AMU –PAST PAPERSMATHEMATICS - UNSOLVED PAPER - 1999
SECTION – I   CRITICAL REASONING SKILLS
01   Problem     If A and B are non-zero square matrices of the same order such that AB = 0, then :     a. Adj A = 0 or ad...
02   Problem              3   3   4     If   A   2   3   4 ,                            then A-1 equal to :              0...
03   Problem     If A, B, C are square matrices of the same order, then which of the following is     true ?     a. AB = A...
04   Problem     The value of is     a. 0     b. abc     c. 4a2b2c2     d. none of these
05   Problem     A speaks truth in 75% and B in 80% of the cases. In what percentage of cases are     they likely to contr...
06    Problem     The matrix (a1x1+a2x2+a3x3) is of order :     a. 1 x 3     b. 1 x 1     c. 2 x 1     d. 1 x 2
07   Problem     Which of the following correct for A – B     a. A    B     b. A’ B     c. A    B’     d. A’   B’
08   Problem     If S denotes the sum to infinity and Sn the sum of n tersm of the series         1    1   1              ...
09   Problem     The series (   2   + 1), 1, (   2 -1)…. is in   :     a. A.P.     b. G.P.     c. H.P.     d. None of these
10   Problem          2 sin2 3x   is equal to :     lim     x  0     x2     a. 12     b. 18     c. 0     d. 6
11   Problem                sin m2   is equal to :     lim            0     a. 0     b. 1     c. m     d. m2
12   Problem     Let f(x + y) = f(x) + f(y) and f(x) = x2g(x) for all x, y R, where g(x) is continuous     function. Then ...
13   Problem                         1         1    1     1     The value of                                 is equal to :...
14   Problem     The function                 x2       1;   x   1                     f (x)        x    1;       x   1    ...
15   Problem     In the expansion of (1+ x)n, then binomial coefficients of three consecutive terms     are respectively 2...
16   Problem     The number of roots of the quadratic equation 8 sec - sec + 1 = 0 is :     a. Infinite     b. 2     c. 1 ...
17   Problem     If 12Pr = 11P6 + 6. 11P5 then r is equal to :     a. 6     b. 5     c. 7     d. none of these
18   Problem                                   1     The value of the expression     ( 3 sin 750   cos 750 ) is :         ...
19   Problem     the number of numbers consisting of four different digits that can be formed with     the digits 0, 1, 2,...
20   Problem     For the curve y = xex, the point :     a. x = -1 is a point of local minimum     b. x = 0 is a point of m...
21   Problem     the function y = x – cot-1 x – log (x   x2   1)   is increasing on :     a. (-    , 0)     b. (     , 0) ...
22   Problem     If x denotes displacement in time t and x = a cos t, then acceleration is given by :     a. - a sin t    ...
23   Problem     Let f differentiable for all x. If f (1) = - 2 and f’(x)   2 for all x   [1, 6],        2 for all x      ...
24   Problem                    0   1     The matrix     1   0                            is the matrix of reflection in t...
25   Problem     Let A and B be two matrices then (AB)’ equals :     a. A’B’     b. A’B     c. - AB     d. 1
26   Problem     If at any point on a curve the subtangent and subnormal are equal, then the     tangent is equal to :    ...
27   Problem     If f(x) = (x + 1) tan-1 (e-2x), then f’(0) is :     a.       1          2     b.       1          4     c...
28   Problem                            dy     If y = x log x, then   dx                               is :     a. 1 + log...
29   Problem     If xy + yz + zx = 1, then :     a. tan-1 x + tan-1 y + tan-1 z = 0     b. tan-1 x + tan-1 y + tan-1 z =  ...
30   Problem     The order of the differential equation whose solution is : y = a cos x + b sin x + ce-     x   is :     a...
31   Problem     If y = a cos px + b sin px, then :           d2y     a.    dx 2     + p2y = 0          d2y     b.   dx 2 ...
32   Problem          1/2               1   x                cos x log           dx is equal to :          1/2            ...
