

−

0 1

1 0

Answers:1. Flow Chart; 2. Decision making; 3.Transistor ; 4. Key Board or Mouse ; 5. 4th;6. Bobbage; 7. Software; 8. BASIC,COBAL, FORTRAN, PASCAL etc.,; 9.Central Processing Unit; 10. Software orprogramming language ; 11. Control unit ;12. 4th; 13. Software ; 14. 2nd ; 15. C.P.U.;16. Hardware ; 17. 1st; 18. Control unit ;19. Memory unit; 20. IIIrd ; 21. 3 ; 22.Algorithm; 23. Arithmetic and Logical Unit(ALU); 24. Output; 25. Beginners Allpurpose Symbolic Instruction Code; 26.Rhombus box; 27. Numan computers; 28.Loop; 29. Algorithm; 30. Monitor; 31.Calculations; 32. Start/Stop; 33. Arithmeticand Logical Unit ;

Paper - IChapter 5 Marks 4 Marks 2 Marks 1 Mark 1/2 MarkStatements & Sets & 1 2 1 5Functions (Mappings) & 2 1 1 5Polynomials 1 1 1 1 6Real Numbers & 1 2 1 6Linear Programming 1 1 1 1 3Progressions & 2 1 1 5

Paper - IIChapter 5 Marks 4 Marks 2 Marks 1 Mark 1/2 MarkGeometry 1 1 1 1 5Analytical Geometry & 2 2 1 5Trignometry 1 1 1 1 5Statistics & 1 1 1 5Matrices & 2 1 1 5Computing & 1 2 1 5

Mathematics Chapter wisemarks weightage analysis chart


9

POLYNOMIALS1. Using graph y = x2 solve the equation

x2–x–2 = 02. Draw the graph y = x2+5x–6 and solve

the equation x2+5x–6 = 0

LINEAR PROGRAMMING1. Maximise f = 5x+7y subject to the

condition 2x + 3y ≤ 12, 3x + y ≤ 12, x ≥0, y ≥ 0

2. Maximise f = 3x+y subject to theconstraints 8x + 5y ≤ 40, 4x + 3y ≥ 12, x≥ 0, y ≥ 0

3. Minimise f = x+y subject to the 2x + y ≥10, x + 2y ≥ 10, x ≥ 0, y ≥ 0

4. A shop keeper Sells not more than 30shirts of each colour. Atleast twice asmany white ones are sold as green ones.If the profit on each of the white be Rs.20 and that of Green be Rs. 25 how manyof each kind be sold to give him amaximum profit?

5. A sweet shop makes gift packet of sweetscombines two special types of sweets Aand B which weight 7 kg. Atleast 3 kg. ofA and no more than 5 kg of B should beused. The shop makes a profit of Rs. 15on A and Rs 20 on B per kg. Determinethe product mix so as to obtain maximumprofit.

STATEMENTS & SETS1. Define Conditional and write truth table?2. Prove that A – (B∪ C) = (A–B) ∩ (A–C)3. A, B, C are three sets then prove that

A∩(B∪ C) = (A∩B) ∪ (A∩C) 4. If A, B are two subsets of a universal Set

µ, then prove that (A∪ B)1 = A1 ∩ B1

5. Show that (p∧ (~q)) ∧ ((~p)∨ q) is acontradiction

FUNCTIONS1. Let f be given by f(x) = x+2 and f has the

domain {x ; 2 ≤ x ≤ 5} find f–1 and itsdomain and Range.

2. Let f: R → R be defined by f(x) = 3x – 5.Show that f has an inverse and find aformula inverse function f–1

3. Let f, g, h be functions defined by f(x) =x, g(x) = 1 – x, h(x) = x + 1 prove that(hog)of = ho(gof)

4. Given f(x) = x–1, g(x) = x2–2, h(x) = x3 –3 for x ∈ R find i) (fog)oh ii) fo(goh)

POLYNOMIALS1. The expression ax2 + bx + c equals – 2

where x = 0, leaves remainder 3 when

divided by (x–1) and remainder – 3 whendivided by (x+1). Find the values of a, band c.

