1. The domain of the function is
2. If f(x) : R R _ satisfies the condition f(x + y) = f(x) + f(y) for all x, y R _ then f(x) is
3. If the sum of n terms of an A.P. is then nth term of the A.P. is____
4. If i 2j 3k,3i 2j k _ _ _ _ are sides of a parallelogram then a unit vector parallel to one of the diagonals of the parallelogram is
5. The vectors AB 3i 4k _ _ and AC 5i 2j 4k _ _ _ are the sides of a triangle ABC, then length of the median through A is
6. The length of the longer diagonal of the parallelogram constructed on 5a 2b and a 3b. _ If it is given that a 2 2 b 3 _ _ and (a, b) _ is ___
7. If a 3i 5j _ _ and b 6i 3j _ _ are two vectors and c is a vector such that c a b _ _ then a : b : c _
8. Let ai bj ck, bi c j ak _ _ _ _ _ _ _ _ and ci a j bk __ _ _ be three coplanar vectors with a b _ , and V i j k _ _ _ then V is perpendicular to
9. If the roots of the equation ax2 + ax + c = 0 are in the ratio p : q then
10. If the roots of the equation x2 – 2ax + a2 + a – 3 = 0 are real and less than 3, then
11. If , , _ _ _ are the roots of the equation x3 + 4x + 1 = 0 then =
12. If A and 3 A 125 _ , then the value of _ is
13. If A is a matrix such that trace (A) = 0 then values of x are
14. Inverse of a skew symmetric matrix of odd order is
15. If the system of equations x+2y+3z= x _ , 3x+y+2z= y _ , 2x+3y+z= z _ has non trivial solution then _=
16. The rank of is
17. A polygon has 44 diagonals, the number of its sides are
18. How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions
19. The number of rational terms in the expansion of _ _ is
20. The coefficient of x6 in is
24. If A is a square matrix such that A(adj A) = 4(I3). Then adj(adj A) = ____
25. If _ , then (J~ò#) 2 n1 cos cos 2 .cos 2 ……..cos 2 _ _ _ _ _ =
26. If , , , _ _ _ _ are solutions of the equation tan 3tan 3 _ , no two of which have equal tangents then the value of tan tan tan tan _ _ _ _ _ _ _ = tan 3tan 3
27. The most general value of _ satisfying 3 tan tan 2 4 is
28. In a ABC _ if A = tan–12, B = tan–13 then C =
29. If x is an acute angle and x y log tan then cosx.coshy =
30. A tree is broken by wind, its upper part touches the ground at a point 10 meters from the foot of the tree and makes an angle 450 with the ground the entire length of the tree is
31. If then triangle ABC is
32. If in ABC _ , the altitudes are in A.P then sides are in
33. If x2 + x + 1 = 0 then the value of
34. If _ and _ are roots of x2 – 2x + 4 = 0 then n n _ _ _ =
35. If 5 3 3 5 sin 6 a cos sin b cos sin c cos sin _ _ _ _ _ _ _ _ _ _ then a + b + c =
36. If the axes are shifted to the point (1, –2) with out rotation then transformed form of y2–4x+4y+8=0 is
37. The equation to the base of an equilateral triangle is 3x – 4y + 15 = 0 and one vertex is (1, 2) then the length of the side is
38. The vertices of a triangle are (0, 0), _ _ _ _ 3,3 , 3,3 _ then the incentre is
39. If (– 4, 5) is one vertex and 7x – y + 8 = 0 is one diagonal of a square then equation of the second diagonal is
40. The distance of the point (2, 3) from the line 2x – 3y + 9 = 0 measured along a line x – y + 1 = 0
41. The distance from a point _ _ , _ _ to a pair of lines passing through the origin is d then equation to the pair of lines is
42. The circum radius of the triangle ABC with vertices A(2, –1, 1), B(1, –3, –5), C(3, –4,–4) is
43. If the line joining the points (2, 3, 4), (0, 1, 2) is perpendicular to the line joining the points (x, 0, 4), (7, –4, 3) then x =
44. The equation of the perpendicular bisecting plane of the line segment joining (–3, 1, 2), (7, 5, 4) is
45. If the lengths of the tangents from two points A, B to a circle are 6,7 respectively. If A, B are conjugate points then AB =
46. If the circle x2 + y2 + 4x + 22y + c = 0 bisects the circumference of the circle x2 + y2 – 2x + 8y–d= 0 then c + d =
47. If (1, 2), (4, 3) are the limiting points of a coaxal system then the equation of the circle in its conjugate system having minimum area is
48. If (2, 3, 5) is the one end of a diameter of a sphere x2 + y2 + z2 – 6x – 12y – 2z + 20 = 0 then the other end of diameter is
