Bca MCQ
Bca MCQ
Bca MCQ
(b) 1
(c) 0
(d) c
(Answer: c)
2.
d u
dx v
(a) vu uv
(b) vu uv
(c)
v u u v
v2
(d)
vu uv
u2
(Answer: d)
3.
d
uv
dx
(a)
vu uv
v2
(b) vu uv (c)
v u u v
v2
(d)
(Answer: b)
4.
d
xn
dx
(a) nx n 1
(Answer: a)
5.
(c) nx n 1
(d) x n 1
(b) 3x 2
(c) 3x
(d) 2x 2
d
x3
dx
(a) 2x 3
(Answer: b)
6.
(b) x n 1
d ax
e
=
dx
(a) xe ax
(b) e ax
(c) ae ax
(d) e ax
(b) ae ax
(c) ae ax
(d) ae ax
(Answer: c)
7.
d ax
e
=
dx
(a) ae ax
(Answer: b)
vu uv
v2
d ax b
e
=
dx
8.
(a) e ax b
(c) be ax b
(b) e ax
(d) ae ax b
(Answer: d)
d
x 5 is
dx
9.
(a) 4x 5
(b) 5x 4
(c) x 5
(d) 5x 4
(Answer: b)
1
10.
d
(x) 4 is
dx
(a)
1
x
4
3
4
(b)
3
x
4
3
4
(c)
1 4
x
4
(d)
1
x
4
3
4
(Answer: a)
MODERATELY
1.
EASY
d
2e 3 x =
dx
(a) e 3 x
(b) 6e 3 x
(c) 6e 3 x
(Answer: b)
2.
d
sin ax =
dx
(a)
cos ax
a
(b)
sin ax
a
(c) a cos ax
(d) a cos ax
(Answer: d)
3.
d
cos ax =
dx
(a) a sin ax
(Answer: a)
(b)
sin ax
a
(c)
cos ax
a
(d) a sin ax
4.
d
sin 3 x =
dx
(a) 3 sin 3 x
(b) 3 cos 3 x
cos 3 x
3
(c)
(d)
sin 3 x
3
(Answer: b)
5.
d
cos 5 x
dx
=
(b) cos 5 x
(a) - 5 sin 5 x
(d) sin 5 x
(c) sin 5 x
(Answer: a)
d
tan x
6. dx
(a) -co
sec 2 x
(c)
(d)
sec x
sec 2 x
(Answer: d)
d
cot x
7. dx
(a) -co
sec 2 x
(d)
sec 2 x
(Answer: a)
d
cos ecx
8. dx
(a) -co
sec 2 x
(Answer: b)
d
sec x
9. dx
(a) -co
sec 2 x
(d)
(Answer b)
d
sin 1 x
dx
10.
1
(a)
1 x
(b)
1
1 x
(c) 1 x 2
(c)
(d)
1
1 x2
(Answer a)
d
cos 1 x
11. dx
1
(a)
1 x
(Answer: c)
d
tan 1 x
dx
12.
(b)
x
1 x
1
1 x
(d)
1
1 x2
sec 2 x
(d)
sec 2 x
(a)
1 x
(b) 1 x 2
(c)
(b) 1 x 2
(c)
1
1 x
(d)
1
1 x2
(d)
1
1 x2
(Answer: d)
d
cot 1 x
dx
13.
1
1 x2
(Answer: a)
(a)
d
cos ec 1 x
dx
14.
1
(a)
x x 1
2
(b)
1
x x 1
2
1
1 x
(c) x x 2 1
(d)
1
x x2 1
(Answer: b)
d
sinh x
dx
15.
a) sinhx
(b) coshx
(c) coshx
(d) tanhx
(b) -coshx
(c) -sinhx
(d) tanhx
(b) -cosechx
(c) sech2x
(d) -sech2x
(Answer: c)
d
cosh x
dx
16.
a) sinhx
(Answer: a)
d
tanh x
dx
17.
a) sinhx
(Answer: c)
d
sin 5 x 6 =
dx
18.