33   Problem            dx                           equals :                   3          x 1 x          1            log...
34   Problem      ex   (sin h x + cos h x) dx equal to :     a. ex sec h x + c     b. ex cos h x + c     c. sin h 2x + c  ...
35   Problem     A man can row 4.5 km/hr in still water and he finds that it takes him twice as long     to row up as to r...
36   Problem               3             4   10     If   m              n            , then :               4             ...
37   Problem     The area between the curve y = 2x4 – x2, the x-axis and the ordinates of two     minima of the curve is :...
38   Problem     If each of the variable in the matrix a b is doubled, then the value of the                              ...
39   Problem     A fair coin is tossed repeatedly. If tail appears on first four tosses, then the     probability of head ...
40   Problem     The reciprocal of the mean of the reciprocals of n observations is the     a. G.M     b. H.M     c. Media...
41   Problem     If the area bounded by the parabola x2 = 4y, the x-axis and the line x = 4 is divided     into two equal ...
42    Problem                                   (a 2b    c ) {(a   b x (a   b   c )} is equal to :      a.     ...
43   Problem     The unit vector perpendicular to the plane determined by A (1, -1, 2), B (2, 0, -1)     and R (0, 2, 1) i...
44   Problem     The probability of occurance of an even A is 0.3 and that of occurance of an event     B is 0.4. If A and...
45   Problem     the probability that a man who is x years old will die in a year in P. Then amongst     n persons A1, A2,...
46   Problem                              the vector   a x (b x c )is   :                           a. parallel to a  ...
47   Problem     the next term of the series 3 + 7 + 13 + 21 + 31 + ….     a. 43     b. 45     c. 51     d. 64
48   Problem     If log3 2, log3 (2x - 5) and log3        7   are in A.P., then x is equal to:                            ...
49   Problem     If the radius of a spherical balloon increases by 0.2%. Find the percentage     increase in its volume : ...
50   Problem                3    5   6       x    10   5     If         7    8   9 , then 5   3    6   equal to :         ...
51   Problem                                 1       1   5     The positive value of sin     sin           is :           ...
52   Problem     three numbers form an increasing G.P. If the middle number is doubled, then the     new numbers are in A....
53   Problem     The nth term of the series 1   (1       2)   (1   2   3)   ….. is equal to :                             ...
54   Problem     Two finite sets have m and n element. The total number of subsets of the first     set is 56 more than th...
55   Problem                               1     The domain of   f ( x)            1   x2   is :                          ...
56   Problem                      sec2 (log x)     The value of                    dx is :                            x   ...
57   Problem     The period of f(x) = cos (x2) is :     a. 2     b. 4       2            2     c.          4     d. none o...
58   Problem     The orthocenter of the triangle formed by the lines xy = 0 and x + y = 1 is :          1 1     a.    ,   ...
59   Problem     The is acute angle and 4 x 2 sin2       1 = x, then tan is :                                         2   ...
60   Problem     The equation of the locus of a point whose abscissa and ordinate are always     equal is :     a. y + x =...
61   Problem     The distance between the parallel lines y = 2x + 4 and 6x = 3y + 5 is :     a.   17/ 3     b. 1     c.   ...
62   Problem     The equation y2 – x2 + 2x – 1 = 0, represents :     a. A pair of straight lines     b. A circle     c. A ...
63   Problem     The intercepts made by the circle x2 + y2 –5x – 13y – 14 = 0 on x-axs and y- axis     are respectively:  ...
64   Problem     The intercepts made by the circle x2 + y2 –5x – 13y – 14 = 0 which are     perpendicular to 3x – 4y –1 = ...
65   Problem     three identical dice are rolled. The probability that the same number will appear     on each of them as ...
66   Problem                                   3     The principal value of sin        is :                               ...
67   Problem                        1   3 cos x       4 sin x          dy     If   y       cos                            ...
68   Problem     The point on y2 = 4ax nearest to the focus has its abscissa equal to :     a.   a     b. - a          a  ...