2. Factorize the expression 4x4 – 12x3 + 7x2

+ 3x – 2 using the remainder theorem.3. Find a quadratic function in 'x' such that

when it is divided by x–1, x–2 and x–3leaves remainders 1, 2 and 4 respectively.

4. Find the independent term of x in

the expansion

REAL NUMBERS

1. If . show that 3y3 – 9y = 10

2. If lmn = 1, show that

3. If ax–1 = bc, by–1 = ca, cz–1 = ab show thatxy+yz+zx = xyz

4. Show that

5. Evaluate

6. Show that

PROGRESSIONS1. The A.M., G.M and H.M of two numbers

are A,G,H respectively show that A ≥ G ≥H

2. If the sum of the first 'n' natural numbersis S1 and that of their squares S2 andcubes S3. Show that 9s2

2 = s3 (1 + 8s1)3. Find the Sum of 'n' terms of the series 0.5

+ 0.55 + 0.555 +........n terms4. Insert 6 H.M's between 1/12 and 1/425. If (b + c), (c + a), (a + b) are in H.P. Show

that 1/a2, 1/b2, 1/c2 will also be H.P.

STATEMENTS and SETS1. Define Disjunction and write truth table?2. Write the inverse and contrapositive of

the statement ''If in a triangle ABC, AB >AC then ∠ C > ∠ B"

3. Prove that if x is even then x2 is even4. Prove that A ∩ B = A – B1 = B – A1

5. If A ∩ B = φ show that B ∩ A1 = B6. Show that (A ∩ B)1 = A1 ∪ B1

7. Show that (~p) ∨ (p∧ q) = p ⇒ q

FUNCTIONS1. Let f(x) = x2+2, g(x) = x2–2 for x∈ r find

(fog)(x), (gof) (x) 2. Show that f(x) = 3x+4 is bijective

function.3. If f:R-{3}→R, is defined by f(x) = x+3/x–3

show that f = 3x+3/x–1 = x for x ≠1

4. If f(x) = x2+2/x–15 for x∈ R findf(x2+2x–15)

5. If f(x) = x+2, g(x) = x2–x–2 find

POLYNOMIAS1. Find the value of m in order that

x4–2x3+3x2–mx+5 may be exactlydivisible by x–3.

2. If 4x2–1 divides 4x4–12x3+ax2+3x–bexactly find the values of a and b

3. If a and b are unequal and x2+ax+b andx2+bx+a have a common factor show thata+b+1=0

4. Solve x2–6x+5<05. Solve x2–4x–21>06. Find the middle term of the expansion of

7. Find the number which exceed its

reciprocal by

LINEAR PROGRAMMING1. Define convex set and profit line?2. Define objective function and feasible

solution?3. For the given vertices (0, 0), (2, 3), (3, 0),

(0, 5) at which point the objectivefunction 2x+3y will have Maximumvalue?

4. Indicate the polygonal region representedby the systems of inequations x≥0, y≥0,x+y ≤ 1.

5. In Linear programming problem theobjective function values 6 and 15 are atthe point of the vertices A(3, 0) and B(0,5) then find the objective function?

REAL NUMBERS

1. If then show that x = 1/2(a – a–1)

2. If a1/3+b1/3+c1/3=0 show that (a+b+c)3 =27abc

3. If a+b+c=0 show that

4. If ax = by = cz, b/a = c/b show that y/z =2z/x+z

5. Show that

6. Evaluate

7. Solve

PROGRESSIONS1. Insert 5 arithmetic means between 4 and

22.2. The sum of first 3 number is 12 and the

product is 48. Find the numbers.3. In an A.P. the 4th term is 7 and 7th term is

4 then show that 11th term is zero.4. The 8th term of G.P. is 192 and common

ratio is 2 then find 12th term.5. The sum of n terms of an A.P. is 2n+3n2

find the 'r'th term6. Which term of the A.P., 5, 2, –1, ....... is –

22.