(a)
cos (5 x 6)
5
cos (5 x 6) . 6
(Answer: c)
(b) cos (5 x 6) . 5
(c) cos (5 x 6) . 5
(d)
d 3
x 2x 2 is
dx
19.
(a) 3 x 2 4 x
(b) 3 x 2 4 x
(c) 3 x 2 2 x 2
(d) 3 x 3 4 x
(Answer: b)
d
4 x 3 9 6 x 2 is
dx
20.
(a) 12 x 2 12 x
(b) 12 x 2 12 x
(c) 12 x 2 12 x
(d) 12 x 2 12 x
(Answer: d)
21. d x 3 x 2 2 x 1
dx
(a) x 3 2 x 2
(b) 3x 2 x 2
(c) 3x 2 2 x 2
(d) 3 x 2 2 x 1
(Answer: c)
22. d 6 x 9 2 x 1 is
dx
8
(a) 54 x 2
1
x2
8
(b) 54 x 2
1
x2
(c) 54 x 8 2 x 2
8
(d) 54 x 2 x
(Answer: b)
d
sin 3 5 x is
dx
23.
(Answer: a)
24.
d d n 1 y
dx dx n 1
d dy
a) dx dx
n
(b) d ny
dx
(c)
dy
dx
(Answer: b)
25.D2(uv) = vD2u + 2Du.Dv + u.D2v. Say true or false
n 1
(d) d n y
dx 1
1
x2
a) true
b) false
(answer: a)
MODERATE
1.
10
d
3 x 2 8 x 1 is
dx
(a) 10 3 x 2 8 x 1 6 x 8
(b) 30 3 x 2 8 x 1
(c) 10 3 x 2 8 x 1 6 x 8
(d)
10 3 x 2 8 x 1
6x 8
(Answer: a)
2.
d x
a is
dx
(a) xa log a
(b) xa log x
(c) ax log x
(d) ax log a
(Answer: d)
3.
d 2
x
dx
1
3
is
1
(a)
2 3
x
3
(b)
2
x
3
1
3
(c)
1
x
3
1
3
(d)
2
x
3
2
3
(Answer: b)
4.
1 x 2 is
dx
(a) 1 x 2
(b) 1 - 2x
(c) 2 x (d) 2x
(Answer: d)
5.
d 4
x 3x 3 x 1 is
dx
(a) 4 x 3 9 x 2 1
(Answer: a)
6.
d
1 x is
dx
(b) 4 x 3 9 x 2 1
(c) x 4 9 x 2 1
(d) (4 x 3 9 x 2 1)
(a)
1
2 1 x
(b)
(Answer: b)
7.
d x 2
dx 2 x
2 1 x
(c)
(d)
1 x
x 1
2 x2
(Answer: b)
(b)
1 2
2 x2
(c)
1 2
2 x2
(d)
5
cos x
cos 5 x
2
2
b)
5
cos x
cos 5 x
2
2
(c)
5
cos x
sin 5 x
2
2
(d)
5
sin x
sin 5 x
2
2
(Answer: a)
d
cos 3 x is
dx
(b) 3 cos 2 x
(c) 3 cos 3 x
(d)
3 cos x sin x
2
(Answer: d)
10.
e 2 x cos 2 x is
dx
1 2
2 x2
d
sin 3x cos 2 x is
dx
(a)
9.
2 1 x
is
(a)
8.
d
log (5 x 4) is
dx
(a)
5
(5 x 4)
(Answer: b)
(b)
5
(c) log (5 x 4).5
(5 x 4)
(d)
log (5 x 4)
5
d
1
is
2
dx 4 x 1
12.
( a ).
4x
8x
2
(b).
4x
8x
2
(c ).
8x
4x
8x
( 4 x 2 1) 2
(d).
(Answer: d)
d
x 4 x 2 1 is
dx
13.
