AMU –PAST PAPERSMATHEMATICS - UNSOLVED PAPER - 1996
SECTION – I   CRITICAL REASONING SKILLS
01   Problem                                                                                  2     The differential equa...
02   Problem     The elimination of constants A, B and C from y = A + Bx – Ce-x leads the     differential equation :     ...
03   Problem     The solution of the differential equation xdy + ydx = 0 is :     a. xy = c     b. x2 + y2 = 0     c. xy l...
04   Problem                                    dy     The solution of the equation        +2y tan x = sin x, is :        ...
05   Problem              x          a                 is equal to:                  dx              x               a x  ...
06    Problem          1/2   dx         1/4                xx   2                          is equal to :               ...
07   Problem                         /2        1     The value of                                        0              ...
08   Problem                          Q   dx     The value of                                            P        x      ...
09   Problem     For a biased dice the probabilities of different faces to turn up are given below :     Face:        1   ...
10   Problem                   1                          x /2     If   A                  1                       tan ...
11   Problem     If f’(x) = (x - a)2n (x - b)2p+1 where x and p are positive integers, then :     a. x = a is a point of m...
12   Problem     the inverse of a symmetric matrix is :     a. diagnol matrix     b. skew symmetric     c. square matrix  ...
13   Problem                           a              p     The matrix product                       equals :     ...
14   Problem     In a group of 52 persons, 16 drink tea but not coffee, while 33 drink tea. How     many persons drink cof...
15   Problem     If the length of major axis of an ellipse is three times the length of minor     axis, then the eccentric...
16   Problem     A conic section with centricity e is a parabola if :     a. e = 0     b. e < 1     c. e > 1     d. e = 1
17   Problem     For the ellipse 3x2 + 4y2 = 12 length of the latusrectum is :     a. 3     b. 4          3     c.   5    ...
18   Problem     If (2, 0) is the vertex and y-axis is the direction of a parabola, then its focus is     a. (2, 0)     b....
19   Problem     The length of tangent from the point (6,-7) to the circle : 3x2 + 3y2 – 7x – 6y = 12     is     a. 6     ...
20   Problem     Which of the following lines is fathest from the origin ?     a. x – y + 1 = 0     b. 2x – y + 3 = 0     ...
21   Problem     The normal to a given curve is parallel to x-axis if :          dy     a.   dx    =0           dy     b. ...
22   Problem     The distance between the lines 3x + 4y = 9 and 6x + 8y = 15 is :          3     a.   2           3     b....
23   Problem     a line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y-     intercept is :      ...
24   Problem     If the volume in cm3 and surface and surface area is cm2 of a sphere are     numerically equal Then the r...
25   Problem     the locus of a point represented by x  a  t  1  y  a  t  1    is :                               ...
26   Problem     The equation of a tangent parallel to y = x drawn   x2 y 2      is :                                     ...
27   Problem     Which of the following is not correct :     a. A function f such that f(x) = x – 1 for every integer x is...
28   Problem                                                         If cos   - 0.6 and 1800 <  < 2700, then tan 4 is ...
29   Problem                                                        z1  z     Let z1 and z2 be two complex number such tha...
30   Problem                        1i 3     The amplitude of           is :                         3 1               ...
31   Problem     In a G.P. if (m + n)th terms is p and (m - 1)th term is q then mth term is :          p     a.   q       ...
32   Problem     In a G.P. of positive terms, any term is equal to the sum of the next two terms.     Then the common rati...
33   Problem     If n+2C8 n-2P4 = 57 : 16, then the value of x is :     a. 20     b. 19     c. 18     d. 17
34   Problem     A library has a copies of one book, b copies of each of two books, c copies of each     of three books, a...
35   Problem     Three identical dice are rolled. The probability that the same number will appear     on each of them is ...
36   Problem     If a, b, c are real numbers a  0. If , is a root of a2x2 + bx + c = 0, is a     root of a2x2 – bx + c =...
37   Problem     The solution of log7log5 (   x 5    x   ) = 0 is :     a. 4     b. 5     c. 6     d. 9
38   Problem                                                                           1     The most general value of  ,...