STATEMENTS and SETS1. Define Tautologies and contradications?2. Write true table "3×6 = 20 ⇒ 2+7 = 93. Write true table of Disjunction?4.

Determine when the current flows from Ato B?

5. If A = {2, 4, 6, 8}, B = {1, 2, 3, 4, 5} thenfind A ∆ B?

6. Prove that (A1)1 = A7. If n(A∪ B) = 50, n(A) = 16, n(B) = 46

find n(A∩B)?8. If A ⊂ B then show that B1 ⊂ A1

FUNCTIONS1. If f(x) = x+1/x–1 then find f(x) + f(1/x)?2. Find the Range and Domain of R = {(x,

y): x = 2y, x, y ∉ N}3. Define constant function and Indetity

function?4. If f(x) = 3x–5 then find f–1?5. If f(x) = 2x+3 then find {f–1(x): 2≤x≤3}6. If f(x) = 1+2x, g(x) = 3–2x then find the

values of (fog) (3) and (gof) (3)7. If f = {(1, 3), (2, 5), (3, 7)}, g = {(3, 7),

(5, 9), (7, 10)} Find gof8. Let f: R→R, f(x) = 2x+3 is difines show

taht f(x) is bijective?

POLYNOMILAS1. Find the roots of the equation x2+x(c–b)

+(c–a) (c–b) = 02. Find the sum and the product of the roots

of the equation √3x2 + 9x + 6√3 = 03. Write the quadratic equation whose roots

are 2+√3 and 2–√3

4x 86

2

− <

2

2x 2

2x 7x 6Lt

5x 11x 2→

− +− +

m mm n

n nx a

x a mLt a

x a n−

→

− =−

2 1 1 1 2 1 1 1 2a b c a b c a b c 3x .x .x x− − − − − −

=

2a x x 1= + +

22

3

13x

2x

7 +

( ) ( ) ( )g 1 g 2 g 3

f ( 4) f ( 2) f (2)

+ +− + − +

a b a c b c b a c a c b

1 1 11

1 x x 1 x x 1 x x− − − − − −+ + =+ + + + + +

x a 2a

x a

+ −−

x 1

x 1Lt 4

x 3 2→

− =+ −

1 1 1

1 1 11

1 m 1 m n 1 n− − −+ + =+ + + + + +l l

3

3

1y 3

3= +

8

22

56x

x −

4 Marks Questions

5 Marks Questions

2 Marks Questions

1 Marks Questions

Draw the Graph X2+5x-6MathematicsPaper - 1IMPORTANT QUESTIONS

°°p

qA B


10

4. Define Ramainder theorem?5. Find the remainder when

x4+4x3–5x2–6x+7 is divided by (x–2)6. The product of two consecutive numbers

is 56. Find the numbers?7. Find the 5th term in the expansion (x/y +

y/x)8

8. Define Mathematical induction?9. Expand Σ a2(b2–c2)

LINEAR PROGRAMMING1. Define open convex region?2. Define feasible region?3. What is Linear programming problem?

REAL NUMBERS1. Simplify (ap/aq)p+q . (aq/ar)q+r . + (ar/ap)r+p

2. Solve if 23x = 4x+1

3. Solve |3 – 12x| = 0

\4. Find the volume of

5. Find

6. Evaluate

7. If x = ap, y = bq and xq.yp = a2/r. Show thatpqr = 1

PROGRESSIONS1. The first term of a G.P. is 2 and the sum to

infinity is 6 find the common ratio?2. –2/7, x, –7/2 are in G.P. then find x value?3. x, 4x/3, 5x/7, ........ are in A.P. then find

10th term?

4. Find the rational number of

5. The nth term of the G.P., 100, –110, 121,..........

6. Find the Harmonic mean of 6 and 247. In an A.P., n = 50, a = 12 and l = 144 then

find Sn= ?

