1) The solution of the equation d2y/dx2 = e-2x

a )   e-2x/4 b )   e-2x/4 + c x + d c )   e-2x/4 + c x2 + d d )   e-2x/4 + c + d

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2) The domain of sin-1[ log3(x/3) ] is

a )   [ 1 , 9 ] b )   [ -1 , 9 ] c )   [ -9 , 1 ] d )   [ -9 , -1 ]

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3) The period of function f (x) = sin4x + cos4x is

a )   π b )   π/2 c )   2π d )   none of these

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4) If α ≠ β and a2 = 5α - 3 , β2 = 5β - 3, then the equation having α/β and β/α as its roots, is

a )   3x2 + 19x + 3 = 0 b )   3x2 - 19x + 3 = 0 c )   3x2 - 19x - 3 = 0 d )   x2 - 16x + 1 = 0

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5) A triangle with vertices (4, 0) , (-1, -1), (3 , 5) is

a )   isosceles and right angled b )   isosceles but not right angled c )   right angled but not isosceles d )   neither right angled nor isosceles

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6) If sin y = x sin(x + y) , then dy/dx is

a )   (sinα) / (sinα sin2(α + y) ) b )   sin2(α + y)/sinα c )   sinα sin2(α + y) d )   sin2(α - y)/sinα

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7) The function f(x) = cot-1x + x increases in the interval

a )   ( 1 , ∞ ) b )   ( -1 , ∞ ) c )   ( -∞ , ∞ ) d )   ( 0 , ∞ )

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8) is equal to

a )   b )   c )   d )   none of these

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9) If y = (x + )n , then is

a )   n2y b )   - n2y c )   - y d )   2x2y

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10) cot-1() = x , then sin x =

a )   tan2(α/2) b )   cot2(α/2) c )   tan α d )   cot(α/2)

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11) , is

a )   20 b )   8 c )   10 d )   18

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12) A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is 1/2 , 1/3 , and 1/4 . Probability that the problem is solved is

a )   3/4 b )   1/2 c )   2/3 d )   1/3

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13) , is

a )   π2/4 b )   π2 c )   zero d )   π/4

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14) The differential equation of all non-vertical lines in a plane is

a )   d2y/dx2 = 0 b )   d2x/dy2 = 0 c )   dy/dx = 0 d )   dx/dy = 0

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15) A parallelopiped is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7) , parallel to the coordinate planes. The length of a diagonal of the parallelopiped is

a )   7 b )   c )   d )   None of these

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16) The equation of the directrix of the parabola y2 + 4y + 4x + 2 = 0 is

a )   x = -1 b )   x = 1 c )   x = - 3/2 d )   3/2

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17) In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72 , then what is the average mark of the girls ?

a )   73 b )   65 c )   68 d )   74

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18) l , m , n are the pth , qth , rth terms of a G.P. (all positive) , then

a )   3 b )   2 c )   1 d )   zero

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19) The value of 21/4 , 41/8 , 81/6 .... ∞ is

a )   1 b )   2 c )   3/2 d )   4

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20) Evaluate

a )   π/4 b )   π/2 c )   zero d )   1

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21) The area bounded by the curve y = 2x - x2 and the straight line y = -x is given by

a )   9/2 b )   43/6 c )   35/6 d )   none of these

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22) The vector    + x + 3 is rotated through an angle θ and is doubled in magnitude , then it becomes 4 + (4x - 2) + 2 . The value of x is

a )   -2/3 , 2 b )   1/3 , 2 c )   2/3 , 0 d )   2 , 7

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23) A and B play a game where each is asked to select a number from 1 to 25 . If the two numbers match, both of them win a prize . The probability that they will not win a prize in a single trial is

a )   1/25 b )   24/25 c )   2/25 d )   None of these

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24) In a triangle ABC , 2ca sin((A - B + C)/2) =

a )   a2 + b2 - c2 b )   c2 + a2 - b2 c )   b2 - c2 - a2 d )   c2 - a2 - b2

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25) The period of sin2θ is

a )   π2 b )   π c )   2π d )   π/2

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26) The order and degree of the differential equation are

a )   (1 , 2/3) b )   (3 , 1) c )   (3 , 3) d )   (1 , 2)

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27) then lim n [ In + In+2 ] equals

a )   1/2 b )   1 c )   ∞ d )   zero

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28) If xy = ex-y then dy/dx is

a )   (1 + x)/(1 + log x) b )   (1 - log x)/(1 + log x) c )   not defined d )   (log x)/(1 + log x)2

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