39   Problem     Three faces of a fair dice are yellow, two faces red and only one is blue. The dice     is tosses three t...
40   Problem     If a2 + b2 + c2 = 1, then ab + bc + ca lies in the interval :     a.   1            2 ,2            ...
41   Problem     The common tangent to the parabola y2 = 4ax and x2 = 4ay is :     a. x + y + a = 0     b. x + y - a = 0  ...
42   Problem     The solution of the equation cos2  + sin  + 1 = 0, lies in the interval :                 a.    4...
43   Problem     If cosec    - cot = q, then the value of cot  is :          1  q2     a.            q          1  q2...
44   Problem     The length of the intercept on the normal at the point (at2, 2at) of the parabola y2     = 4ax made by th...
45   Problem     From the top of a light house 60 metres high with its base at the sea level, the     angle of depression ...
46   Problem     The expression   1  sin      1  sin               equal to :                                       ...
47   Problem                                                                   x2   y2     If m1 and m2 are the slopes of ...
48   Problem     If f’(x) = sin (log x) and y = f        2 x  3  , then dy   equals :                                  ...
49   Problem     The derivatives of tan-1   2x      w.r.t. sin-1  2x       is :                                   2 ...
50   Problem                    x             m        equals to :     lim 1      x              x                ...
51   Problem                       x 2     If y  f (x )           then :                       x 1     a. f(1) = 3    ...
52   Problem                                                             x     The co-ordinates of the points on the curve...
53   Problem     the maximum value of xy subjected to x + y = 8 is :     a. 8     b. 16     c. 20     d. 24
54   Problem                      df     If f = xy then        is equal to :                      dx     a. x log f       ...
55   Problem     The curve y - exy + x = 0 has a vertical tangent at the point :     a. (1, 1)     b. at no point     c. (...
56   Problem     The sum of the series           1         1               :                             1              ...
57   Problem     Let S be a finite set containing n elements. Then the total number of binary     operations on S is :    ...
58   Problem     The ratio of the volume of a cube to that of the sphere which will fit inside the     cube :     a. 5 : ...
59   Problem     The function f(x) = cos (log (x +   x2  1   )) is :     a. Even     b. Constant     c. Odd     d. None o...
60   Problem     The perimeter of a given rectangle is x, its area will maximum of its sides are :     a.   x x           ...
61   Problem                                                             d 3y   dy     Which of the following functions ho...
62   Problem                                                                0.5     the domain of definition of the funct...
63   Problem     If a, b, c, d are in H.P. then :     a. ab > cd     b. ad > bc     c. ac > bd     d. none of these
64   Problem     If                1 x        then the value of    cos   x    is :          tan               tan , ...
65   Problem     A round balloon of radius r subtends an angle at the eye of the observer while     the angle of elevation...
66   Problem                                        1 a    1      1     If a-1 + b-1 + c-1 = 0 such that    1     1 b   ...
67   Problem              4    5     2      If A =                     then adj. (A) equals :              5    4 ...
68   Problem     The statement of k = 1 10 by 2, do remit in :     a. 3 cycles     b. 2 cycles     c. 8 cycles     d. 9 cy...
69   Problem     The Newton’s method converges first of f’(x) is :     a. Small     b. mid     c. large     d. zero
70   Problem                                                                                                    are unit ...
71   Problem     The area of ABC with vertices A (1, -1, 2), B (2, 1, -1) and C (3, -1, 2) is :     a. 13      2   sq. uni...
72   Problem     If p, q, r be three non-zero vectors, then equation p . q = p . r implies :     a. q = r     b. p is orth...
73   Problem                                                     j      ˆ        i      j      ˆ       i      j      ˆ ...
74   Problem                                     The scalar a.{(b  c ) x (a  b  c )} equals :     a. 0           ...
75   Problem     If f(x) = x1/x-1 for all positive x = 1 and if f is continuous at 1, then equals :     a. 0          1   ...
