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02.
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4006
3006
4006
3)
3008
MATHEMATICS
1.
The position vectors of A, B, C are
a , b , c and the points D, E, F are
dividing BC, CA, AB respectively in
the ratio m : n then centroid of
DEF
a b c
1)
3
3)
2.
2)
a b c(m n)
3
4.
5.
6.
If A = Lt
x
4) O
12x 2 + 3x +11
,
3x 2 7x +8
C = Lt
1
1
1
....n terms
1.2 2.3 3.4
x
D =
x
ascending order is
1) C, D, B, A
3) A, B, D, C
7.
14.
0 1
15.
1 sin x
If f(x) =
1 0 0
8.
ex e
2
1
18.
is
x
=
1) tanh2 x
3) cosh2 x
2) sech2 x
4) tanh x
x
for x
1 |x|
9.
If f(x) =
10.
is
1) 0
2) –1
3) 1
4) does not exists
The nth term of the series
2
1
3
11.
2
1
2
5
2
2
1
2
19.
R then f ’(0)
20.
2
2 3
7
.... is
n(n 2)
n(n 1)
2)
1)
6
4
n(n 1)
n(2n 1)
4)
3)
6
6
1
If tn = (n + 2)(n + 3) for n = 1, 2, 3,
4
1 1 1
1
=
…. then + + +....+
t1 t 2 t 3
t 2003
0
21.
0
6
0
0
0
6
6
6
18 12
6
If 1 b
a3
b3 = k a
1
b
1
c and a, b,
a2
b2
c2
c3
1
c are different values then k =
1) a + b + c
2) ab + bc + ca
3) a2 + b2 + c2
4) abc
A lottery contains 100 tickets in
which only one tickets contains
prize. If a person purchases tickets
of it one after one, until he gets
prize ticket then probability that he
gets it in 50th attempt is
1) 1/50
2) 50/100
3) 1/100
4) 99/100
There are 10 bulbs in which 6 are
good bulbs and a room has 3 holders
in which only 2 are good holders. If
a person randomly picked 3 bulbs
and fit them in 3 holders the
probability for the room to get light
is
1) 13/15
2) 4/5
3) 29/30
4) 2/3
The probability of a bomb hitting a
bridge is ½ and one hit is sufficient
to destroy it. The least number of
bombs required so that the
probability of the bridge being
destroyed is greater than 0.8 is
1) 2
2) 3
3) 4
4) 5
If the mean of a binomial
distribution with 9 trials is 6, then its
variance is
32e4/3
81
32e 4/3
3)
81
32.
24.
26.
27.
28.
29.
e4/3
27
32e 4/3
4)
27
2)
Slopes of the tangents to the circle
x2 + y2 = 10 drawn through the
points (4, –2) are
3) –3, –
If the equation 3x – 2y + z = 0, x –
14y + 15z = 0, x + 2y + 3z = 0 has
non zero solution the =
1) 0
2) 29
3) 32
4) –30
2
31.
1
1) 3, –
3
4) 12 6 18
0 0 1
then their
1 sin x
6
2) 0
0
3) 0 1 0
16.
23.
25.
6 0 0
1) 0 6 0
0 0 6
1) 2
2) 3
3) 4
4) 2
With Poisson distribution 3P(x = 2)
= 2P(x = 1) then P(x = 3) =
1)
1
–
3 then [A(Adj A)A
1
]A =
1 c2
x
22.
1
continuous every where then f(0) =
1) 1/2
2) – 2
3) 1
4) 2
d
sin tan
dx
If A = 2 1
3 2
17.
2) C, A, B, D
4) A, C, D, B
2)
A stone is projected vertically
upward which rises ‘s’ feet in ‘t’
seconds is given by s = 112t – 16t2.
The maximum height reached by the
stone is
1) 196
2) 216
3) 144
4) 28
The value of ‘a’ for which the
function f(x) = a sin x + 1/3 sin 3x
has an extremum at x = /3, is
1) 1
2) – 1
3) 0
4) 2
Angle between the two curves x2 –
3xy2 + 2 = 0 and 3x2y – y3 = 2 is
2) /3
1) /4
4) 0
3) /2
1 a2
sin 7x sin 5x
x
Lt
13.