GEOMETRY1. Construct a cyclic quadrilateral ABCD,

where AB = 3cm, BC = 6cm, AC = 4cmand AD = 2cm.

2. Construct a triangle ABC in which BC =7cm, ∠ A = 70° and foot of theperpendicular D on BC from A is 4.5cmaway from B.

3. Construct a triangle ABC in which BC =5cm. ∠ A = 70° and median. AD throughA = 3.5 cm.

TRIGONOMETRY1. Two pillars of equal height stand at a

distance of 100 mts. At a point in betweenthem, the elevation of their tops are foundto be 30° and 60° respectively. Determinethe height of the pillars and the positionof the point of observation.

2. There are two temples, one on each bankof a river, just opposite to each other. Oneof the temples A is 40 mts high. Asobserved from the top of this temple A,the angles of depression of the top andfoot of the other temple B are 12°30' and21°48' respectively. Find the width of theriver and the height of the temple B.

3. An aeroplane at an altitude of 2500 mtsobserve the angles of depression ofopposite points on the two banks of ariver to be 41°20' and 52°10'. Find inmetres, the width of the river.

4. From the ground and first floor of abuilding, the angle of elevation of the topof the spire of a church was found to be60° and 45° respectively. The first floor is5 mts high. Find the height of the spire.

GEOMETRY1. Prove that alternate segment theorem.2. Define and prove Basic proportionality

(Thales) theorem.3. Prove that Pythagorean theorem.4. Prove that the converse of alternate

segment theorem.5. Prove that vertical angle bisector

theorem.

ANALYTICAL GEOMETRY1. Find the equation of the line

perpendicular to the line joining (3, –5),(5, 7) and passing through (2, –3).

2. Find the equation of a line passingthrough (4, 3) and making intercepts onthe co-ordinate axis whose sum is equalto –1.

3. Find the equation of a line that cuts offintercepts a and b on the x and y axis suchthat a+b = 3 and ab = 2.

4. If the three points A(2, 3/2), B(–3, –7/2)and C(x, 5/2) are collinear. Find the valueof 'x'.

5. In what ratio is the segment joining thepoints (–3, 2) and (6, 1) divided by y-axis.

6. Find the point of intersection of themedians of a triangle whose vertices are(2, –5), (–3, 4) and (0, –3).

7. If A(–1, 2), B(4, 1), C(7, 16) are the threevertices of the parallelogram ABCD.Find the co-ordinates of the fourth vertexD and find its area.

8. Find the equation of a line whose slope is4/5 and which bisects the line joining the

points P(1, 2) and Q(4, –3).

TRIGONOMETRY1. If Secθ + Tanθ = P then show that

2. Show that 3(Sinx – Cosx)4 + 6(Sinx +Cosx)2 + 4(Sin6x + Cos6x) = 13.

3. Prove that

4. Eliminate 'θ' for the following equations.xCosθ + ySinθ = a, xSinθ – y Cosθ = b.

5. If Sinθ = 15/17 then find

STATISTICS1. Find the median of the following

frequency distribution.Class60–64 65–69 70–74 75–79 80–84 85–89Frequency

13 28 35 12 9 32. Find the mean of the data using short-cut

method.Class21–40 41–60 61–80 81–100 101–120Frequency

10 25 40 20 5

MATRICES

1. Given that find

the matrix D, satisfying AD = DA = A.

2. If then show that A(BC) = (AB)C

3.3. If

then show that (AB)–1 = B–1A–1.4. Solve the given equations by using

Cramer's Method4x–y = 16 and 3x–7 / 2 = y

5. Solve the equations by matrix inversionmethod2x–3y+6 = 0, 6x+y+8 = 0.

COMPUTING1. Given the principal amount and the rate

of interest, write an algorithm to obtain atable of simple interest at the end of each

year for 1 to 5 years and draw a flowchart.

2. Execute the flow chart, obtain the totalamount to be paid at the end of 6 years, ifP = Rs. 1000 and r = 12% and also writealgorithm.