76   Problem     the point equidistant from the four points (0, 0, 0), (3/2, 0, 0), (0,5/2, 0) and     (0, 0, 7/2) is :   ...
77   Problem     The area bounded by the curve y = x sin x and the x-axis between x = 0 and x = 2           is :     a. 2...
78   Problem     The value of (i)I where i2 = -1 is :     a. Whole imaginary number     b. Whole real number     c. Zero  ...
79   Problem     The equations of the sphere with A (2, 3, 5) and B (4, 9, -3) as the ends of a     diameter is :     a. x...
80   Problem     If (2, 0) is the vertex and y-axis the direction of a parabola, then its focus is :     a. (2, 0)     b. ...
81   Problem     If f(x) = log (x + a), for x  a , then the value of f’(x) is equal to :             1     a.    x a   ...
82   Problem     In a collection of 6 mathematics books and 4 physics books, the probability that 3     particular mathema...
83   Problem     Find the mode from the data given below :     Marks             0-5       10-15    15-20   15-20   20-25 ...
84   Problem     If the mean of four observations is 20 and when a constant c is added to each     observation, the mean b...
85   Problem     The area of surface generated by rotating the circle x = b =  cos y = a + b sin  ,          0    2 ...
86   Problem     The eigin values of the matrix       5   4   are :                                      A           ...
87   Problem                                                                           x   y 2 z 3     the length of per...
88   Problem     the angle A, B, C of a triangle are in the ratio of 3 : 5 : 4, then a + i   2   is equal to :     a. 3b  ...
89   Problem     If the angle between the lines joining the foci of an ellipse to an extremity of the     minor axis is 90...
90   Problem     If a man running at the rate of 15 km per hour crosses a bridge in 5 minutes, the     length of the bridg...
91   Problem     If    x   y  15,  x 2   y 2  49,  xy  44   and n = 5, then byx is equal to :            1     a...
92   Problem     If (x + 1) is a factor of x4 + (p -3)x3 – (3p - 5)x2 + (2p -10) x + 5 then the value of p is     :     a....
93   Problem     Two finite sets have m and n elements. The total number of subsets of the first     set is 56 more than t...
94   Problem     The circle x2 = y2 – 2ax – 2ay + a2 = 0 touches :     a. x-axis only     b. y-axis only     c. both axis ...
95   Problem     If |A| = 2 and A is a 2 x 2 matrix, what is the value of det, {adj. {adj. (adj. A2)}} is     equal to    ...
96   Problem     If y = (4x - 5) is a tangent to the curve y2 = px3 + q at (2, 3), then :     a. p = -2, q = -7     b. p =...
97   Problem     given that x > 0, y > 0, x > y and z 0. the inequality which is not always correct is :     a. x + z > y ...
98   Problem     Given that log10343 = 2.5353. The least n such that 7n > 105 is :     a. 4     b. 3     c. n     d. 6
99   Problem     the smallest angle of the triangle whose sides are   6   12,   48,   24   is :               a.   4    ...
100   Problem                     1                  p                                       If f’(x) = (1  cos x) for...