(a)
4x 3 2x 1
x x 1
4
2x
(b) 2 x x x x 1 (c)
3
(d)
x x 1
4
2x
x x 1
4
(Answer: c)
3
d
x 2 5 is
dx
14.
(a) 6 x x 2 5
(b)
6x
2
(c) 6 x x 2 5
(d) 6 x x 2 5
(Answer: c)
d 2 250
x
is
dx
x
15.
(a) x 2 250
(c) 2 x
(b) 2 x 250
250
x2
(d) 2 x
250
x2
(Answer: c)
16.
d
log e 2 x is
dx
(a)
1
2x
(b) 2
(c)
2
e2x
(d) 1
(Answer: b)
17. If y tan x, then
(a) tan 2 x
(Answer: a)
dy
dx
(b)
cos x
(c)
log sec x
(c) 1 cos x
(d) sec 2 x
(Answer: c)
2
d
4 x 2 is
dx
19.
(a) 16 x 4 x 3
(b) 16 x 4 x 3
(c) 16 x 4 x 3
(d)
16 x 4 x 3
(Answer: d)
20. d 5 sin x log x is
dx
(a) 5 cos x
1
x
(b) 5 cos x
1
x
(Answer: b)
21.
d x
e sin x is
dx
(a) e x cos x
(b) e x cos x
(c) e x cos x
(d) e x cos x
(Answer: a)
22.
d
xe x log x is
dx
(a) e x 1 log x x x log x (b) e x 1 log x x x log x
(c) e x 1 log x x log x
(Answer: c)
23.
d
log sin x 2 is
dx
(a) 2 log sin x tan x (b) 2 log cos x cot x (c) 2 log sin x cot x (d)
2(log sin x ) cot x
(Answer: d)
24.
d
x 2 sin x is
dx
1
x
(a) x 2 cos x 2 x sin x (b) x 2 cos x 2 x sin x (c) x 2 cos x 2 x sin x (d)
x 2 cos x 2 x sin x
(Answer: a)
d
cos x log x is
dx
25.
cos x
cos x
sin x log x (b)
sin x log x (c) x cos x sin x log x (d)
x
x
cos x
sin x log x
x
(a)
(Answer: b)
d2
( 2 x 5) 3 is
2
dx
26.
(a) 6 (2x+5)
(c) 6 (2x+5)2
(b) 24 (2x+5)
(d) (2x+5)
(Answer: b)
27. Given x = a sin ; y a 1 cos then
(a) tan
(b) cot
(c) cot
dy
=
dx
(d) tan
(Answer: c)
28. If xy 64 0, then
(a) y
x
dy
.
dx
(b) y
x
(c)
y
x2
(d)
y
x2
(Answer: b)
29.The nth derivative of eax is
(a)
ane-ax
(b) - ane-ax
(c) aneax
(d) aneanx
(Answer: c)
MODERATELY DIFFICULT
d
1
dx ( x 3) (3 x 2) is
1.
6x 7
( x 3) 2 (3 x 2) 2
6x 7
(c)
( x 3) (3 x 2)
6x 7
( x 3) 2 (3 x 2) 2
6x 7
(d)
( x 3) (3 x 2)
(a)
(b)
(Answer: a)
d2
x 3 12 x is
2
dx
2.
(a) 3 x 2 12
(b) 6x
(c) 6
(d) 6x
(Answer: d)
d2 3
x 6 x 2 9 x 15 is
2
dx
3.
(a) 6x 12
(b) 6x + 12
(c) 12 6x
(d) 6x 12
(Answer: a)
d3
8x 5 is
dx 3
4.
(a) 40x 4
(b) 160 x3
(c) 480 x2
(d) 480 x
(Answer: c)
d3
log (1 x ) is
dx 3
5.
