AMU –PAST PAPERSMATHEMATICS - UNSOLVED PAPER - 2000
SECTION – I   CRITICAL REASONING SKILLS
01   Problem     Let A = {1, 2, 3, 4} and let R = {(2, 2), (3, 3,), (4, 4), (1, 2)} be a relation on A. Then     R is     ...
02   Problem     The equation of family of curve for which the length of the normal is equal to the     radius vector is :...
03   Problem                       dy     y = eax cos bx,   dx                            equals :     a. eax (a cos bx + ...
04   Problem                       dy   ax   h     The solution of                 represents a parabola when :           ...
05   Problem                                                 2     The equation x          2a            a(1       )   whe...
06    Problem     Let z be the set of integers and 0 be binary operation of z defined as a 0 b =a + b -     ab for all a, ...
07   Problem     Which term of the G.P. 2,2   2   , 4, ….. is 64 :     a. 9th term     b. 7th term     c. 4th term     d. ...
08   Problem     If two events a and b such that a – b = 6, then the solution of m x a = b for m is :     a. Unique     b....
09   Problem                                         x3     The value of           sin x    x        is :                 ...
10   Problem              cos x equals :     lim     x          2   x                  2     a. - 6     b. - 1     c.     ...
11   Problem              kx 2 ,   if x   2   If (x) is continuous at x = 2, then the value of k :     f (x)              ...
12   Problem                                           f (m)   f (n)     For which of the following function      m    n  ...
13   Problem     If x and y are two unit vectors and   is the angle between them, then   |x       y|                      ...
14   Problem                                                                                                     ...
15   Problem     the general solution of the equation, 3(sin   cos ) (sin   cos ) 2 is :     a.   2n                4     ...
16   Problem                                 1/2   x sin 1 x     The value of the integral                      dx, is    ...
17   Problem     Suppose that the velocity of a moving particle is = 30 – 2t m/sec. The total     distance in metres it tr...
18   Problem                                                  9 2     The least value of the function f (x)   4x         s...
19   Problem     The distance between the line 3x + 4y = 9 and 6x + 8y = 15, is :          3     a.          2           3...
20   Problem     The angel between the tangent from the point (4, 3) to the circle x2 + y2 –2x – 4y     = 0 is :     a. 30...
21   Problem     The value of                dx             is :                           2     4        3/4             ...
22   Problem     If standard deviation of a variate x is   , then standard deviation of   ax  b                           ...
23   Problem     The value of the determinant   x   1   x   2    x   4    is :                                    x   3   ...
24   Problem     Given 12 points in a plane, no three of which are collinear. Then number of line     segments can be dete...
25   Problem     There are 10 true-false questions in a examination. Then these questions can be     answered in :     a. ...
26   Problem                  1   2     The value of ex dx lies in the interval :                 0     a. [0, 1]     b. [...
27   Problem     If 30Cn + 2 = 30Cn - 2, then n equals :     a. 8     b. 15     c. 30     d. 32
28   Problem           |x   a | equals :     lim     x   a  x   a     a. 2     b. - 1     c. 1     d. 0
29   Problem     If x, y, z are positive integers then (x + y) (y + z) (z + x) is :     a. < 8xyz     b. = 8xyz     c. > 8...
30   Problem     The nth term of the series, 1 + 3 + 6 + 10 …….. is :          n(n 1)     a.             2          n     ...
31   Problem     If cos , cos , cos     are direction cosines of line, then value of     sin2     sin2   sin2     is :    ...
32   Problem     The line lx + my + n = 0 touches the circle x2 + y2 = 1 if :                     1     a. l2 + m2 =      ...
33   Problem     The value of       /2                             ( tan x   cot x )dx, is                    0     a.    ...
34   Problem                                 If     a        3i   ˆ                          k, b   ˆ                   ...
35   Problem     Forces acting on a particle are represented in magnitude and direction by the                        ...
36   Problem     The value of a third order determined is 5, then this value of the square of the     determinant formed b...