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AMU - Mathematics - 1996

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  • AMU - Mathematics - 1996

    1. 1. AMU –PAST PAPERSMATHEMATICS - UNSOLVED PAPER - 1996
    2. 2. SECTION – I CRITICAL REASONING SKILLS
    3. 3. 01 Problem 2 The differential equation of all ‘Simple Harmonic Motions’ of given period n is : x = a cos (nt + b) d2 x a. dt 2 + nx = 0 d2 x b. + n 2x = 0 dt 2 d2 x c. - n2 x = 0 dt 2 d2 x 1 d. + x=0 dt 2 n2
    4. 4. 02 Problem The elimination of constants A, B and C from y = A + Bx – Ce-x leads the differential equation : a. y’ + y’’ = 0 b. y’’ – y’’’ = 0 c. y’ + ex = 0 d. y’’ + ex = 0
    5. 5. 03 Problem The solution of the differential equation xdy + ydx = 0 is : a. xy = c b. x2 + y2 = 0 c. xy logx = 1 d. log xy = c
    6. 6. 04 Problem dy The solution of the equation +2y tan x = sin x, is : dx a. y sec2 x = sec x + c b. y sec x = tan x + c c. y = sec x + c sec2 x d. none of these
    7. 7. 05 Problem x a is equal to: dx x a x a. c log a b. 2a x c log a x c. 2a .log a  c d. None of these
    8. 8. 06 Problem 1/2 dx  1/4 xx 2 is equal to :  a. 6  b. 3  c. 4 d. 0
    9. 9. 07 Problem  /2 1 The value of  0 3 1  tan x dx is : a. 0 b. 1 c.  /4 d. 2 
    10. 10. 08 Problem Q dx The value of  P x , (P  Q) is : a. log (Q - P) b. log P c. log Q d. log (P Q)
    11. 11. 09 Problem For a biased dice the probabilities of different faces to turn up are given below : Face: 1 2 3 4 5 6 Probabili 0.1 0.32 0.21 0.15 0.05 0.17 ty The dice is tossed and you are told that either the face 1 or 2 has turned up. The probability that it is face is : a. 1 7 4 b. 7 5 c. 21 4 d. 21
    12. 12. 10 Problem 1 x /2 If A  1 tan x dx and B   x / 2 cot x dx then A + B is equals : a. 0 b. 1 c. 2  d. 4
    13. 13. 11 Problem If f’(x) = (x - a)2n (x - b)2p+1 where x and p are positive integers, then : a. x = a is a point of minimum b. x = a is a point of maximum c. x is not a point of maximum or minimum d. none of these
    14. 14. 12 Problem the inverse of a symmetric matrix is : a. diagnol matrix b. skew symmetric c. square matrix d. a symmetric matrix
    15. 15. 13 Problem  a  p The matrix product     equals :  b  x[xyz ]x q  c    r    pqr  abc a. xyz b. xyz  pqr abc c. pqr  abc xyz d. none of these
    16. 16. 14 Problem In a group of 52 persons, 16 drink tea but not coffee, while 33 drink tea. How many persons drink coffee but not tea : a. 17 b. 36 c. 23 d. 19
    17. 17. 15 Problem If the length of major axis of an ellipse is three times the length of minor axis, then the eccentricity is : 1 a. 3 1 b. 2 1 c. 3 2 2 d. 3
    18. 18. 16 Problem A conic section with centricity e is a parabola if : a. e = 0 b. e < 1 c. e > 1 d. e = 1
    19. 19. 17 Problem For the ellipse 3x2 + 4y2 = 12 length of the latusrectum is : a. 3 b. 4 3 c. 5 2 d. 5
    20. 20. 18 Problem If (2, 0) is the vertex and y-axis is the direction of a parabola, then its focus is a. (2, 0) b. (-2, 0) c. (4, 0) d. (-4, 0)
    21. 21. 19 Problem The length of tangent from the point (6,-7) to the circle : 3x2 + 3y2 – 7x – 6y = 12 is a. 6 b. 9 c. 7 d. 13