(a)
1
1 x
(b)
1 x
(c)
1 x
(d)
(Answer: c)
6.
d 3 3x
e
is
dx 3
(a) 27e 3 x
(b) 9e 3 x
(Answer: a)
7. If x = at2, y = 2at, then dy
dx
(c) 3e 3 x
(d) e 3 x
1 x 4
(a)
1
t
(b)
1
t
(c) t
(d) - t
(Answer: b)
2
8. If y 8 x, then
(a)
4
y
dy
.
dx
(b)
4
y2
(c)
4
y
(d)
4
y2
(Answer: c)
2
x
9. If y e , then
(a) 2 xe x
(Answer: b)
(b) 2 xe x
10.Given x = 4t, y =
(a)
dy
dx
1
t2
(c) 2 xe x
(d) 2 xe x
dy
4
, then
t
dx
(b)
1
t2
(d) t 2
(c) t 2
(Answer: a)
11. Given x = sint, y =cos2t, then
(a) 4 cos t
dy
dx
4 sin t
(d) 4 sin t
(Answer: c)
dy
dx
2e t
et
(d)
t
t
(a)
e
t2
(b) e t
(c)
(Answer: d)
13. If sinx = y, then that angle x lying between ----- such that sinx = y is called the principal
value of sin-1y
(a)
(Answer: d)
(b) 0,
(c)
0, 2
(d)
1
x
1
x
(b) e
x2
1
x
e
x
(c)
(d)
1
x
e
x2
(Answer: d)
15.If y =
3
dy
,
2 then
dx
4 x
6x
(a) (4 x 2 ) 2
(b)
6x
(4 x 2 ) 2
(c)
3
(4 x 2 ) 2
(d)
3x
(4 x 2 ) 2
(Answer: b)
16.In the case of a function consisting of a number of factors, it is convenient to take the
logarithm before differentiating. Say true or false
a) true
b) false
(answer: a)
b) false
(answer:b)
18.If the two variables x and y are connected by a relation of the form f(x, y) = 0, it is often
difficult or impossible to find y explicitly in terms of x and then obtain its derivative. Say true
or false
a) true
b) false
(answer: a)
19.The new function may be differentiable, in which case, the derivative of the first derivative is
called the second derivative of the original function. Say true or false
a) true
b) false
(answer: a)
(a) 0, 2
(b)
(c)
(Answer: c)
22. The principal value of tan-1y lies between ------
(d) 0,
(a) 0, 2
(b)
(c)
(d) 0,
(Answer: b)
23.The principal value of cos-1y lies between -----
(a) 0, 2
(b)
(c)
(d) 0,
(Answer: d)
24. d x 1 3x 1 is
dx
(b) 6 x 4
(a) -6x +4
(c) 6x + 4
(d) -6x +4
(Answer: b)
dy
dx
(b) 6cos3x
(c) -6sin3xcos3x
(Answer: c)
DIFFICULT
1. If y = eax, then
dny
dx n
(a) aneax
(b) a!eax
(c) aeax
(d) xneax
(Answer: a)
2.
d
tan 1
dx
(a)
2x
2 is
1 x
2
1 x2
(b)
2
1 x2
(c)
2
1 x2
(d)
2
1 x2
(Answer: a)
dy
dx
(c) cot 2
4
4
3.Given x a cos , y b sin , then
(a) tan 2
(b) cot 2
(d) tan 2
(d) 2sin3xcos3x
(Answer: a)
4 .Given x a cosh , y a sinh , then
(a)
b
sec h
a
(b)
b
coth
a
dy
dx
b
coth
a
(c)
(d)
b
cos ech
a
(Answer: b)
5. The nth derivative of sin(ax + b) is
n
ax b
2
n
(a) a sin
(c) a n sin n ax b
ax b
2
n
(b) a sin
ax b
2
(d) sin
(Answer: b)
6. The nth derivative of cos(ax + b) is
n
ax b
2
(b) a n cos n ax b
ax b
2
(d) cos
n
(a) a cos
n
(c) a cos
ax b
2
(Answer: c)
7.