37   Problem     Out of 40 consecutive integers, two are chosen at random, the probability that     their sum is odd is : ...
38   Problem     an anti-aircraft gun takes a maximum of four shots at an enemy plane moving     away from it. The probabi...
39   Problem     The area enclosed by the curve y2 = x2 (1 – x2) is :          1     a.   3   sq. units     b.   2   sq. u...
40   Problem     The value of cos 200 -   2 cot 200 is :     a. 0     b. -1     c. 2     d. 3
41   Problem     The function f(x) = x4 – 62x2 + ax + 9 attains its maximum value in the interval     [0, 2] at x = 1. The...
42   Problem     If     ,   are the roots of the quadratic equation ax2 + bx + c = 0, then          2       2             ...
43   Problem     Two equals circle of radius r intersect such that each passes through the centre of     the other. The le...
44   Problem     The angle of intersection of the curves y = x2, 6y = 7- x3 at (1, 1) is :     a.          4     b.       ...
45   Problem     The maximum value of   sin x       cos x       in the interval   0,       is attained                    ...
46   Problem     Origin is a limiting point of a coaxial system of which x2 + y2 – 6x – 8y + 1 = 0 is a     member. The ot...
47   Problem     A vector has constant magnitude but its direction varies with time. The derivative     of such a vector i...
48   Problem                                         2           3                           a b   1 a b       1 a b     S...
49   Problem     If one vertex of an equilateral triangle is at (2, - 1) and the base is x + y – 2 =     0, then the lengt...
50   Problem     The eccentricity of an ellipse whose pair of a conjugate diameter are y = x and 3y     = -2x is     a. 2 ...
51   Problem     (8C1 + 8C2 + 8C3 - 8C4 + 8C5 - 8C6 + 8C7 ) equals :     a. 0     b. 1     c. 70     d. 256
52   Problem     The equation of the circle which has its centre at (a, b) and which touches the y-     axis is :     a. x...
53   Problem     The focus of the parabola y2 – 4y – 8x + 4 = 0 is :     a. (1, 1)     b. (1, 2)     c. (2, 1)     d. (0, 2)
54   Problem     Two dice are tossed 6 times. Then the probability that 7 will show an exactly four     of the tosses is :...
55   Problem     The standard deviation of 7, 9, 11, 13, 15 is :     a. 2.82     b. 2.4     c. 2.7     d. 2.5
56   Problem                                               x     The period of the function f(x) = 2 sin       2          ...
57   Problem     If A is a square matrix of order n x n and   is scalar. Then Adj (A ) is equal to :     a. (Adj.A)    n  ...
58   Problem                                   cos 1 x     The domain of         f (x)             is :                   ...
59   Problem     If z is a complex number, then arg z + arg ( z)is equal to :     a. 0     b. 2     c.          2     d.   4
60   Problem     If p, q are the roots of the equation. x2 + mx + m2 + a = 0, then p2 + pq + p2 + a will     be equal to :...
61   Problem     The co-ordinate of the centre of the sphere, 2x2 + 2y2 + 2z2 – 4x + 6y – 8z – 10 = 0     are :     a.    ...
62   Problem     A point moves so that its distance from the x-axis half of its distance from the     origin. The equation...
63   Problem                         x    x2   x3     If x       y   z and y   y2   y3   0   , then xyz is equal to :     ...
64   Problem     On the set I, binary operation * is defined as follows : a*b = a + b + 1 Then     identity element of the...
65   Problem     If n is a positive integer, then (n + 1) (n + 2) (n + 3) ………..(2n) is a multiple of :     a. 2n     b. 2(...
66   Problem     P.I. of the differential equation (D2 – 4D + 3) y = ex, is :     a.     b. ex                1     c.   2...
67   Problem                                        x       1   y   z       1         x       4   y   z   z       5     Th...
68   Problem     The area bounded by the parabola y = 2 - x2 and the line x + y = 0 is :          9     a.   2          7 ...