69   Problem     The vertex of the parabola x2 + 8x + 12y + 4 = 0 is :     a. (- 4, 1)     b. (4, - 1)     c. (- 4, -1)   ...
70   Problem     The standard deviation for the data : 7, 9, 11, 13, 15 is :     a. 2.4     b. 2.5     c. 2.7     d. 2.8
71   Problem     While dividing each entry in a data by a non-zero number a, the arithmetic mean     of the new data :    ...
72   Problem     Two circles which passes through the points A (0, a) and B (0, -a) an touch the     line     y = mx + c w...
73   Problem                                                           2   2     If ,        are the roots of ax2 + bx + c...
74   Problem     The maximum value of   5 sin   3 sin       3   is :                                            3     a. 1...
75   Problem     If   x=      y = 15, x2 = y2 = 49 xy = 44 and x = 5, then byx is equal to:     a.       1              3 ...
76   Problem     The number of terms which are free from radical sings in the expansion of (x1/5 +     y1/10)55 is :     a...
77   Problem     The sum of the co-efficient in the expansion of (x + 2y + x)10 is :     a.   10C                x+y     b...
78   Problem     There are 10 points in a plane, out of which 4 points are collinear. The number of     triangles formed w...
79   Problem     If the co-ordinate of the centroid of a triangle are (3, 2) and co-ordinates of two     vertices are (4, ...
80   Problem     the argument of   1   i 3   is :                       1   i 3          4     a.   3          2     b.   ...
81   Problem     In how many ways can a constant and a vowel be chosen out of the word     COURAGE ?     a.   7C          ...
82   Problem     The length of the latusrectum of the ellipse 5x2 + 9y2 = 45 is :     a. 5          3     b. 10           ...
83   Problem     The projections of a line segment on the coordinate axes are 12, 4, 3. The     direction cosine of the li...
84   Problem                                                 n     The least positive value of n if   i(1 3)       is posi...
85   Problem     lim sec           loge (2x )   is equal to :     x          1       4x          2     a. 0     b.        ...
86   Problem     The distance between the planes gives by ,                       ˆ                            ˆ      r ...
87   Problem     If the coefficient of correlation between X and Y is 0.28, covariance between X     and Y is 7.6 and the ...
88   Problem                1         1   3     If   sin       tan         , then   equals :                              ...
89   Problem          (x       1)                             2     If                 4   , then the value of x         1...
90   Problem          (x       1)                  x3 1     If                 2 cos , then        equals :               ...
91   Problem     The mode of the given distribution is :        Weight (in kg)        40        43     46   49   52   55  ...
92   Problem     The factors of   x    a   b     are :                      a   x    b                      a   b    x    ...
93   Problem                                                    7                             1     The equation of a curv...
94   Problem     The general value of x satisfying is given by cos x =   3   (1 – sin x ) :     a.   x       n            ...
95   Problem     The angle of elevation of the tops of two vertical tower as seen from the middle     point of the line jo...
96   Problem     If an angle            is divided into two parts A and B such that A – B = x and     tan A : tan B = k : ...
97   Problem     In triangle ABC and DEF, AB = DE, AC = EF and   A   2 E   . Two triangles will     have the same area if ...
98   Problem     the even function is :     a. f(x) = x2 (x2 + 1)     b. f(x) = x (x + 1)     c. f(x) = tan x + c     d. f...
99   Problem     The middle term in the expansion of (1 + x)2n will be :     a. (n + 1)th     b. (n - 1)th     c. nth     ...
100   Problem      For the equation | x |2 | | x | - 6 = 0      a. There is only one root      b. There are only two disti...