(a)
d
cos x
tan 1
dx
1 sin x
1
2
(b)
1
2
(c)
(d)
(Answer: a)
8. The nth derivative of sinx is
n
(d) sin n x
(Answer: b)
9. The nth derivative of cosx is
(a) cos n x
x
2
x
2
(d) cos
(Answer: c)
9.
d
(3 x 7) (4 x 3) is
dx
(a) 24 x 37
(b) 24 x 37
(c) 24 x 38
(d) 25 x + 37
(Answer: a)
d
( x 2 e x ) is
dx
10.
(a) e x 2 x x 2
(b) e x 2 x x 2
(c) e x 2 x x 2
(d) e x 2 x x 2
(Answer: c)
dx
(a)
x n 1
c, n 1
n 1
xn
c
n
(b)
(c) x n1 c
(d)
(Answer: a)
2.
dx
ax
(a) e ax c
(b) ae ax c
ax
(c) e c
(Answer: d)
3.
x n 1
c, n 1
n 1
sin axdx
ax
(d) e c
(a) a cos ax c
(b)
sin ax
c
a
(c)
cos ax
c
a
(d)
cos ax
c
a
(Answer: c)
4.
cos axdx
(a) a sin ax c
(b)
sin ax
cos ax
c (c)
c
a
a
(d)
sin ax
c
a
(Answer: b)
5.
sec
xdx
(a) tan x c
(c) tan x c
(Answer: a)
6.
cos ec
xdx
(a) tan x c
(b) cot x c
(c) cot x c
(b) sec x c
(c) cot x c
(b) sec x c
(c) cot x c
(Answer: c)
7.
(a) tan x c
(Answer: b)
8.
(a) tan x c
(Answer: d)
9.
dx
1 x
(a) tan 1 x c
(b) cos 1 x c
(c) tan x c
(d) sin 1 x c
(b) sin 1 x c
(c) cos ec 1 x c
(d) cos 1 x c
(Answer: a)
10.
dx
1 x2
(a) tan 1 x c
(Answer: b)
MODERATELY EASY
1. cosh axdx
(a)
sinh ax
c
a
sinh ax
c
a
(d) a sinh ax c
(Answer: c)
2.
sinh axdx
(a)
sinh ax
c
a
(b)
cosh ax
c
a
(c)
sinh ax
c
a
(d)
(Answer: d)
3.The value of
dx is
2
4
(b) x c (c) x c
(a) 4 x 4 c
(Answer: c)
4.The value of the integral
x dx
is
4
(d) x c
cosh ax
c
a
(a) 2 x 2 c
3
(Answer: a)
5.The value of the integral
(a)
3
2
(b) 2 x
3
3x
3x
c
3
(c) 3 x 2 c
2
(d) 3 x
2
3
2
c.
is
dx
(b) x 4 c
(c)
x4
c
4
(d)
3x 4
c
4
(Answer: d)
6.The value of
f x dx
is
2
(b) f x c
(a) f x c
(c) f ( x) c
(d) f x c
2
(Answer: c)
7.The value of the integral
(a) 3e 3 x c
3x
is
dx
(b)
e 3x
c
3
(b)
e 2 x 3
c (c) e 2 x 3 c
2
(c) e 3 x c
(d)
(Answer: b)
8.
2 x 3
(a)
e 3 x
c
3
dx
e 2 x 3
c
3
(d) 2 e 2 x 3 c
(Answer: b)
e x dx
x
(Answer: a)
10.The value of the integral
(a) x tan 1 x c
(Answer: d)
11.
dx
3x 4
x2
1 x 2 dx
(b) x tan 1 x c
1
log (3 x 4) c
3
log (3 x 4) c
1
3
(a)
(d)
(Answer: a)
12.The value of the integral
(a)
1
cos 2 x c
4
sin x cos x dx is
(b)
1
1
cos 2 x c (c) sin 2 x c
4
4
(b)
3
2
(cos x) 2 c
3
(b)
1
tan 5 x c
5
(d)
1
sin 2 x c
4
(Answer: a)
13.