3. Explain the structure of a computer bymeans of a block diagram.

4. Find the selling price of an item, giventhe gain percentage and the C.P. of anitem. Execute the flow chart for a gain of25% and C.P. = Rs. 300.

GEOMETRY1. ABCD is a rhombus, prove that

AB2 + BC 2 + CD2 + AD2

= AC2 + BD2.2. In an equilateral triangle with side 'a'

prove that the altitude is

of length

3. If PAB is secant to a circle intersectingthe circle at A and B and PT is a tangentsegment than show that PT2 = PA.PB.

4. Show that the lengths of the two tangentsdrawn from an external point to a circleare equal.

5. ∆ABC is an obtuse triangle, obtuseangled at B. If AD⊥ CB prove that AC2 =AB2 + BC2 + 2BC.BD

6. A vertical stick 12 cm long casts ashadow 8cm long on the ground. At thesame time a tower casts the shadow 40mlong on the ground. Determine the heightof the tower.

7. In a triangle ABC, AD is drawperpendicular to BC. Prove that AB2 –BD2 = AC2 – CD2.

ANALYTICAL GEOMETRY1. Find the point on x-axis that is equi

distant from (2, 3) and (4, –2).2. Find the co-ordinates of the point which

divides the join of (2, –4) and (5, 6) in theratio 5:3 externally.

3. Find the point of intersection of themedians of a triangle whose vertices are(–1, 0), (5, –2) and (8, 2).

4. Find the co-ordinates of the points oftrisection of a segments joining A(–3, 2)and B(9, 5).

5. Find the area of the triangle whosevertices are A(–4, –1), B(1, 2) and C(4,–3).

6. Find the equation of the line passingthrough (1, 1) and is parallel to 4x–5y+3= 0.

7. Find the equation of the line passingthrough (4, –3) and perpendicular to the

3a.

2

2 1 2 0A , B

3 1 5 3

− = = − −

2 4 2 5 1 2A , B , C

3 6 6 1 3 0

− = = =

1 2A ,

3 4

− = −

15Cot 17Sin

8Tan 16Sec

θ + θθ + θ

Tan + Sec 1 1 Sin

Tan Sec 1 Cos

θ θ − + θ=θ − θ + θ

2

2

P 1Sin

P 1

−θ =+

0.234

2

x 0

x 5xLt

x→

+

( )( )( )x

(3x 1) 2x 5Lt

x 3 3x 7→∞

− +− +

3

x 3

x 27Lt

x 3→

−−

MathematicsIMPORTANT QUESTIONS

Prove that alternate segment theorem

4 Marks Questions

2 Marks Questions

Matehmatics Paper-25 Marks Questions


11

line 2x–5y+4 = 0.8. Find the area of the triangle formed by

the line 2x – 4y –7 = 0 with the co-ordinate axis.

TRIGONOMETRY1. If Sinθ = 12/13 then find Cosθ and

Tanθ.2. If Tan(A–B) = 1/√3, SinA = 1/√2 find the

value of θ in circular measure.3. Show that 4(sin4 30 + cos460) –3 (cos245

– sin290) = 2.4. Prove that

5. Eliminate 'θ' x = aSinθ – bCosθ, y =aCosθ + bSinθ.

6. If sec θ =

then find sinθ.7. The angle of depression of a point 100

mts from the foot of the tree is 60°. Findthe height of the tree.

8. Show that (1–sin6θ + cos6θ) = 3sin2θ.cos2θ.

9. Find the value of 32 cot2π/4 – 8sec2π/3 +8cot3π/6.

MATRICES

1. If find order of M

and determine the matrix M.

2. If find m if AB = BA.

3. If show that

A2–(a+d) A = (bc–ad)I

4. If

then find B+A–1.

5. If then show that

A+A–1 = A–1A = I6. If

find x, y.

7. if find 'P'.

STATISTICS1. Write the merits of arithmetic mean.

2. Write the formula for mean by short cutmethod.

3. The mean of 20 observations is 12.5. Byan error, one observation is registered as–15 instead of 15. Find the correct mean.