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  • AMU - Mathematics - 1999

    1. 1. AMU –PAST PAPERSMATHEMATICS - UNSOLVED PAPER - 1999
    2. 2. SECTION – I CRITICAL REASONING SKILLS
    3. 3. 01 Problem If A and B are non-zero square matrices of the same order such that AB = 0, then : a. Adj A = 0 or adj B = 0 b. | A | = 0 or | B | = 0 c. adj A = 0 and adj B = 0 d. | A | = 0 and | B | = 0
    4. 4. 02 Problem 3 3 4 If A 2 3 4 , then A-1 equal to : 0 1 1 a. A b. A2 c. A3 d. A4
    5. 5. 03 Problem If A, B, C are square matrices of the same order, then which of the following is true ? a. AB = AC b. (AB)2 = A2B2 c. AB = 0 A = 0 or B = 0 d. AB = I AB = BA
    6. 6. 04 Problem The value of is a. 0 b. abc c. 4a2b2c2 d. none of these
    7. 7. 05 Problem A speaks truth in 75% and B in 80% of the cases. In what percentage of cases are they likely to contradict each other narrating the same incident ? a. 35% b. 45% c. 15% d. 5%
    8. 8. 06 Problem The matrix (a1x1+a2x2+a3x3) is of order : a. 1 x 3 b. 1 x 1 c. 2 x 1 d. 1 x 2
    9. 9. 07 Problem Which of the following correct for A – B a. A B b. A’ B c. A B’ d. A’ B’
    10. 10. 08 Problem If S denotes the sum to infinity and Sn the sum of n tersm of the series 1 1 1 1 1 ......, such that S Sn , then the least value of n is : 2 4 4 1000 a. 8 b. 9 c. 10 d. 11
    11. 11. 09 Problem The series ( 2 + 1), 1, ( 2 -1)…. is in : a. A.P. b. G.P. c. H.P. d. None of these
    12. 12. 10 Problem 2 sin2 3x is equal to : lim x 0 x2 a. 12 b. 18 c. 0 d. 6
    13. 13. 11 Problem sin m2 is equal to : lim 0 a. 0 b. 1 c. m d. m2
    14. 14. 12 Problem Let f(x + y) = f(x) + f(y) and f(x) = x2g(x) for all x, y R, where g(x) is continuous function. Then f’(x) is equal to : a. g(x) b. g(0) c. g(0) + g’(x) d. 0
    15. 15. 13 Problem 1 1 1 1 The value of is equal to : r2 r12 r22 r33 a2 b2 c2 a. a2 b2 c2 b. 2 a2 b2 c2 c. 3 a2 b2 c2 d.
    16. 16. 14 Problem The function x2 1; x 1 f (x) x 1; x 1 2; x 1 a. Continuous for all x b. Discontinuous at x = -1 c. Discontinuous for all x d. Continuous x = -1
    17. 17. 15 Problem In the expansion of (1+ x)n, then binomial coefficients of three consecutive terms are respectively 220, 495 and 792. The value of n is : a. 10 b. 11 c. 12 d. 13
    18. 18. 16 Problem The number of roots of the quadratic equation 8 sec - sec + 1 = 0 is : a. Infinite b. 2 c. 1 d. 0
    19. 19. 17 Problem If 12Pr = 11P6 + 6. 11P5 then r is equal to : a. 6 b. 5 c. 7 d. none of these
    20. 20. 18 Problem 1 The value of the expression ( 3 sin 750 cos 750 ) is : 2 a. 1 b. 2 c. 2 d. 2 2
    21. 21. 19 Problem the number of numbers consisting of four different digits that can be formed with the digits 0, 1, 2, 3 is : a. 16 b. 24 c. 30 d. 72
    22. 22. 20 Problem For the curve y = xex, the point : a. x = -1 is a point of local minimum b. x = 0 is a point of maximum c. x = -1 is a point of maximum d. x = 0 is a point of maximum
    23. 23. 21 Problem the function y = x – cot-1 x – log (x x2 1) is increasing on : a. (- , 0) b. ( , 0) c. (0, ) d. (- , )