sin x cos x dx
(a)
3
2
sin x 2 c
3
3
3
2
2
(cos x) 2 c (d) (sin x) 2 c
3
3
(c)
(Answer: d)
14.
tan
x sec 2 x dx
(a) tan 5 x c
(c) 5 tan 5 x c
(d)
1
tan 5 x c
5
(Answer: b)
15.
x2
ex
(a)
dx
3
1
log e x c
3
1
3
x3
3e
x3
(d)
1
3e x
(Answer: a)
16. sin( 2 x 3) dx
(a) cos(2 x 3) c (b) cos(2 x 3) c (c)
1
1
cos(2 x 3) c (d) cos( 2 x 3) c
2
2
(Answer: c)
3
17. x 3 x dx
(a) 3 x 2 3 c
(b)
x4
3x 2 c
4
(c) 4 x 4 6 x 2 c
(d)
x 4 3x 2
c
4
2
10 x
c (c) 5 log(1 x 2 ) c
(1 x 2 ) 2
(d)
5
log(1 x 2 ) c
2x
(Answer: d)
18.
5
dx
1 x2
(a) 5 tan 1 x c
(b)
(Answer: a)
19.The value of the integral
log x dx
is
(c) -xlogx+x+c
(d) -xlogx-x+c
(Answer: a)
20.
3
2
dx
(a) x
1
2
(b) 2 x
1
2
1
2
(c) 2 x c
2
(d) x c
2
(Answer: b)
21.The value of integral
1
sin 3x 3 sin x c
6
1
(c) sin 3 x 3 sin x c
6
(a)
(d)
1
sin 3x 3 sin x c
6
(Answer: a)
x
dx
2
22. cos
(a) 2 cos
x
1
x
c (b) sin c
2
2
2
(c)
1
x
x
cos c (d) 2 sin c
2
2
2
(c)
5 2
5 2
2 c (d) 3 c
x x
x x
(Answer: d)
23. The value of the integral
5x 1
dx is
x3
5 2
5 2
2 c (b) 2 c
x x
x x
(Answer: a)
(a)
( x 2)
dx is
(a) ( x 2) 4 4 (b) ( x 2) c
4
(c)
( x 2)4
4
(d) ( x 2) 4 c
(Answer: c)
b
25.
f ( x)dx
false
a) true
b) false
(Answer: b)
MODERATE
1. If u, v are two functions of x, then
(a) uv vdu
udv
(b) uv vdu
(c) uv vdv
(d)
uv udu
(Answer: a)
2.The value of the integral
(a)
2 cos x c
1 cos 2 x dx is
(b)
2 cos x c
(c)
2 sin x c
(d)
2 sin x c
(Answer: b)
3.
xe
dx
(a) xe x e x c
(b) xe x e x c
c) xe x e x c (d) xe x e x c
(Answer: b)
4.
3x 2
1 x 3 dx
(a)
1
log 1 x 3 c
3
(d) 0
(b) ex+c
(Answer: c)
5.
ex
1 ex
(a) 1 e x c
(Answer: d)
6.
2x 1
dx .
x 1
1
c (c) x 2 x 1 c (d) log (2x +1)+c
log x x 1
7.
x2 1
dx
x2 1
(a) x 2 tan 1 x c
(b) x 2 tan 1 x c
(Answer: c)
8.
1 2 x 3 dx
x4
1 9 x 36 x 2
(a)
log x c
3x 3
(c)
1 9 x 36 x 2
c
3x 3
(Answer: b)
x x2
1 9 x 36 x 2
(b)
8 log x c
3x 3
1 9 x 36 x 3
(d)
log x c
3x 3
dx
(a) x 3 x
4
(c) x
12 6
x c
7
(b) x x 3 x 7 6 c
3 4 3 12 7 6
x x c
4
7
(d) x x 4 x 7 c
(Answer: a)
10.
tan
xdx
(Answer: d)
11.