    22. 22. 20 Problem Which of the following lines is fathest from the origin ? a. x – y + 1 = 0 b. 2x – y + 3 = 0 c. x + 2y – 2 = 0 d. x + y – 2 = 0
    23. 23. 21 Problem The normal to a given curve is parallel to x-axis if : dy a. dx =0 dy b. dx =1 c. dx =0 dy dx d. =1 dy
    24. 24. 22 Problem The distance between the lines 3x + 4y = 9 and 6x + 8y = 15 is : 3 a. 2 3 b. 10 c. 6 d. 9 4
    25. 25. 23 Problem a line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y- intercept is : 1 a. 3 b. 2 3 c. 1 4 d. 3
    26. 26. 24 Problem If the volume in cm3 and surface and surface area is cm2 of a sphere are numerically equal Then the radius of the sphere in cm is : a. 2 b. 3 c. 4 d. 5
    27. 27. 25 Problem the locus of a point represented by x  a  t  1  y  a  t  1  is : 2 t    2 t    a. an ellipse b. a circle c. a pair of straight lines d. none of these
    28. 28. 26 Problem The equation of a tangent parallel to y = x drawn x2 y 2 is :  1 3 2 a. x – y + 1 = 0 b. x – y + 2 = 0 c. x + y – 1 = 0 d. x – y + 2 = 0
    29. 29. 27 Problem Which of the following is not correct : a. A function f such that f(x) = x – 1 for every integer x is binary operation b. The binary operation positive on IR is commutative c. The set{(a, b)/a I and b = - a} is a binary operation on I d. The division on IR – [0] is not as associative operation
    30. 30. 28 Problem  If cos   - 0.6 and 1800 <  < 2700, then tan 4 is equal to : a. 5 2 (1  5) b. 2 c. (1  5) 2 ( 5  1) d. 2
    31. 31. 29 Problem z1 z Let z1 and z2 be two complex number such that  2  1. Then : z2 z1 a. z1, z2 are collinear b. z1, z2 and the origin form a right angled triangle c. z1, z2 and the origin form an equilateral triangle d. none of these
    32. 32. 30 Problem 1i 3 The amplitude of is : 3 1  a. 6  b. 4  c. 3  d. 2
    33. 33. 31 Problem In a G.P. if (m + n)th terms is p and (m - 1)th term is q then mth term is : p a. q q b. p c. Pq d. pq
    34. 34. 32 Problem In a G.P. of positive terms, any term is equal to the sum of the next two terms. Then the common ratio of the G.P. is a. 2 cos 180 b. sin 18 c. cos 18 d. 2 sin 18
    35. 35. 33 Problem If n+2C8 n-2P4 = 57 : 16, then the value of x is : a. 20 b. 19 c. 18 d. 17
    36. 36. 34 Problem A library has a copies of one book, b copies of each of two books, c copies of each of three books, and single copies of d books. The total number of ways in which these books can be distributed is : (a  b  c  d)! a. a! b ! c ! (a  2b  3c  d)! b. a !(b !)2 (c !)3 (a  2b  3c  d)! c. a! b ! c ! d. None of these
    37. 37. 35 Problem Three identical dice are rolled. The probability that the same number will appear on each of them is : 1 a. 6 1 b. 36 1 c. 18 3 d. 28
    38. 38. 36 Problem If a, b, c are real numbers a  0. If , is a root of a2x2 + bx + c = 0, is a root of a2x2 – bx + c = 0 and 0 < a < b, then the equation a2x2 + 2bx + 2c = 0 has a root that always satisfied : a.      2 b.      2 c.   d.     
    39. 39. 37 Problem The solution of log7log5 ( x 5  x ) = 0 is : a. 4 b. 5 c. 6 d. 9
    40. 40. 38 Problem 1 The most general value of  , satisfying the two equations, cos  = , tan   1 2 is 5 a. 2n  4  b. 2n  4 5 c. n  4  d. (2n  1)  4