4. Observation of some data arex/4, x, x/5, x/3, x/2, where x > 0.If the median of the data is 5. Find thevalue of x.

5. The mean and median of uni-modalgrouped data are 39 and 38 respectively.Find the mode.

6. Find the mean of 2/5, 5/3, 1/3, 5/6, 1/6.

COMPUTING1. What are the different boxes used in a

flow chart?2. State any four languages you have to

known, that are used in computers.3. What should be kept in mind while

writing an algorithm?4. Define algorithm and flow chart.5. What is meant by computer?

GEOMETRY1. When two polynomials are similar?2. Define converse of Pythagorian theorem.3. A man goes 150m due east and then

200m due north. How far is he from thestarting point?

4. If two circles of radii 5cm and 6cm. touchexternally, then the length of theirtransverse common tangent is ____

5. Write two conditions of similar triangles.6. Define Appollonius theorem.7. There is a circle of radius 3. From a point

P which is at a distance of 5cm from thecentre of the circle, a tangent is drawn tothe circle. Find the length of the tangent?

8. The circles of radii 5cm and 7cm. touchexternally, find the distance between theircenters.

9. In ∆ ABC, D and E are the points on ABand AC respectively. D is the mid point ofAB and DE||BC find AE/EC.

10. Define converse of alternate segmenttheorem.

ANALYTICAL GEOMETRY1. Find the slope and y-intercept of the line

x/a + y/b = 1.2. Find the slope of the perpendicular to

2x+3y+5 = 0.3. Two end points of the diameter in the

circle are (9, 3) and (1, –1). Find thecenter of the circle.

4. Find the area of the triangle enclosedbetween the co-ordinate axis and the linejoining the points (3, 0) and (0, 4).

5. Write the equation of the line passing

through (3, –5) and slope is 7/3.6. Write the equation of the line passing

through the points (4, –7) and (1, 5).7. Find the equation of the line 60° with the

positive direction of x-axis and having y-intercept is 3.

8. Find the distance between the two pointsA(7, 5) and B(2, 4).

9. Find the equation of the line makingintercepts 4 and –7 on the x and y-axis.

10. Find the equation of the line passingthrough (–2, 3) and making equalintercepts of x and y-axis.

TRIGONOMETRY1. Express the centesimal measure of 5πc/2.2. Eliminate 'θ' from x = 2Sinθ, y = 2Cosθ.3. Find the value of Cos0° + Sin90° + √2

Sin 45°.4. Prove that (Sinθ + Cosθ)2 + (Sinθ –

Cosθ)2 = 2.5. Show that Secθ (1–Sinθ) (Secθ + Tanθ) =

1.6. Find the value of Cot 240°.7. Prove that 1/Cosθ – Cosθ = Tanθ . Sinθ.8. Express Tanθ value interms of Secθ.9. Eliminate 'θ', x = Cosecθ + Cotθ and

y = Cosecθ – Cotθ.10. The radius of a circle is 14 cms. The

angle subtend by an arc of the circle at thecentre is 45°. Find the length of the arc.

MATRICES

1.find the

matrix 'X' satisfying A–B+x = 0.

2. Given find the matrix R

satisfying P+R = I.

3. If find A–1.

4. Define scalar and non-scalar matrices.5. Inverse does not exist the matrix

of

then find 'a'.

6. If find 'd'.

7. If

then find 3A+2B.

8. If find A + AT.

9. Iffind AB.

STATISTICS1. The observations of an ungrouped data are

x1, x2 and 2x1 and x1 < x2 < 2x1. If the mean

and median of the data are each equal to 6.

Find the observations of the data.

2. The sum of the 15 observations is 420then find mean.

3. The mean of 9, 11, 13, P, 18, 19 is P thenfind the value 'P'.

4. The mean of the ungrouped data is 9. Inevery observation multiplied by 3 and 1then find the mean of the new data.

5. Write Median formula for grouped data?6. The mean of 11 observations is 17.5. If an

observation 15 is deleted. Find the meanof the remaining observations.