69   Problem     If f (x)    x         (1   t)       then f(x) is :                     log           dt,                 ...
70   Problem     The pedal equation of the curve r 2   a2 cos 2   is :     a. p = ar3     b. a2p = r3     c. p2 = ar3     ...
71   Problem                                                           n                                                  ...
72   Problem     If   is the angle between the plane 4x – y – 12 = 1 and the line whose direction     ratio’s are (1, -1, ...
73   Problem                                                           A straight line    r   a   b   meets the plane...
74   Problem     The arithmetic mean of a set of observations is . If each observation is divided by     then is increased...
75   Problem     The maximum area of rectangle inscribed in a circle of diameter R is :     a. R2          R2     b.   2  ...
76   Problem                                                                           Let holds a     (ˆ           ...
77   Problem     The equation whose roots are twice the roots of the equation, x2 – 3x + 3 = 0 is :     a.   4x2 + 6x + 3 ...
78   Problem                                     x   3 7     If (x + 9) = 0 is a factor of   2   x   2   = 0, then the oth...
79   Problem     If cos         sin   2 cos , then cos   sin   is equal to :     a.   2   sin     b.   2   cos     c.   2 ...
80   Problem     The total number of ways of selecting six coins out of 20 one rupee coins, 10     fifty paise coins an 7 ...
81   Problem     The sum of the coefficients of the polynomial (1+x3x2)2143is :     a. 1     b. -1     c. 0     d. 2
82   Problem     The radius of the incircle triangle whose sides are 18, 24 and 30 cm is:     a. 2cms     b. 4cms     c. 6...
83   Problem     The equations of tangent to the hyperbola 4x2-3y2=24 which make an angle of     600 with x-axis are:     ...
84   Problem     Suppose n people enter a chess tournament in which each person is to play one     game against each of th...
85   Problem     If the sides of a triangle are 7cm, 4 3 cm and   13   cm, then the smallest angel of     the triangle is ...
86   Problem     A curve has the parametric equation x-         t2   1    and y= b t 2 1 , then                           ...
87   Problem                                        1   4    20     The solution set of the equation   1    2    5     0  ...
88   Problem     If a square matrix satisfies the relation A2+A-I=0 then A-1     a. Exists and equals I+A     b. Exists an...
89   Problem          2           2                              equals :      axb         b   a     a. 0           ...
90   Problem     If x        then the (r+1)th term the expansion of (1-x)2 is :     a. (r+1)xr     b. rxr-1     c. rx-r+1 ...
91   Problem     When m varies, the locus of the point of intersection of the straight lines       x   y               x  ...
92   Problem                                             1   sin x   cos x     The differential coefficient of   tan      ...
93   Problem     The coefficient of correlation between x and y ;     x : 65     66       67        67        69         7...
94   Problem     the length of the subnormal at the point (1, 3) of the curve, y = x2 + x + 1 is :     a. 1     b. 3     c...
95   Problem     The differential equation y dy             x      a (a is any constant) represents :                     ...
96   Problem                                        1     2     3     4     The value of the infinte series               ...
97   Problem     Distance between the parallel planes 2x – y + 3z + 4 = 0 and 6x – 3y + 9z –3 = 0 is     :           5    ...
98   Problem     Three numbers m + 2, 4m –6, 3m – 2 are in A.P. in m equals to :     a. 3     b. 2     c. 1     d. 0
99   Problem     The first derivative of the expression (xx + ax) is :     a. xx log x + ax log e     b. xx log x + ax log...
100   Problem      Counters marked 1, 2, 3 are placed in a bag and one is drawn and replaced. The      operation is repeat...