49. If PSP| is a focal chord of a parabola y2 = 4ax and SL is its semi latusrectum then SP, SL, SP| are in
50. The condition that the line y = mx + C be the tangent to the parabola y2 = 4a(x + a) is
51. If the latus rectum LL| subtends a right angle at the centre of the ellipse then e =
52. Product of the perpendiculars from any point on hyperbola _ _ to its asymptotes is
53. The equation represents an ellipse if
54. The angle between the circles r a cos( ), f bsin( ) _ R _B _ R _B is
55. The quadratic equation whose roots are ,m _ where 3sin 4sin Lt and 2 tan m Lt 1 tan R is
56. The points of discontinuity of f(x) = log x are
57. I : If f(x) = _ , then (J~ò#) f | (a) = 0.
II : If f(x) = x – x2 + x3 – x4 + ……. _, x 1 _ , then (J~ò#) f | (x) = _ _2
58. If y = sin x sin x sin x ….. _ _ _ __ then (J~ò#)
59. The function f(x) 1 sin x _ is
60. If u sin x y then (J~ò#) xux + yuy =
61. The radius of a circular plate is increasing at the rate of 0.01 cm/sec when radius is 12 cm, then the rate of increase in its area is
sq. cm/sec
62. If there is an error of 0.05 cm while measuring the side of an equilateral triangle as ‘a’ cm. Then the percentage error in area is
63. The sub tangent, ordinate and sub normal to the parabola y2 = 4ax at a point different from origin are in
64. The perimeter of a sector is given the area is maximum when the angle of sector is
65. If y = xn–1 logx then (J~ò#) yn =
70. If _ _ then (J~ò#) _ _
71. The area enclosed between the curves y2 = x and y = x is
72. Solution of differential equation _ _ _ _ 2 2 2 2 y xy 2x y dx x xy x y dy 0 _ _ _ _ is
73. The solution of given y = 0, x = 1 is
74. A fair die is rolled, the probability that the 1st time 1 occurs at even throws is
75. A bag contains 4 balls, two balls are drawn and found to be white, the probability that all the balls are white is
76. If the range of the random variable X is {0, 1, 2, 3 ……..} with P(X = K) = , for K 0 _ then a =
77. Out of 10,000 families with 4 children each the probable number of families all of whose children are daughters is
78. _ for 0 x 1 _ _ and the interval (0, 1) is divided into 2 equal subintervals using trapezoidal rule, the value of _ _ is
80. Assertion (A) : The unknown coefficient of the equation x2 + bx + 3 = 0 is determined by throwing an ordinary six faced die, then the probability that the equation has real root is 1/2.
Reason (R) : For the quadratic equation ax2 + bx + c = 0 condition for real roots is b2 – 4ac _0.
The the correct answer is
Ans: A and R are true and R is the correct explanation of A.
Answers:
1) 4 2) 3 3) 2 4) 1 5) 3 6) 3 7) 2 8) 4 9) 1 10) 1
11) 3 12) 3 13) 1 14) 4 15) 1 16) 4 17) 3 18) 3 19) 3 20) 1
21) 2 22) 3 23) 3 24) 1 25) 1 26) 4 27) 1 28) 2 29) 3 30) 3
31) 1 32) 3 33) 4 34) 2 35) 4 36) 3 37) 1 38) 1 39) 1 40) 4
41) 3 42) 3 43) 2 44) 1 45) 2 46) 2 47) 3 48) 2 49) 3 50) 1
51) 4 52) 1 53) 3 54) 3 55) 2 56) 3 57) 3 58) 2 59) 3 60) 2
61) 1 62) 3 63) 2 64) 2 65) 3 66) 2 67) 1 68) 1 69) 4 70) 1
71) 3 72) 1 73) 1 74) 2 75) 2 76) 2 77) 1 78) 3 79) 2 80) 1