Q1
Q2
Q3
Q4
Q5
Q6
~(pΛq) is logically equivalent to
a) p V q
b) p Λ q
c) ~ p V ~q
d) ~ p Λ ~q
Which of the following is not a statement
a) √3 is a prime number
b) √2 is an irrational number
c) Mathematics is interesting
d) 5 is an integer
If A and B are two matrices such that A+B and AB are both defined then
a) A & B are square matrices of same order
b) No of columns of A = no of rows of B
c) A & B are to matrices not necessarily of same order
d) A & B are any two matrices.
4 1
If =
such that
− 6 + 7 = 0 then k=
−1
a) 1
b) 3
c) 2
d) 4
1
4 −2
If
= −2 −5 4 and | | = 3 then Adj A =
1 −2 1
1 −2 1
a)
4 −5 −2
−2 4
1
1
2 1
b) −4 −5 2
−2 −4 1
1
4 −2
c)
−2 −5 4
1 −2 1
1
4 −2
d) −2 −5 4
1 −2 1
The principal solutions of √3 cot − 1 = 0 are
a)
,
b)
c)
Q7
Q8
,
,
d)
,
The polar coordinates of the point whose Cartesian coordinates are(0,-2) are
a) (-2,π/2)
b) (-2,3 /2)
c) (2,π/2)
d) (2,3 /2)
In ∆
if ∠ = 90 then
( )+
( )=
a) /8
Q9
b) /2
c)
/4
d) /6
The combined equation of pair of lines passing through origin and perpendicular to the lines
given by 2 x 2  3 xy  y 2  0 is
x 2  3 xy  2 y 2
b) x 2  3 xy  2 y 2
c) 2 x 2  3 xy  y 2
d) 2 x 2  3 xy  y 2
a)
Q 10
Q 11
Q 12
Q13
0
0
0
0
If the slope of the lines represented by 3 x 2  kxy  y 2  0 differ by 4 then k =
a) 2
b) -2
c) 2
d) 4
Area of the triangle formed by the lines x 2  4 xy  y 2  0 and x  y  10 is
a) 8 sq. units
b) 16 sq. units
c) 32 sq. units
d) 64 sq. units
If eˆ1 , eˆ2
a)
b)
c)
d)
and eˆ1  eˆ2 are unit vectors then the angle between eˆ1 and eˆ2 is
900
1200
4500
1350
   
a. a a. b
   
a. b b . b
a) 0
b) a 2 b 2
 
(a  b )2
  2
d) a. b
c)
Q 14
Q 15
 
If C is midpoint of AB and P is a point outside AB then
⃗+ ⃗ = ⃗
a)
⃗+ ⃗+ ⃗ =0
b)
⃗+ ⃗ =2 ⃗
c)
⃗+ ⃗+2 ⃗ =0
d)
   
 
2
If  a  b b  c c  a     a b c  then


a)
b)
c)
d)
2
3
0
1


Q 16
If the line is inclined at 600 and 300 with X and Y axes respectively, then the angle which it makes
with Z-axis is
a) 0
b) 
c)

d) 
Q 17
4
2
6
The direction cosines of a line passing through the points (-4,2,3) and (1,3,-2) are
25
2
5
,
,
51
51
51
5
2
5
,
,
b) 
51
51
51
5
1
5
,
,
c) 
2 51 2 51 2 51
5
1
5
,
,
d) 
51
51
51
a)
Q 18
The equation of X - axis is
x
1
x
b)
0
x
c)
1
x
d)
0
a)
Q 19
Q 20
Q 21

y
0
y

1
y

1
y

0

z
0
z

1
z

1
z

1

The straight line is
x  3 y  2 z 1
is


3
1
0
a) Parallel to X axis
b) Parallel to Y axis
c) Parallel to Z axis
d) Perpendicular to Z axis
The angle between the lines 2 x  3 y   z & 6 x   y  4 z is
a) 00
b) 300
c) 450
d) 900
If the planes ax  by  cz  d  0 & a1 x  b1 y  c1 z  d1  0 be mutually perpendicular, then
a b c
 
a1 b1 c1
a b c
  0
b)
a1 b1 c1
a)
aa1  bb1  cc1  1
d) aa1  bb1  cc1  0
c)
Q 22
The distance of point (1,0,2) from the point of intersection of the line
the plane x  y  z  16 is
x  2 y 1 z  2
and


3
4
12
a) 3 21
Q23
Q 24
Q 25
Q 26
b) 2 14
c) 13
d) 8
If the planes 3 x  2 y  2 z  17  0 & 4 x  3 y  kz  25 are mutually perpendicular, then k=
a) 3
b) -3
c) 9
d) -6
Region represented by the inequalities x  0 & y  0 is
a) First Quadrant
b) Second Quadrant
c) Third Quadrant
d) Fourth Quadrant
The constraints x  y  1; x  y  0; x  0; y  0 and the objective function z  x  y has
a) Unbounded solution
b) No unique solution
c) Bounded solution
d) Unique solution
If f(x) is continuous at x=0 where ( ) =
Q27
a)
b)
c)
d)
4
2
2
2
If f(x) is continuous at x=0 where ( ) =
a)
b)
c)
d)
Log 9
Log 3
Log 1
Log e
kx
⎧ (e  1) sin kx for x  0
2
⎨
⎩
x
4 for x  0
x
x
⎧ 3  3 for x  0
⎨
⎩
sin x
k for x  0
then k=
Q 28
If f(x) is continuous on [-  ,  ] where ( ) =
a)
b)
c)
d)
Q29
Q 30