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  • AMU - Mathematics - 2000

    1. 1. AMU –PAST PAPERSMATHEMATICS - UNSOLVED PAPER - 2000
    2. 2. SECTION – I CRITICAL REASONING SKILLS
    3. 3. 01 Problem Let A = {1, 2, 3, 4} and let R = {(2, 2), (3, 3,), (4, 4), (1, 2)} be a relation on A. Then R is a. Reflexive b. Symmetric c. Transitive d. None of these
    4. 4. 02 Problem The equation of family of curve for which the length of the normal is equal to the radius vector is : a. y2 x2 = k2 b. y x=k c. y2 = kx d. none of these
    5. 5. 03 Problem dy y = eax cos bx, dx equals : a. eax (a cos bx + b sin ax) b. eax (a cos bx - b sin ax) c. eax (a sin bx + b sin ax) d. eax (a sin ax - a cos ax)
    6. 6. 04 Problem dy ax h The solution of represents a parabola when : dx by k a. a = 1, b = 2 b. a = 0, b = 0 c. a = 0, b 0 d. a = 2, b = 1
    7. 7. 05 Problem 2 The equation x 2a a(1 ) where a is constant in the parametric 2 ,y 2 1 1 equation of the curves : a. x2 + y2 = - a2 b. x2 - y2 = a2 c. x2 + y2 = a2 d. x2 + y2 - 2a2 = 0
    8. 8. 06 Problem Let z be the set of integers and 0 be binary operation of z defined as a 0 b =a + b - ab for all a, b z. The inverse of an element a( 1) z is : a a. a 1 b. 1 1 a c. a 1 a d. none of these
    9. 9. 07 Problem Which term of the G.P. 2,2 2 , 4, ….. is 64 : a. 9th term b. 7th term c. 4th term d. 11th term
    10. 10. 08 Problem If two events a and b such that a – b = 6, then the solution of m x a = b for m is : a. Unique b. Does not exist c. Exist when a b d. None of these
    11. 11. 09 Problem x3 The value of sin x x is : lim 6 x 0 x5 a. 0 b. 1 60 c. 1 120 d. 1
    12. 12. 10 Problem cos x equals : lim x 2 x 2 a. - 6 b. - 1 c. d. -
    13. 13. 11 Problem kx 2 , if x 2 If (x) is continuous at x = 2, then the value of k : f (x) 3, if x 2 a. 2 b. 3 2 c. 3 3 d. 4
    14. 14. 12 Problem f (m) f (n) For which of the following function m n is constant for all numbers m and n m n: a. f(x) = log x b. f (x) = cos x c. f(x) = 4x + 7 d. f(x) = x2 + 1
    15. 15. 13 Problem If x and y are two unit vectors and is the angle between them, then |x y| 2 is equal to a. | sin | sin b. 2 c. | 2 sin | cot 2 d.
    16. 16. 14 Problem          a.(b x c ) b.(a x c ) If a, b, c are non-coplanar vector, then       is equal to : (c x a).b c.(a x b) a. 0 b. 1 c. 2 d. 13
    17. 17. 15 Problem the general solution of the equation, 3(sin cos ) (sin cos ) 2 is : a. 2n 4 3 b. 2n 4 12 c. 2n 4 3 d. 2n 6 12
    18. 18. 16 Problem 1/2 x sin 1 x The value of the integral dx, is 0 2 1 x a. 1 3 2 2 1 b. 2 12 3 c. 1 3 2 12 1 3 d. 2 2
    19. 19. 17 Problem Suppose that the velocity of a moving particle is = 30 – 2t m/sec. The total distance in metres it travels between the times t = 0 and t = 20 seconds is : a. 200 b. 225 c. 250 d. 275
    20. 20. 18 Problem 9 2 The least value of the function f (x) 4x sin x is : x a. 10 -1 b. 11 -1 c. 12 -1 d. 14 -1
    21. 21. 19 Problem The distance between the line 3x + 4y = 9 and 6x + 8y = 15, is : 3 a. 2 3 b. 10 c. 6 d. none of these
    22. 22. 20 Problem The angel between the tangent from the point (4, 3) to the circle x2 + y2 –2x – 4y = 0 is : a. 300 b. 450 c. 600 d. 900
    23. 23. 21 Problem The value of dx is : 2 4 3/4 x (x 1) 1/4 a. 1 1 c x4 b. (x4 + 1)1/4 + c 1/4 1 c. - 1 c x4 1/4 1 d. 1 c x4
