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1)
The solution of the equation d2y/dx2 = e-2x
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a )
e-2x/4
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b )
e-2x/4 + c x + d
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c )
e-2x/4 + c x2 + d
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d )
e-2x/4 + c + d
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| see the answer see the solution |
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2)
The domain of sin-1[ log3(x/3) ] is
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a )
[ 1 , 9 ]
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b )
[ -1 , 9 ]
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c )
[ -9 , 1 ]
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d )
[ -9 , -1 ]
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| see the answer see the solution |
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3)
The period of function f (x) = sin4x + cos4x is
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a )
π
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b )
π/2
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c )
2π
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d )
none of these
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| see the answer see the solution |
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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
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a )
3x2 + 19x + 3 = 0
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b )
3x2 - 19x + 3 = 0
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c )
3x2 - 19x - 3 = 0
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d )
x2 - 16x + 1 = 0
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| see the answer see the solution |
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5)
A triangle with vertices (4, 0) , (-1, -1), (3 , 5) is
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a )
isosceles and right angled
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b )
isosceles but not right angled
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c )
right angled but not isosceles
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d )
neither right angled nor isosceles
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| see the answer see the solution |
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6)
If sin y = x sin(x + y) , then dy/dx is
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a )
(sinα) / (sinα sin2(α + y) )
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b )
sin2(α + y)/sinα
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c )
sinα sin2(α + y)
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d )
sin2(α - y)/sinα
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| see the answer see the solution |
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7)
The function f(x) = cot-1x + x increases in the interval
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a )
( 1 , ∞ )
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b )
( -1 , ∞ )
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c )
( -∞ , ∞ )
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d )
( 0 , ∞ )
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| see the answer see the solution |
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8)
is equal to
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a )
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b )
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c )
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d )
none of these
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| see the answer see the solution |
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9)
If y = (x +  )n ,
then
is
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a )
n2y
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b )
- n2y
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c )
- y
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d )
2x2y
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| see the answer see the solution |
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10)
cot-1( ) = x , then sin x =
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a )
tan2(α/2)
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b )
cot2(α/2)
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c )
tan α
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d )
cot(α/2)
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| see the answer see the solution |
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11)
 ,
is
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a )
20
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b )
8
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c )
10
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d )
18
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| see the answer see the solution |
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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
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a )
3/4
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b )
1/2
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c )
2/3
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d )
1/3
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| see the answer see the solution |
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13)
 ,
is
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a )
π2/4
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b )
π2
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c )
zero
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d )
π/4
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| see the answer see the solution |
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14)
The differential equation of all non-vertical lines in a plane is
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a )
d2y/dx2 = 0
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b )
d2x/dy2 = 0
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c )
dy/dx = 0
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d )
dx/dy = 0
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| see the answer see the solution |
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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
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a )
7
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b )
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c )
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d )
None of these
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| see the answer see the solution |
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16)
The equation of the directrix of the parabola y2 + 4y + 4x + 2 = 0 is
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a )
x = -1
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b )
x = 1
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c )
x = - 3/2
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d )
3/2
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| see the answer see the solution |
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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 ?
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a )
73
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b )
65
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c )
68
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d )
74
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| see the answer see the solution |
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18)
l , m , n are the pth , qth , rth terms of a G.P. (all positive) , then
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a )
3
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b )
2
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c )
1
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d )
zero
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| see the answer see the solution |
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19)
The value of 21/4 , 41/8 , 81/6 .... ∞ is
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a )
1
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b )
2
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c )
3/2
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d )
4
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| see the answer see the solution |
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20)
Evaluate
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a )
π/4
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b )
π/2
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c )
zero
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d )
1
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| see the answer see the solution |
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21)
The area bounded by the curve y = 2x - x2 and the straight line y = -x is given by
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a )
9/2
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b )
43/6
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c )
35/6
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d )
none of these
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| see the answer see the solution |
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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
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a )
-2/3 , 2
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b )
1/3 , 2
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c )
2/3 , 0
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d )
2 , 7
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| see the answer see the solution |
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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
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a )
1/25
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b )
24/25
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c )
2/25
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d )
None of these
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| see the answer see the solution |
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24)
In a triangle ABC , 2ca sin((A - B + C)/2) =
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a )
a2 + b2 - c2
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b )
c2 + a2 - b2
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c )
b2 - c2 - a2
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d )
c2 - a2 - b2
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| see the answer see the solution |
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25)
The period of sin2θ is
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a )
π2
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b )
π
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c )
2π
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d )
π/2
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| see the answer see the solution |
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26)
The order and degree of the differential equation
are
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a )
(1 , 2/3)
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b )
(3 , 1)
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c )
(3 , 3)
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d )
(1 , 2)
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| see the answer see the solution |
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27)
then lim n [ In + In+2 ] equals
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a )
1/2
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b )
1
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c )
∞
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d )
zero
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| see the answer see the solution |
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28)
If xy = ex-y then dy/dx is
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a )
(1 + x)/(1 + log x)
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b )
(1 - log x)/(1 + log x)
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c )
not defined
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d )
(log x)/(1 + log x)2
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| see the answer see the solution |