    24. 24. 22 Problem If x denotes displacement in time t and x = a cos t, then acceleration is given by : a. - a sin t b. a sin t c. a cos t d. - a cos t
    25. 25. 23 Problem Let f differentiable for all x. If f (1) = - 2 and f’(x) 2 for all x [1, 6], 2 for all x [1, 6], then : a. f(6) < 8 b. f(6) 8 c. f(6) 5 d. f(6) 5
    26. 26. 24 Problem 0 1 The matrix 1 0 is the matrix of reflection in the line : a. x = 1 b. y = 1 c. x = y d. x + y = 1
    27. 27. 25 Problem Let A and B be two matrices then (AB)’ equals : a. A’B’ b. A’B c. - AB d. 1
    28. 28. 26 Problem If at any point on a curve the subtangent and subnormal are equal, then the tangent is equal to : a. Ordinate b. 2 ordinate c. 2(ordinate) d. none of these
    29. 29. 27 Problem If f(x) = (x + 1) tan-1 (e-2x), then f’(0) is : a. 1 2 b. 1 4 c. 5 6 d. none of these
    30. 30. 28 Problem dy If y = x log x, then dx is : a. 1 + log x b. log x c. 1 – log x d. 1
    31. 31. 29 Problem If xy + yz + zx = 1, then : a. tan-1 x + tan-1 y + tan-1 z = 0 b. tan-1 x + tan-1 y + tan-1 z = c. tan-1 x + tan-1 y + tan-1 z = 4 d. tan-1 x + tan-1 y + tan-1 z = 2
    32. 32. 30 Problem The order of the differential equation whose solution is : y = a cos x + b sin x + ce- x is : a. 3 b. 2 c. 1 d. none of these
    33. 33. 31 Problem If y = a cos px + b sin px, then : d2y a. dx 2 + p2y = 0 d2y b. dx 2 - p2y = 0 d2y c. dx 2 + py2 = 0 d2y d. dx 2 - py = 0
    34. 34. 32 Problem 1/2 1 x cos x log dx is equal to : 1/2 1 x 1 a. 2 1 b. - 2 c. 0 d. none of these
    35. 35. 33 Problem dx equals : 3 x 1 x 1 log( 1 x3 ) c a. 3 1 1 x3 1 log c b. 3 1 x 3 1 2 1 log c c. 3 1 x 3 2 1 x3 1 d. log c 3 1 x3 1
    36. 36. 34 Problem ex (sin h x + cos h x) dx equal to : a. ex sec h x + c b. ex cos h x + c c. sin h 2x + c d. cos h 2x + c
    37. 37. 35 Problem A man can row 4.5 km/hr in still water and he finds that it takes him twice as long to row up as to row down the river. The rate of the stream is : a. 1.5 km/hr b. 2 km/hr c. 2.25 km/hr d. 1.75 km/hr
    38. 38. 36 Problem 3 4 10 If m n , then : 4 3 11 a. m = - 2, n = 1 b. m = 22, n = 1 c. m = - 2, n = -23 d. m = 9, n = -10
    39. 39. 37 Problem The area between the curve y = 2x4 – x2, the x-axis and the ordinates of two minima of the curve is : a. 7 120 9 b. 120 11 c. 120 15 d. 120
    40. 40. 38 Problem If each of the variable in the matrix a b is doubled, then the value of the c d determinant of the matrix is : a. Not changed b. Doubled c. Multiplied by 4 d. Multiplied by 8
    41. 41. 39 Problem A fair coin is tossed repeatedly. If tail appears on first four tosses, then the probability of head appearing on fifth toss equals : a. 1 32 1 b. 2 3 c. 2 1 d. 5
    42. 42. 40 Problem The reciprocal of the mean of the reciprocals of n observations is the a. G.M b. H.M c. Median d. Average
    43. 43. 41 Problem If the area bounded by the parabola x2 = 4y, the x-axis and the line x = 4 is divided into two equal area by the line x = , then the value of is : a. 21/3 b. 22/3 c. 24/3 d. 25/3