    41. 41. 39 Problem Three faces of a fair dice are yellow, two faces red and only one is blue. The dice is tosses three times. The probability that the colour yellow, red and blue appears in the first, second and the third tosses respectively is : a. 1 30 b. 1 25 1 c. 36 1 d. 32
    42. 42. 40 Problem If a2 + b2 + c2 = 1, then ab + bc + ca lies in the interval : a. 1   2 ,2   b. [-1, 2]  1  c.   2 ,1    1 d.  1, 2   
    43. 43. 41 Problem The common tangent to the parabola y2 = 4ax and x2 = 4ay is : a. x + y + a = 0 b. x + y - a = 0 c. x - y + a = 0 d. x - y - a = 0
    44. 44. 42 Problem The solution of the equation cos2  + sin  + 1 = 0, lies in the interval :    a.  4 , 4     3  b.  4 , 4     3 5  c.  4 , 4     5 7  d.  4 , 4   
    45. 45. 43 Problem If cosec  - cot = q, then the value of cot  is : 1  q2 a. q 1  q2 b. q q c. 1  q2 q d. 1  q2
    46. 46. 44 Problem The length of the intercept on the normal at the point (at2, 2at) of the parabola y2 = 4ax made by the circle on the line joining the focus and p as diameter is : a. a 1  t2 b. a 1  t2 c. a 1t d. a 1t
    47. 47. 45 Problem From the top of a light house 60 metres high with its base at the sea level, the angle of depression of a boat is 150. The distance of the boat from the foot of the light house is :  3  1   3  1  a.   60 metres  3  1   3  1  b.   60 metres  3  1 c.   3  1  metres   d. none of these
    48. 48. 46 Problem The expression 1  sin  1  sin   equal to :  for   1  sin  1  sin  2 2 cos  a. cos2  2 sin  b. sin2  2 cos  c. sin2  d. none of these
    49. 49. 47 Problem x2 y2 If m1 and m2 are the slopes of the tangent to the parabola  1 , which 15 16 passes through the point (6, 2) the value of (m1 + m2) is : a. 14 11 4 b. 11 11 c. 4 24 d. 11
    50. 50. 48 Problem If f’(x) = sin (log x) and y = f  2 x  3  , then dy equals :  3  2x    dx 1 a. sin (log x) . x log x 12   2x  3   b. 2 sin log   (3  2x)   3  2x     2x  3   c. sin log     3  2x   d. none of these
    51. 51. 49 Problem The derivatives of tan-1  2x  w.r.t. sin-1 2x  is :  2  1  x 2  1  x    a. 2 b. 4 c. 1 d. 2
    52. 52. 50 Problem x  m equals to : lim 1  x   x   a. em b. e-m c. m-e d. me
    53. 53. 51 Problem x 2 If y  f (x )  then : x 1 a. f(1) = 3 b. 2 = f(4) c. f is rational function of x d. y increases with x for x < 1
    54. 54. 52 Problem x The co-ordinates of the points on the curve, f (x)  1  x where the tangent to 2 the curve has greatest slope is : a. (0, 2) b. (0, 0) c. (0, 1) d. (1, 1)
    55. 55. 53 Problem the maximum value of xy subjected to x + y = 8 is : a. 8 b. 16 c. 20 d. 24
    56. 56. 54 Problem df If f = xy then is equal to : dx a. x log f y b. xy . x c. xy log x d. yx
    57. 57. 55 Problem The curve y - exy + x = 0 has a vertical tangent at the point : a. (1, 1) b. at no point c. (0, 1) d. (1, 0)
    58. 58. 56 Problem The sum of the series 1 1 : 1   ... (1  2) (1  2  3) a. 1 2 b. 1 c. 2 3 d. 2
    59. 59. 57 Problem Let S be a finite set containing n elements. Then the total number of binary operations on S is : 2 a. nn b. nn c. n2 2 d. 2n
    60. 60. 58 Problem The ratio of the volume of a cube to that of the sphere which will fit inside the cube : a. 5 :  b. 7 :  c. 6 :  d. 3 : 