    24. 24. 22 Problem If standard deviation of a variate x is , then standard deviation of ax b c where a,b,c are constant is : a. a c c b. a 2 c. c a b d. c
    25. 25. 23 Problem The value of the determinant x 1 x 2 x 4 is : x 3 x 5 x 8 x 7 x 10 x 14 a. - 2 b. x2 + 2 c. 2 d. 3
    26. 26. 24 Problem Given 12 points in a plane, no three of which are collinear. Then number of line segments can be determined, are : a. 76 b. 66 c. 60 d. 80
    27. 27. 25 Problem There are 10 true-false questions in a examination. Then these questions can be answered in : a. 100 ways b. 20 ways c. 512 ways d. 1024 ways
    28. 28. 26 Problem 1 2 The value of ex dx lies in the interval : 0 a. [0, 1] b. [1, 2] c. [1, e] d. [1, 3]
    29. 29. 27 Problem If 30Cn + 2 = 30Cn - 2, then n equals : a. 8 b. 15 c. 30 d. 32
    30. 30. 28 Problem |x a | equals : lim x a x a a. 2 b. - 1 c. 1 d. 0
    31. 31. 29 Problem If x, y, z are positive integers then (x + y) (y + z) (z + x) is : a. < 8xyz b. = 8xyz c. > 8xyz d. none of these
    32. 32. 30 Problem The nth term of the series, 1 + 3 + 6 + 10 …….. is : n(n 1) a. 2 n 1 b. 2 c. n(n 1) 2 d. n 1 2
    33. 33. 31 Problem If cos , cos , cos are direction cosines of line, then value of sin2 sin2 sin2 is : a. 1 b. 2 c. - 1 d. 3
    34. 34. 32 Problem The line lx + my + n = 0 touches the circle x2 + y2 = 1 if : 1 a. l2 + m2 = n2 b. l2 + m2 = 2n2 n2 c. l2 + m2 = 2 d. l2 + m2 = n2
    35. 35. 33 Problem The value of /2 ( tan x cot x )dx, is 0 a. 2 b. 2 c. 2 d. 2
    36. 36. 34 Problem   If a 3i ˆ k, b ˆ i 2ˆ j are and joint sides of a parallelogram, then its area is : a. 1 17 2 1 b. 7 2 c. 41 1 d. 41 2
    37. 37. 35 Problem Forces acting on a particle are represented in magnitude and direction by the       sides AB,BC ,CD, and DE , of regular pentagon ABCDE. The resultant of there forces is : a. EA b. AE c. AE 5 d. EA 5
    38. 38. 36 Problem The value of a third order determined is 5, then this value of the square of the determinant formed by its co-factors will be : a. 125 b. 250 c. 25 d. 5
    39. 39. 37 Problem Out of 40 consecutive integers, two are chosen at random, the probability that their sum is odd is : a. 14 29 21 b. 29 22 c. 39 20 d. 39
    40. 40. 38 Problem an anti-aircraft gun takes a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane is : a. 0.2412 b. 0.21 c. 0.16 d. 0.6976
    41. 41. 39 Problem The area enclosed by the curve y2 = x2 (1 – x2) is : 1 a. 3 sq. units b. 2 sq. units 3 c. 1 sq. units 4 d. 3 sq. units
    42. 42. 40 Problem The value of cos 200 - 2 cot 200 is : a. 0 b. -1 c. 2 d. 3
    43. 43. 41 Problem The function f(x) = x4 – 62x2 + ax + 9 attains its maximum value in the interval [0, 2] at x = 1. Then the value of a is : a. 120 b. - 120 c. 52 d. 102
    44. 44. 42 Problem If , are the roots of the quadratic equation ax2 + bx + c = 0, then 2 2 2 equals : a. 0 bc b. a2 c. Abc c(a b) d. a2
    45. 45. 43 Problem Two equals circle of radius r intersect such that each passes through the centre of the other. The length of the common chord is : a. 2 b. 2r c. 3 r d. 3
    46. 46. 44 Problem The angle of intersection of the curves y = x2, 6y = 7- x3 at (1, 1) is : a. 4 b. 3 c. 2 d.