    44. 44. 42 Problem         (a 2b c ) {(a b x (a b c )} is equal to : a.   [abc ]   b. 2 [abc ]   c. 3 [abc ] d. 0
    45. 45. 43 Problem The unit vector perpendicular to the plane determined by A (1, -1, 2), B (2, 0, -1) and R (0, 2, 1) is : 1 i j ˆ (2ˆ ˆ k ) a. 6 1 ˆ b. (2ˆ i ˆ j k) 3 1 ˆ c. (2ˆ i ˆ j k) 32 d. none of these
    46. 46. 44 Problem The probability of occurance of an even A is 0.3 and that of occurance of an event B is 0.4. If A and B are mutually exclusive, then the probability that neither occurs nor B occurs is : a. 0.2 b. 0.35 c. 0.3 d. none of these
    47. 47. 45 Problem the probability that a man who is x years old will die in a year in P. Then amongst n persons A1, A2,…., An each x years old now, the probability that A1 will die in one year is 1 a. n2 b. 1 – (1 - P)n 1 c. n2 [1 – (1 - P)n] 1 d. n2 [1 – (1 - P)n]
    48. 48. 46 Problem    the vector a x (b x c )is :  a. parallel to a  b. perpendicular to a c. parallel to d. perpendicular to
    49. 49. 47 Problem the next term of the series 3 + 7 + 13 + 21 + 31 + …. a. 43 b. 45 c. 51 d. 64
    50. 50. 48 Problem If log3 2, log3 (2x - 5) and log3 7 are in A.P., then x is equal to: 2x 2 a. 2 b. 3 c. 4 d. 2, 3
    51. 51. 49 Problem If the radius of a spherical balloon increases by 0.2%. Find the percentage increase in its volume : a. 0.8% b. 0.12% c. 0.6% d. 0.3%
    52. 52. 50 Problem 3 5 6 x 10 5 If 7 8 9 , then 5 3 6 equal to : 10 x 5 8 7 9 a. b. - c. x d. 0
    53. 53. 51 Problem 1 1 5 The positive value of sin sin is : 2 3 a. 5 6 3 b. 5 2 c. 5 2 d. 5
    54. 54. 52 Problem three numbers form an increasing G.P. If the middle number is doubled, then the new numbers are in A.P. The common ratio of the G.P. is : a. 2 - 3 b. 2 + 3 c. 3 -2 d. 3 + 3
    55. 55. 53 Problem The nth term of the series 1 (1 2) (1 2 3) ….. is equal to : 2 3 a. n2 (n -1) (n 1)(2n 1) b. 2 n 1 c. 2 n(n 1) d. 2
    56. 56. 54 Problem Two finite sets have m and n element. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The value of m and n are : a. m = 7, n = 6 b. m = 6, n = 3 c. m = 5, n = 1 d. m = 8, n = 7
    57. 57. 55 Problem 1 The domain of f ( x) 1 x2 is : 2x 1 1 a. ,1 2 b. [- 1, [ c. [1, [ d. none of these
    58. 58. 56 Problem sec2 (log x) The value of dx is : x a. tan (log x) + c b. tan x + c c. log (tan x) + c d. none of these
    59. 59. 57 Problem The period of f(x) = cos (x2) is : a. 2 b. 4 2 2 c. 4 d. none of these
    60. 60. 58 Problem The orthocenter of the triangle formed by the lines xy = 0 and x + y = 1 is : 1 1 a. , 2 2 1 1 b. , 3 3 c. (0,0) 1 1 , d. 4 4
    61. 61. 59 Problem The is acute angle and 4 x 2 sin2 1 = x, then tan is : 2 a. x2 1 b. x2 1 c. x 2 d. none of these
    62. 62. 60 Problem The equation of the locus of a point whose abscissa and ordinate are always equal is : a. y + x = 0 b. y – x = 0 c. y + x – 1 = 0 d. y – x + 1 = 0
    63. 63. 61 Problem The distance between the parallel lines y = 2x + 4 and 6x = 3y + 5 is : a. 17/ 3 b. 1 c. 3/ 5 d. 17 5 /15