    61. 61. 59 Problem The function f(x) = cos (log (x + x2  1 )) is : a. Even b. Constant c. Odd d. None of these
    62. 62. 60 Problem The perimeter of a given rectangle is x, its area will maximum of its sides are : a. x x , 2 2 x x b. , 3 3 x x c. , 6 3 x x d. , 4 4
    63. 63. 61 Problem d 3y dy Which of the following functions hold the property of 3  =0? dx dx a. y = ex b. y = cos x c. y = tan x d. y = sin x
    64. 64. 62 Problem 0.5 the domain of definition of the function : x.1  2( x  4) + (x + 4)0.5 + 2  ( x  4)0.5 4(x + 4)0.5 is : a. R b. (- 4, 4) c. R+ d. (-4, 0)  (0, )
    65. 65. 63 Problem If a, b, c, d are in H.P. then : a. ab > cd b. ad > bc c. ac > bd d. none of these
    66. 66. 64 Problem If  1 x  then the value of cos   x is : tan  tan , 2 1 x 2 1  x cos  a. sin x b. cos x c. cos  d. sin 
    67. 67. 65 Problem A round balloon of radius r subtends an angle at the eye of the observer while the angle of elevation of its centre is  , then the height of the centre of balloon is : a. r tan  sin    b. r cosec  2    c. r tan  and    d. r sin 2   cosec , 
    68. 68. 66 Problem 1 a 1 1 If a-1 + b-1 + c-1 = 0 such that 1 1 b 1  then the value of  1 1 1 c is : a. 0 b. - abc c. abc d. none of these
    69. 69. 67 Problem 4 5 2  If A =   then adj. (A) equals : 5 4 2  2  2 8  36 36 18    a. 36 36 18 18 18  9    36 36 18  b.    36 36 18  18  18 9   0 0 0 c.   0 0 0 0 0 0   d. none of these
    70. 70. 68 Problem The statement of k = 1 10 by 2, do remit in : a. 3 cycles b. 2 cycles c. 8 cycles d. 9 cycles
    71. 71. 69 Problem The Newton’s method converges first of f’(x) is : a. Small b. mid c. large d. zero
    72. 72. 70 Problem  are unit vectors and  is the angle between them then    If a and b a  b 2 is :  a. sin 2 b. sin  c. 2 sin  d. sin 2 
    73. 73. 71 Problem The area of ABC with vertices A (1, -1, 2), B (2, 1, -1) and C (3, -1, 2) is : a. 13 2 sq. units b. 3 6 sq. units c. 13 sq. units d. 15 3 sq. units
    74. 74. 72 Problem If p, q, r be three non-zero vectors, then equation p . q = p . r implies : a. q = r b. p is orthogonal to both q and r c. p is orthogonal to q – r d. either q = r or p is orthogonal to q – r.
    75. 75. 73 Problem   j ˆ i j ˆ  i j ˆ ˆ  a2 ˆ  a3 k, b  b1ˆ  b2 ˆ  b3 k, c  c1ˆ  c2 ˆ  c3 k, be three non- Let a  a1i   zero vectors such that is a unit vector perpendicular to both a and b . If the    a1 a2 a3 a and b is angle between 6 then b1 b2 b3 is equal to : c1 c2 c3 a. 0 b. 1 1  2  2 | a||b| c. 4 3  2  2 d. | a||b| 4
    76. 76. 74 Problem       The scalar a.{(b  c ) x (a  b  c )} equals : a. 0    b. 2 [a b c ]    c. [a b c ] d. none of these
    77. 77. 75 Problem If f(x) = x1/x-1 for all positive x = 1 and if f is continuous at 1, then equals : a. 0 1 b. e c. e d. e2
    78. 78. 76 Problem the point equidistant from the four points (0, 0, 0), (3/2, 0, 0), (0,5/2, 0) and (0, 0, 7/2) is :  2 1 2 a.  3 3 5     3 b.  3,2, 5    3 5 7 c. 4, 4, 4   1   2 , 0, 1  d.  
    79. 79. 77 Problem The area bounded by the curve y = x sin x and the x-axis between x = 0 and x = 2  is : a. 2  b. 3  c. 4  d. 