    47. 47. 45 Problem The maximum value of sin x cos x in the interval 0, is attained 6 6 2 at : a. 12 b. 6 c. 3 d. 2
    48. 48. 46 Problem Origin is a limiting point of a coaxial system of which x2 + y2 – 6x – 8y + 1 = 0 is a member. The other limiting point is : a. (- 2, - 4) 3 4 , b. 25 25 3 4 , c. 25 25 4 3 d. , 25 25
    49. 49. 47 Problem A vector has constant magnitude but its direction varies with time. The derivative of such a vector is always : a. 0 b. perpendicular to itself c. parallel to itself d. a unit of vector
    50. 50. 48 Problem 2 3 a b 1 a b 1 a b Sum of the series : ..... is : a 2 a 3 a a. log a – log b b. log (a - b) c. e(a - b)/a –1 d. e1 – b/a
    51. 51. 49 Problem If one vertex of an equilateral triangle is at (2, - 1) and the base is x + y – 2 = 0, then the length of each side is : a. 3 2 b. 2 3 c. 2 3 d. 3 2
    52. 52. 50 Problem The eccentricity of an ellipse whose pair of a conjugate diameter are y = x and 3y = -2x is a. 2 3 b. 1 3 1 c. 3 2 d. 3
    53. 53. 51 Problem (8C1 + 8C2 + 8C3 - 8C4 + 8C5 - 8C6 + 8C7 ) equals : a. 0 b. 1 c. 70 d. 256
    54. 54. 52 Problem The equation of the circle which has its centre at (a, b) and which touches the y- axis is : a. x2 + y2 = b2 b. (x - a)2 + (y - b)2 = b2 c. x2 + y2 = a2 d. (x - a)2 + (y - b)2 = a2
    55. 55. 53 Problem The focus of the parabola y2 – 4y – 8x + 4 = 0 is : a. (1, 1) b. (1, 2) c. (2, 1) d. (0, 2)
    56. 56. 54 Problem Two dice are tossed 6 times. Then the probability that 7 will show an exactly four of the tosses is : 225 a. 18442 116 b. 20003 125 c. 15552 117 d. 17442
    57. 57. 55 Problem The standard deviation of 7, 9, 11, 13, 15 is : a. 2.82 b. 2.4 c. 2.7 d. 2.5
    58. 58. 56 Problem x The period of the function f(x) = 2 sin 2 is : a. b. 2 c. 3 d. 6
    59. 59. 57 Problem If A is a square matrix of order n x n and is scalar. Then Adj (A ) is equal to : a. (Adj.A) n b. (Adj.A) -n c. (Adj.A) n-1 d. none of these
    60. 60. 58 Problem cos 1 x The domain of f (x) is : [x] a. [-1, 1] b. [-1, 0] c. [-1, 0] {1} d. [- 1, - 1]
    61. 61. 59 Problem If z is a complex number, then arg z + arg ( z)is equal to : a. 0 b. 2 c. 2 d. 4
    62. 62. 60 Problem If p, q are the roots of the equation. x2 + mx + m2 + a = 0, then p2 + pq + p2 + a will be equal to : a. 0 b. 1 c. - m d. m2 + a
    63. 63. 61 Problem The co-ordinate of the centre of the sphere, 2x2 + 2y2 + 2z2 – 4x + 6y – 8z – 10 = 0 are : a. 3 ,1, 2 2 3 b. 1, ,2 2 3 c. 1,2, 2 3 d. ,2,1 2
    64. 64. 62 Problem A point moves so that its distance from the x-axis half of its distance from the origin. The equation of its locus is ; a. x2 = 2y2 b. x2 = 3y2 c. x = 2y d. 2x = y
    65. 65. 63 Problem x x2 x3 If x y z and y y2 y3 0 , then xyz is equal to : z z2 z3 a. 1 b. -1 c. 0 d. x + y + z
    66. 66. 64 Problem On the set I, binary operation * is defined as follows : a*b = a + b + 1 Then identity element of the group (I, *) is : a. 1 b. -1 c. 0 d. 2