COMPUTING1. In which bases the ability of the computer

is decided?2. Define Loop?3. Expand C.P.U.4. Draw the structure of computer block

diagram.5. What is meant by hardware?6. What are the different parts of C.P.U.?7. What is computer?

2 4 2 6A , B

6 0 1 3

− − = = −

1 3A

5 6

=

2 4 4 3A , B

6 5 5 7

− = = −

d 2 50

4 2

−=

−

2a 5

6 3

2 3A

5 1

=

3 5P ,

4 2

− = −

1 2 2 4A ; B ,

3 4 3 5

= =

1 3 2 P

0 1 1 1

= − −

3x 2y 6 5 6

2 2x 3y 2 1

+ = − −

7 4A

5 3

=

1 2 2 0A , B

1 3 5 3

= = −

a b 1 0A and I

c d 0 1

= =

1 4 2 mA , B ,

0 1 0 1 / 2

= = − −

( )1 2M 2 3

0 5

× =

m n

2 mn

+

1 CosCosec Cot

1 Cos

+ θ = θ + θ− θ

MathematicsIMPORTANT QUESTIONS

What is Meant by HardWare?

1 Marks Questions

Important symbols

1. Negation2. And3. Or4. Implie5. If and only if6. For all7. For some8. Belongs9. Not belongs10. Subset11. Superset12. Union13. Intersection14. Powerset15. Null set16. Complement of A17. Cartesion product of A, B is18. Identify function19. Discriminant20. Transpose of A21. Inverse of A22. Fistle funciton A to B23. Composite function of f and g24. Sum of first 'n' natural numbers

25. nth term26. Sum of 'n' terms27. Arithmetic mean28. Sum of frequencies

∼∼∧∧∨∨⇒⇒⇔⇔∀∀∃∃∈∈∉∉⊂⊂⊃⊃∪∪∩∩µµφφ

A1 / Ac

A × BI (A)∆∆ or D

A T

A–1

f:A→→BgofΣΣ ntnsnx

ΣΣf or N


12

MathematicsDiscriptionsFormulas

PolynomialsItem

1. (x - α) (–x –β) < 0 ( α < β)2. (x - α) (x–β) > 0 ( α < β)

Explanation/formula1. Solution: α < x < β2. Solution: x < α ∪ x > β

Real Numbers

Item Problem1. Modules of a real number |x|2. |x| = a solution3. |x| ≤ a4. |x| ≥ a

5.

6.m m

n nx a

x aLt

x a→

− =−

n n

x a

x aLt

x a→

− =−

Formula1. |x| = x, if x > 0 = – x if x < 0 = 0 if x = 02. x = a or x = –a3. – a ≤ x ≤ a4. x ≥ a or x ≤ – a

5. nan–1

6. m/n am–n

Progressions

Item1. nth term in A.P.2. Sum of n terms in A.P.3. Arithmetic Mean of a, b4. nth term in G.P.5. Sum of n terms of G.P.

6. Geometric Mean of a, b7. nth term in H.P.8. Harmonic mean of a, b9. Σn10. Σn2

11. Σn3

Explanation / Formula1. tn = a+(n–1) d2. Sn = n/2[2a+(n–1) d] or = n/2 [a + l]3. A.M. = a+b/24. tn = a.rn–1

5. Sn = a(rn –1)/r–1 if r > 0 or= a(1–rn)/1–r if r < 0

6. G.M. = √ab7. tn = 1/a+(n–1) d8. H.M. = 2ab/a+b9. n(n+1)/210. n(n+1) (2n+1)/611. n2 (n+1)2/4

Discoveries in MathematicsTopic

1. Sets; 2. Binominal Theorem ; 3. Arithmetic Triangle ; 4. Σn, Σn3 formula5. Σn2 formula ; 6. Basic proportionality theorem; 7. Analytical Geometry ; 8. Trigonometrty; 9. Statistics ;10. Matrices ;