 1,   1
 1,   1
 1,   1
 1,   1
If y  1  x 
a)
b)
c)
d)
y
–y
1
0
If y  elog x then
dy

dx
elog x
1
b)
x
Q32
c) 0
d) 1
dy

dx
a) x x (1  x log x)
b) x x (1  x log x)
c) x x (1  log x)
d) x x (1  log x)
If y  x x then
d2y

If x  f (t ), y  g (t ) then
dx 2
f ' (t ) g '' (t )  g ' (t ) f '' (t )
a)
[ f ' (t )]2
b)
c)
d)
⎨
⎪
⎪
⎩
dy
x 2 x3 x 4

   ...   then
dx
2! 3! 4!
a)
Q 31
⎧ 2sin x for    x  
⎪
2
⎪
f ' (t ) g '' (t )  g ' (t ) f '' (t )
[ f ' (t )]3
f '' (t ) g ' (t )  g '' (t ) f ' (t )
[ f ' (t )]2
f '' (t ) g ' (t )  g '' (t ) f ' (t )
[ f ' (t )]3
 sin x   for
cos x for


 x  then
2
2

 x 
2
Q33
Q34
Q35
The equation of normal to the curve y  3 x 2  4 x  5 at (1,2) is
a) x  10 y  21  0
b) x  10 y  21  0
c) x  10 y  21  0
d) x  10 y  21  0
A ladder 10 m long rest against a vertical wall with the lower end on the horizontal ground. The
lower end of the ladder is pulled along the ground away from the wall at the rate of 3 cm/sec.
The height of the upper end while it is descending at the rate of 4 cm/sec is
a) 8
b) 6
c) 4√3
d) 5√3
The function
1
e
b) has maximum value e
1
c) has minimum value
e
d) has minimum value e
e5log x  e 4log x
 e3log x  e2log x dx 
a) e(33 x )  c
b) e3 log x  c
a) has maximum value
Q36
x3
c
3
x3
c
d)
6
sin 2 x
 1  cos2 xdx 
1
log 1  cos 2 x  c
a)
2
1
log 1  cos 2 x  c
b)
2
c) 2 log 1  cos 2 x  c
c)
Q37
d)  log 1  cos 2 x  c
Q38
 x log xdx 
a)
b)
x2
(2 log x  1)  c
4
x2
(2 log x  1)  c
4
x2
(log x  1)  c
2
x2
(log x  1)  c
d)
2
 (sin(log x)  cos(log x))dx 
c)
Q39
a)  x sin(log x)  c
b) x sin(log x)  c
c)  x cos(log x)  c
d) x cos(log x)  c
Q40
Q41
 2
dx

tan x
0
3
a)
2
3
b)
4

c)
2

d)
4
10
dx
3 ( x  1)( x  2) 
 1
 32 

 9 
 9 
b) log  
 32 
 32 
c) log 

 27 
 27 
d) log 

 32 
a) log 
Q42
Q43
The area enclosed between the curve y  log e ( x  e) and the coordinate axes is
a) 3 sq. units
b) 4 sq. units
c) 2 sq. units
d) 1 sq. units
The area of the region bounded by the curves y  x 2 and y  x is
32
sq. units
3
16
b)
sq. units
3
a)
c)
d)
Q 44
Q45
8
sq. units
3
4
sq. units
3
  dy  2 
1    
 dx  
Order and degree of the differential equation   
d2y
dx 2
3/2
is
a) 2,2
b) 2,3
c) 2,1
d) 1,4
The differential equation of the family of the circles with fixed radius 5 units and center on the
line y=2 is
2
 dy 
a) ( y  2)    25  ( y  2) 2
 dx 
2
 dy 
2
  25  ( y  2)
 dx 
b) ( y  2) 
2
 dy 
c) ( x  2)    25  ( y  2) 2
 dx 
2
 dy 
d) ( x  2)    25  ( y  2) 2
 dx 
Q 46 Solution of the differential equation ( y 2  1) tan 1 xdx  2 y (1  x 2 )dy  0 is
1
tan 1 x  log 1  y 2  c
a)
2
1
tan 1 x  log 1  y 2  c
b)
2
1
(tan 1 x) 2  log 1  y 2  c
c)
2
1
(tan 1 x) 2  log 1  y 2  c
d)
2
Q47
1 5
Cx , x  0,1, 2,..,5
The p.m.f. of a r.v. is ( ) = 25
then
0 , otherwise
a) P ( X  2)  2 P ( X  3)
b) P ( X  2)  2 P ( X  3)
c) P ( X  2)  P ( X  3)
d) P ( X  2)  2 P ( X  3)
Q48
The p.m.f. of a r.v. X is
X=x
P(X=x)
a)
0
q3
1
3pq2
2
3p2q
3
p3
pq
b) 2 pq
c)
3 pq
d)
Q49
Q50
3 pq
If X  B (n, p ) & E ( X )  12 , Var ( X )  4 then the value of n is
a) 3
b) 48
c) 18
d) 36
A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of
distribution of success is
a) 8/3
b) 3/8
c) 4/5
d) 5/4