    67. 67. 65 Problem If n is a positive integer, then (n + 1) (n + 2) (n + 3) ………..(2n) is a multiple of : a. 2n b. 2(n + 1) c. 2(n + 1) d. 2n
    68. 68. 66 Problem P.I. of the differential equation (D2 – 4D + 3) y = ex, is : a. b. ex 1 c. 2 ex e 4e 3 d. 1 xe x 2
    69. 69. 67 Problem x 1 y z 1 x 4 y z z 5 The value of for which the lines and , 2 3 4 3 3 are perpendicular is : a. 6 b. 1 6 c. - 6 1 d. - 6
    70. 70. 68 Problem The area bounded by the parabola y = 2 - x2 and the line x + y = 0 is : 9 a. 2 7 b. 2 17 c. 6 34 d. 7
    71. 71. 69 Problem If f (x) x (1 t) then f(x) is : log dt, 0 (1 t) a. An odd function b. A period function c. A symmetric function d. None of these
    72. 72. 70 Problem The pedal equation of the curve r 2 a2 cos 2 is : a. p = ar3 b. a2p = r3 c. p2 = ar3 d. p = a2r3
    73. 73. 71 Problem n px 1 5 If the 4th term in the binomial expansion of is , then : x 2 a. n = 8, p = 6 1 b. n = 8, p = 2 1 c. n = 6, p = 2 d. n = 6, p = 6
    74. 74. 72 Problem If is the angle between the plane 4x – y – 12 = 1 and the line whose direction ratio’s are (1, -1, 1) then sin given by : a. 3 6 6 b. 3 3 c. 2 3 d. 6
    75. 75. 73 Problem      A straight line r a b meets the plane r n 0 in P. The position vector of P is :    a n a. a  b b n   b.  a n a  b b n   c.  a n a  a b n    a n  d. a  a b n
    76. 76. 74 Problem The arithmetic mean of a set of observations is . If each observation is divided by then is increased by 10, then the man of the new series is : a. x b. x 10 c. x 10 d. x 10
    77. 77. 75 Problem The maximum area of rectangle inscribed in a circle of diameter R is : a. R2 R2 b. 2 R2 c. 4 R2 d. 8
    78. 78. 76 Problem       Let holds a (ˆ i ˆ j ˆ) and b pk (ˆ i j ˆ ˆ k ) then| a b | | a | | b | for : a. p = - 1 b. p = 1 c. all real p d. no real p
    79. 79. 77 Problem The equation whose roots are twice the roots of the equation, x2 – 3x + 3 = 0 is : a. 4x2 + 6x + 3 = 0 b. 2x2 - 3x + 3 = 0 c. x2 - 3x + 6 = 0 d. x2 - 6x + 12 = 0
    80. 80. 78 Problem x 3 7 If (x + 9) = 0 is a factor of 2 x 2 = 0, then the other factor is : 7 6 x a. (x - 2) (x - 7) b. (x - 2) (x - a) c. (x + 9) (x - a) d. (x + 2) (x + a)
    81. 81. 79 Problem If cos sin 2 cos , then cos sin is equal to : a. 2 sin b. 2 cos c. 2 tan d. 2 sec
    82. 82. 80 Problem The total number of ways of selecting six coins out of 20 one rupee coins, 10 fifty paise coins an 7 twenty five paise coins is : a. 37C 6 b. 56 c. 28 d. 29
    83. 83. 81 Problem The sum of the coefficients of the polynomial (1+x3x2)2143is : a. 1 b. -1 c. 0 d. 2
    84. 84. 82 Problem The radius of the incircle triangle whose sides are 18, 24 and 30 cm is: a. 2cms b. 4cms c. 6cms d. 9cms
    85. 85. 83 Problem The equations of tangent to the hyperbola 4x2-3y2=24 which make an angle of 600 with x-axis are: a. y 3x 10 b. y 10x 3 c. y 10x 3 y 3x 3 d.