    80. 80. 78 Problem The value of (i)I where i2 = -1 is : a. Whole imaginary number b. Whole real number c. Zero d. E  /2
    81. 81. 79 Problem The equations of the sphere with A (2, 3, 5) and B (4, 9, -3) as the ends of a diameter is : a. x2 + y2 + z2 – 6x – 12y – 2z + 20 = 0 b. 2x2 + 2y2 + 2z2 – x - y – z + 1 = 0 c. 3x2 + 3y2 + 3z2 – 2x – 2y –2z –1 = 0 d. none of these
    82. 82. 80 Problem If (2, 0) is the vertex and y-axis the direction of a parabola, then its focus is : a. (2, 0) b. (-2, 0) c. (4, 0) d. (-4, 0)
    83. 83. 81 Problem If f(x) = log (x + a), for x  a , then the value of f’(x) is equal to : 1 a. x a 1 b. | x  a| 1 c. | x  a| 1 d. | x  a|
    84. 84. 82 Problem In a collection of 6 mathematics books and 4 physics books, the probability that 3 particular mathematics books will be together is : 1 a. 8 1 b. 10 1 c. 15 1 d. 20
    85. 85. 83 Problem Find the mode from the data given below : Marks 0-5 10-15 15-20 15-20 20-25 25-30 Obtained 18 20 25 30 16 14 a. 16.1 b. 16.2 c. 16.7 d. 16.3
    86. 86. 84 Problem If the mean of four observations is 20 and when a constant c is added to each observation, the mean becomes 22. The value of c is : a. - 2 b. 2 c. 4 d. 6
    87. 87. 85 Problem The area of surface generated by rotating the circle x = b =  cos y = a + b sin  , 0    2 abut x-axis is : a.  ab sq. units b. ab sq. units x c. 2 loge x c d. ( x )a loge x c
    88. 88. 86 Problem The eigin values of the matrix 5 4 are : A    1 2 a. 2, 4 b. 1, 6 c. 3, -3 d. 1, -2
    89. 89. 87 Problem x y 2 z 3 the length of perpendicular from the point P(3, -1, 11) to the line   2 3 4 is : a. 2 13 b. 53 c. 2 14 d. 8
    90. 90. 88 Problem the angle A, B, C of a triangle are in the ratio of 3 : 5 : 4, then a + i 2 is equal to : a. 3b b. 2b c. 2b d. 4b
    91. 91. 89 Problem If the angle between the lines joining the foci of an ellipse to an extremity of the minor axis is 900, the eccentricity of the ellipse is : 1 a. 8 11 b. 4 c. 3 2 1 d. 2
    92. 92. 90 Problem If a man running at the rate of 15 km per hour crosses a bridge in 5 minutes, the length of the bridge in metres is : a. 7500 b. 1250 c. 1000 1 d. 1333 3
    93. 93. 91 Problem If  x   y  15,  x 2   y 2  49,  xy  44 and n = 5, then byx is equal to : 1 a. - 3 2 b. - 3 c. - 1 4 1 d. - 2
    94. 94. 92 Problem If (x + 1) is a factor of x4 + (p -3)x3 – (3p - 5)x2 + (2p -10) x + 5 then the value of p is : a. 2 b. 1 c. 3 d. 4
    95. 95. 93 Problem Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n are : a. 7, 6 b. 6, 3 c. 5, 1 d. 8, 7
    96. 96. 94 Problem The circle x2 = y2 – 2ax – 2ay + a2 = 0 touches : a. x-axis only b. y-axis only c. both axis d. none of these
    97. 97. 95 Problem If |A| = 2 and A is a 2 x 2 matrix, what is the value of det, {adj. {adj. (adj. A2)}} is equal to a. 4 b. 16 c. 64 d. 128
    98. 98. 96 Problem If y = (4x - 5) is a tangent to the curve y2 = px3 + q at (2, 3), then : a. p = -2, q = -7 b. p = -2, q = 7 c. p = 2, q = -7 d. p = 2, q = 7
    99. 99. 97 Problem given that x > 0, y > 0, x > y and z 0. the inequality which is not always correct is : a. x + z > y + z b. x – z > x – z c. xz > y > z x y  2 d. z 2 z
    100. 100. 98 Problem Given that log10343 = 2.5353. The least n such that 7n > 105 is : a. 4 b. 3 c. n d. 6
    101. 101. 99 Problem the smallest angle of the triangle whose sides are 6 12, 48, 24 is :  a. 4  b. 6 c.  3 d. none of these
    102. 102. 100 Problem 1 p   If f’(x) = (1  cos x) for 0  x  2 and that f(0) = 3, then f 2   lies in the interval : a. 1   2 ,1      b. 4 , 2      c. 3, ,3    4  2    d. 3  ,3    4 2
    103. 103. FOR SOLUTIONS VISIT WWW.VASISTA.NET

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