MathematicianGeorge ComptorNewtonPascalAryabhattaArchimedesThalesRene descartesHipparchusR.A. FisherAuthor Cayley

Analytical GeometryName1. Slope 'm'

2. Distance between two points

3. General equation of line4. Slope of ax+by+c = 05. Mid point6. Division of a segment internally m:n is7. Divisional of a segment externally in

the ratio8. Gradiant or slope form of line9. Slope - intercept form of line10. Slope - point form of line11. Two intercepts form of line12. Two points form of line13. Area of a triangle14. Centroid

Formula1. m = y2–y1/x2–x1

2.

3. ax + by + c = 04. m = –a/b5. (x1+x2/2, y1+y2/2)6. (mx2+nx1/m+n, my2+ny1/m+n)7. (mx2–nx1/m–n, my2–ny1/m+n)

8. y = mx9. y = mx+c10. y–y1 = m(x–x1)11. x/a + y/b = 112. (y–y1) (x2–x1) = (x–x1) (y2–y1)13. 1/2 | x1(y2–y3) + x2(y3–y1) + x3 (y1–y2) | 14. (x1+x2+x3 / 3, y1+y2+y3 / 3)

( ) ( )2 2

2 1 2 1x x y y− + −

Geometry

Item1. Basic proportionality

theorem2. vertical Angle

Bisector theorem3. Pythagorean theorem4. Appolonius theorem5. Circum Center

6. In center7. Centroid8. Orthocenter

Discription1. In ∆ABC, DE || BC then AD/DB = AE/EC

2. In ∆ABC, the Bisector of A intersect BC inD then AB/AC =BD/DC

3. In ∆ABC, right angled at B then AC2 = AB2 + BC2

4. ∆ABC, AD is Median, AN ⊥ BC then AB2 + AC2=2(BD2+AD2)5. Concurrence of perpendicular bisectors of the sides of the

Triangle6. Concurrence point of Angles bisects of the Triangle7. Concurrence of the Medians of a Triangle8. Concurrence of the heights of a Traingle

Matrices

Linear Programming1. Convex set

2. Linear ProgrammingProblem

3. Objective Function

4. Feasible Region5. ISO Profit line

1. x is convex if the line segment joining any two points P, Qin x is contained in x

2. Minimising or Maximising a function f = ax + 1 a, b ∈ R

3. In L.P.P, the expression f = ax+by, which is to be Maximisedor Minimised.

4. A set of points which satisfy all the constraints of L.P.P.5. Any line belonging to the system of parallel lines given by

the objective function for various values of the objectivefunction.

1. A = AT is Symmetric Matrix2. AT = –A is non-Symmetric Matrix.3. If AB = BA = I then B = A–1

4. If A = then

A–1 = 1/ad–bc

5. If number of columns of the matrix A isequal to number of rows of the matrixthen AB is exist.

6. If AX = B then X = A–1B.

d b

c a

− −

a b

c d

Trigonometry1. Sinθ. Cosecθ = 1

Cosθ.Secθ = 1Tanθ.Cotθ = 1

2. Sin2θ + Cos2θ = 1Sec2θ – Tan2θ = 1Cosec2θ – Cot2θ = 1

3. Sin0° = Cos90° = 0Sin 30° = Cos 60° = 1/2Sin 45° = Cos 45° = 1/√2Sin 60° = Cos 30° = √3/2 Sin 90° = Cos0° = 1

4. Range of Sinθ = [–1, 1]Range of Cosθ = [–1, 1]Range of Tanθ = (–α, α)

Statistics1. Ungrouped data mean = Σx/n2. Grouped data mean = Σfx/N3. By-short cut method mean =

4. Grouped data median =

5. Grouped data mode =

6. The relation between Mean, Median andMode isMode = 3 Median – 2 Mean.

( )( )

11

1 2 1 2

f f CCL or L

2f f f

−∆+ +∆ + ∆ − +

fdA C

N

Σ+ ×

N / 2 FL C

f

−+ ×

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