    64. 64. 62 Problem The equation y2 – x2 + 2x – 1 = 0, represents : a. A pair of straight lines b. A circle c. A parabola d. An ellipse
    65. 65. 63 Problem The intercepts made by the circle x2 + y2 –5x – 13y – 14 = 0 on x-axs and y- axis are respectively: a. 5,15 b. 6,15 c. 9,15 d. none of thes
    66. 66. 64 Problem The intercepts made by the circle x2 + y2 –5x – 13y – 14 = 0 which are perpendicular to 3x – 4y –1 = 0 are : a. 3x + 4y = 3, 3x + 4y + 25 = 0 b. 4x + 3y = 5, 3x + 4y - 25 = 0 c. 3x - 4y = 5, 3x - 4y + 25 = 0 d. none of these
    67. 67. 65 Problem three identical dice are rolled. The probability that the same number will appear on each of them as : a. 1 6 1 b. 18 1 c. 9 1 d. 36
    68. 68. 66 Problem 3 The principal value of sin is : 2 a. - 6 b. 6 2 c. - 3 2 d. 3
    69. 69. 67 Problem 1 3 cos x 4 sin x dy If y cos then equals : 5 dx 1 a. 1 x3 b. 1 1 c. 1 x3 d. - 1
    70. 70. 68 Problem The point on y2 = 4ax nearest to the focus has its abscissa equal to : a. a b. - a a c. 2 d. 0
    71. 71. 69 Problem The vertex of the parabola x2 + 8x + 12y + 4 = 0 is : a. (- 4, 1) b. (4, - 1) c. (- 4, -1) d. (4, 1)
    72. 72. 70 Problem The standard deviation for the data : 7, 9, 11, 13, 15 is : a. 2.4 b. 2.5 c. 2.7 d. 2.8
    73. 73. 71 Problem While dividing each entry in a data by a non-zero number a, the arithmetic mean of the new data : a. Is multiplied by a b. Does not change c. Is divided by a d. Is diminished by a
    74. 74. 72 Problem Two circles which passes through the points A (0, a) and B (0, -a) an touch the line y = mx + c will cut orthogonally if : a. c = a 2 m2 b. a = a 2 m2 c. m2 = a2 (1+ c2) d. m = - a 1 c2
    75. 75. 73 Problem 2 2 If , are the roots of ax2 + bx + c = 0, then equals : a. c(a b) a2 b. 0 bc c. a2 d. abc
    76. 76. 74 Problem The maximum value of 5 sin 3 sin 3 is : 3 a. 11 b. 10 c. 9 d. 12
    77. 77. 75 Problem If x= y = 15, x2 = y2 = 49 xy = 44 and x = 5, then byx is equal to: a. 1 3 2 b. 3 1 c. 4 1 d. 2
    78. 78. 76 Problem The number of terms which are free from radical sings in the expansion of (x1/5 + y1/10)55 is : a. 5 b. 6 c. 11 d. 9
    79. 79. 77 Problem The sum of the co-efficient in the expansion of (x + 2y + x)10 is : a. 10C x+y b. x+yC 10 c. 26.4Cx d. none of these
    80. 80. 78 Problem There are 10 points in a plane, out of which 4 points are collinear. The number of triangles formed with vertices as there points is : a. 20 b. 120 c. 40 d. 116
    81. 81. 79 Problem If the co-ordinate of the centroid of a triangle are (3, 2) and co-ordinates of two vertices are (4, 1) and (2, 5), then co-ordinates to the third vertex are : a. (6, 8) b. (2, 8/3) c. (0, - 4) d. (6, 0)
    82. 82. 80 Problem the argument of 1 i 3 is : 1 i 3 4 a. 3 2 b. 3 7 c. 6 d. 3
    83. 83. 81 Problem In how many ways can a constant and a vowel be chosen out of the word COURAGE ? a. 7C 2 b. 7P 2 c. 4P x 3P1 1 d. 4P x 3P1 1