8 | x | 3x
,
3 | x | 2x
B = Lt
x
12.
a b c
3(m n)
With 3 non-zero, non-collinear
vectors a , b , c . If 3 a + b is
collinear with c and a + 3 c in
collinear with b then for some nonzero scalar K, 3 a + b + 9 c is
1) k( a + b + c )
2) k a
4) O
3) k c
If a , b are two unit vectors such that
a +
2 b and 5 a –
4 b are
perpendicular to each other then
angle between is
2) 60o
1) 90o
o
3) 45
4) 30o
If area of triangle ABC is and D is
any
point
then
| AB CD BC AD CA BD | =
2)
1) /2
4) 4
3) 2
((i – j) (j – k) (i + 5k)) =
1) 5i – 4j – k
2) 3i – 2j + k
3) 4i – 5j – k
4) 5i + 4j – k
3.
4003
3007
4006
4)
3009
1)
1
3
33.
1
2) –3,
3
1
4) 3,
3
2 10x 10
3 10x 10
2)
1
3
30.
34.
35.
36.
37.
2
3
8
3)
9
1)
1
2 3x
log
6
2 3x
1 x
then the value of f(5x)
If f(x) =
2x
interms of f(x) is
1) 5f(x)
2) 1/5f(x)
3) 1/5[f(x) + 2]
4) 5[f(x) + 1/2]
Let n(A) = 4 and n(B) = 5, the
number of all possible many – one
functions from A to B is
1) 625
2) 505
3) 120
4) 20
The arithmetic mean of the first n
odd natural numbers is
1) n
2) (n + 1)/2
3) (n – 1)
4) 2n
The arithmetic mean of the squares
of the first n natural numbers is
(n 1)
6
(n 2 1)
3)
6
38.
2)
4) n
n(n 1)
2
2) n(n + 1)
3) (n + 1)
e2
39.
If I1 =
0
4)
dx
and I2 =
log x
1) I1 < I2
3) I1 = I2
40.
41.
2)
42.
(n 1)(2n 1)
6
The mean of first n natural numbers
is
1)
4
3
5
4)
3
4 2
3
2 2
4)
3
2 3x
2 3x
1)
2)
The value of m for which the line
y mx 2 becomes a tangent to the
hyperbola 4 x 2 9 y 2 36 is
is
4)
dx
4 cos 2 x 9 sin 2 x
1
3
1) tan 1 tan x
6
2
n 1
2
2
ex
then
x
1
2) I1 > I2
4) I1 = –I2
C
2)
1
2 3 tan x
log
12
2 3 tan x
3)
1
2 3 tan x
log
4
2 3 tan x
C
4)
1
2 3 tan x
log
6
2 3 tan x
C
of the semi major axis is
2
3
8
3)
3
x
1
2 3x
log
2
2 3x
3) log10
1
and eccentricity is , then the length
2
1)
x
1 x
1 x
1) log10
Equation of the common radical axis
of the conjugate coaxial system of
the given coaxial system x2 + y2 +
4x – 3y – 2 + (2x – 3y + 5) = 0
1) 2x – 3y + 5 = 0
2) 3x + 2y + 5 = 0
3) 2x – 3y + 17/2 = 0
4) 3x + 2y + 3 = 0
The two circles x2 + y2 – 2x – 2y – 7
= 0 and x2 + y2 + 4x + 6y – 3 = 0 are
such that
1) touch extremely
2) touch internally
3) cut orthogonally
4) neither intersect nor touch
[A] : The locus of point of
intersection of perpendicular tangent
drawn to the circle x2 + y2 – 4x – 6y
– 12 = 0 is the circle x2 + y2 – 4x –
6y + 12 = 0.
[R] : Locus of point of intersection
of perpendicular tangents, is a circle
which is concentric with given circle
and radius is 2 times of radius of
given circle.
1) Both A and R are true and R is
the correct explanation of A
2) Both A and R are true but R is not
the correct explanation of A
3) A is false R is true
4) A is true R is false
Length of the double originate of the
parabola y2 = 8x which subtends an
angle 60o at the vertex is
2) 16
1) 16 3
4) 32
3) 8 3
Slope of common tangent to the
parabola y2 = 4x and x2 = 32y is
1) 1/2
2) – 1/2
3) 2
4) – 2
The focus of an ellipse is at the
origin the directrix is the line x 4
If a = 3i – 2j + k, b = 2i – 4j – 3k, c
= –i +2j + 2k then a + b + c =
1) 3i – 4j
2) 3i + 4j
3) 4i – 4j
4) 4i + 4j
The points 2i + 4j – k, 4i + 5j + k, 3i
+ 6j – 3k from
1) an equilateral triangle
2) an isosceles triangle
3) a right angled triangle
4) a right angled isosceles triangle
Inverse of the function f(x) =
C
The area bounded by the curve y = x
and y = x3 is
1) 1/4
2) 1/6
3) 1/12
4) 1/2
Area of the region bounded by
y x , the x-axis and the ordinates