    86. 86. 84 Problem Suppose n people enter a chess tournament in which each person is to play one game against each of the others. The total number of games that will be played in the tournament is : n n 1 a. 2 n n 1 b. 2 c. n(n+1) d. n(n-1)
    87. 87. 85 Problem If the sides of a triangle are 7cm, 4 3 cm and 13 cm, then the smallest angel of the triangle is : a. 150 b. 450 c. 300 d. 600
    88. 88. 86 Problem A curve has the parametric equation x- t2 1 and y= b t 2 1 , then 2t 2t its equation in rectangular Cartesian co-ordinate is : x2 y2 a. a2 14 b2 b. x2+y2=a2b2 c. b2x2-a2y2=a2b2 d. none of these
    89. 89. 87 Problem 1 4 20 The solution set of the equation 1 2 5 0 is : 1 2x 5x 2 a. {0,1} b. {1,2} c. {1,5} d. {2,-1}
    90. 90. 88 Problem If a square matrix satisfies the relation A2+A-I=0 then A-1 a. Exists and equals I+A b. Exists and equals I-A c. Exists and equals A2 d. None of these
    91. 91. 89 Problem   2   2 equals : axb b a a. 0   a.b b. 2 2 c. 2 a .b 2 2 d. a .b
    92. 92. 90 Problem If x then the (r+1)th term the expansion of (1-x)2 is : a. (r+1)xr b. rxr-1 c. rx-r+1 d. (r+1)xr-1
    93. 93. 91 Problem When m varies, the locus of the point of intersection of the straight lines x y x y 1 is : m and a b a b m a. A parabola b. A hyperbola c. An ellipse d. A circle
    94. 94. 92 Problem 1 sin x cos x The differential coefficient of tan w.r.t x is : cos x sin x a. 0 1 b. 2 c. 1 d. 2
    95. 95. 93 Problem The coefficient of correlation between x and y ; x : 65 66 67 67 69 70 72 y : 67 68 65 68 72 69 71 is given by : a. 0.5 b. 0.53 c. 0.6 d. 0.7
    96. 96. 94 Problem the length of the subnormal at the point (1, 3) of the curve, y = x2 + x + 1 is : a. 1 b. 3 c. 9 d. 3 10
    97. 97. 95 Problem The differential equation y dy x a (a is any constant) represents : dx a. A set of circles having centre on the y-axis b. A set of circles centre on the x-axis c. A set of ellipse d. None of these
    98. 98. 96 Problem 1 2 3 4 The value of the infinte series ……. Is : 2.3 2.5 2.7 2.9 2 a. 3 b. 2e e c. 2 1 d. 2e
    99. 99. 97 Problem Distance between the parallel planes 2x – y + 3z + 4 = 0 and 6x – 3y + 9z –3 = 0 is : 5 a. 3 4 b. 6 5 c. 14 3 d. 2 3
    100. 100. 98 Problem Three numbers m + 2, 4m –6, 3m – 2 are in A.P. in m equals to : a. 3 b. 2 c. 1 d. 0
    101. 101. 99 Problem The first derivative of the expression (xx + ax) is : a. xx log x + ax log e b. xx log x + ax log a c. xx log x - ax log a d. xx log x - ax log e
    102. 102. 100 Problem Counters marked 1, 2, 3 are placed in a bag and one is drawn and replaced. The operation is repeated three times. The chance of obtaining a total of 6 is : 7 a. 27 20 b. 27 13 c. 27 14 d. 27
    103. 103. FOR SOLUTIONS VISIT WWW.VASISTA.NET

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