    84. 84. 82 Problem The length of the latusrectum of the ellipse 5x2 + 9y2 = 45 is : a. 5 3 b. 10 3 c. 2 5 5 5 d. 3
    85. 85. 83 Problem The projections of a line segment on the coordinate axes are 12, 4, 3. The direction cosine of the line are : 12 4 3 a. , , 13 13 13 12 4 3 b. , , 13 13 13 12 4 3 c. , , 13 13 13 d. None of these
    86. 86. 84 Problem n The least positive value of n if i(1 3) is positive integer, is : 1 i2 a. 1 b. 2 c. 3 d. 4
    87. 87. 85 Problem lim sec loge (2x ) is equal to : x 1 4x 2 a. 0 b. 2 2 c. 4 d. 2
    88. 88. 86 Problem The distance between the planes gives by ,  ˆ  ˆ r .(ˆ i 2ˆ j 2k ) 5 0 and r .(ˆ i 2ˆ j 2k ) 8 0 is : a. 1 unit 13 b. 3 units c. 13 units d. none of these
    89. 89. 87 Problem If the coefficient of correlation between X and Y is 0.28, covariance between X and Y is 7.6 and the variance X is 9, then the standard deviation of Y series is : a. 9.8 b. 10.1 c. 9.05 d. 10.05
    90. 90. 88 Problem 1 1 3 If sin tan , then equals : 4 3 a. 5 b. 1 2 c. 5 3 d. 4
    91. 91. 89 Problem (x 1) 2 If 4 , then the value of x 1 is : x x 2 a. 4 b. 10 c. 16 d. 18
    92. 92. 90 Problem (x 1) x3 1 If 2 cos , then equals : x x3 1 cos 3 a. 2 b. 2 cos c. cos3 1 cos 3 d. 3
    93. 93. 91 Problem The mode of the given distribution is : Weight (in kg) 40 43 46 49 52 55 Number of children 5 8 16 9 7 3 a. 40 b. 55 c. 49 d. 46
    94. 94. 92 Problem The factors of x a b are : a x b a b x a. x – a, x – b and x + a + b b. x + a, x + b and x + a + b c. x + a, x + b and x - a - b d. x – a, x – b and x - a - b
    95. 95. 93 Problem 7 1 The equation of a curve passing through 2, and having gradient 1 at (x, y) 2 x2 is : a. y = x2 + x + 1 b. xy = x2 + x + 1 c. xy = x + 1 d. none of these
    96. 96. 94 Problem The general value of x satisfying is given by cos x = 3 (1 – sin x ) : a. x n 2 b. x n x x m ( 1)n c. 3 6 x n d. 3
    97. 97. 95 Problem The angle of elevation of the tops of two vertical tower as seen from the middle point of the line joining the foot of the towers are 600 and 300 respectively. The ratio of the height of the tower is : a. 1 : 2 b. 2 : 4 c. 4 : 2 d. 2 : 1
    98. 98. 96 Problem If an angle is divided into two parts A and B such that A – B = x and tan A : tan B = k : 1, then the value of sin x : a. k 1 sin k 1 k sin b. k 1 k 1 sin c. k 1 d. None of this
    99. 99. 97 Problem In triangle ABC and DEF, AB = DE, AC = EF and A 2 E . Two triangles will have the same area if angle A is equal to : a. 3 b. 2 2 c. 3 5 d. 6
    100. 100. 98 Problem the even function is : a. f(x) = x2 (x2 + 1) b. f(x) = x (x + 1) c. f(x) = tan x + c d. f(x) = sin2 x + 2
    101. 101. 99 Problem The middle term in the expansion of (1 + x)2n will be : a. (n + 1)th b. (n - 1)th c. nth d. (n + 2)th
    102. 102. 100 Problem For the equation | x |2 | | x | - 6 = 0 a. There is only one root b. There are only two distinct roots c. There are only three distinct roots d. There are four distinct roots
    103. 103. FOR SOLUTIONS VISIT WWW.VASISTA.NET
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