1 cos 2 x
1 cos 2 x dx
(Answer: b)
x
x
x
x
12. e e e e dx
(a) e x e x c (b)
2
(c)
2
1 x
e ex c
2
(Answer: c)
13. x sinh xdx
2
1 x
e ex c
2
(d) 2 e x e x c
2
(Answer: b)
14. e
3x
sin 4 x dx
(a)
e3x
3 sin 4 x 4 cos 4 x c
25
3x
(b) e 4 sin 4 x 3 cos 4 x c
(c)
e3x
3 sin 4 x 4 cos 4 x c
25
(d)
25
e3x
3 sin 4 x 4 cos 4 x c
25
(Answer: c)
15. e
2x
cos xdx
e2x
2 cos x sin x c
5
e2x
sin x 2 cos x c
(c)
5
e2x
2 cos x sin x c
5
e2x
2 cos x sin x c
(d)
5
(a)
(b)
(Answer: a)
16.
cos x
1 sin x
(a)
dx
1
c
1 sin x
(b)
1
c
1 sin x
(Answer: b)
17.
1 log x 2
x
(a)
(c)
1
1 log x c
3
1
1 log x 3 c
3
1
3
(d) 1 log x c
3
(b)
1
1 log x 3 c
3
(Answer: d)
18. The value of the integral
(2 x 3)( x 1)dx
2x3 x 2
3x c
3
2
2x3 x 2
3x c
(c)
3
2
(a)
(Answer: a)
is
(b)
2x3 x 2
3x c
3
2
(d) 2 x 3 x 2 3x c
a)
1 e
dx is
(Answer: d)
1
dx
2
0 1 x
20.
(a)
(b)
(c)
(d)
(Answer: d)
2
x4
dx is
x2
(a) log 2
(b) log 2 2
(Answer: d)
2
(c)
(d) log 2 2
dx is
(a) 7
(c) 3
(b) 3
(d) 15
64
(Answer: b)
1
xe
dx is
(a)
1 2e
(b)
2e 1
(c)
(d)
1 2e 1
(Answer: d
b
x
24. e dx
a
(a) ea eb
(b) e b e a
(Answer: c)
(c) e b e a
(a) 2
(b)
(c) 1
(d) 2
(d) e a e b
(d) log(1 e x ) c
(Answer: d)
26.
cos 2 xdx is
a) 1 (b)
(c)
(d)
(Answer: d)
a
27.
a) true
b) false
(Answer: a)
28.
a) true
29.
b) false
30.
(Answer: b)
b) false
(Answer: a)
a) true
b) false
(Answer: a)
MODERATELY DIFFICULT
x 2 5 x 41
dx
1.
x 3 ( x 1) (2 x 1)
(c)
5
47
25
log ( x 3)
log ( x 1)
log (2 x 1) c
4
4
2
(Answer: b)
2.Evaluate
dx
1
1
log x 1 / x 1 c
2
1
(d) log x 1 / x 1 c
2
(a) log x 1 / x 1 c
(b)
(c) log x 1 / x 1 c
(Answer: b)
3.
sin 3 x cos 3 x
sin 2 x cos 2 x dx
x4 x2 1
dx
2 x 2 1
1 3
x 3 tan 1 x c
6
1 3
1
(d) x tan x c
6
(a) x 3 3 tan 1 x c
(c)
(b)
1 3
x 3 tan 1 x c
6
(Answer: c)
3
5. x cos xdx
(a) x 3 6 x sin x 3 ( x 2 2) cos x c
(c) x 3 6 x cos x 3 ( x 2 2) sin x c
(Answer: a)
2
2
6. x sin xdx
(a)
1 2 1
1
x 1 2 x 2 sin 2 x x cos 2 x c
6
8
4
(c)
1 3 1
1
1
1
1
x 1 2 x 2 sin 2 x x sin 2 x c (d) x 3 1 2 x 2 cos 2 x x cos 2 x c
6
8
4
6
8
4
(b)
1 3 1
1
x 1 2 x 2 sin 2 x x cos 2 x c
6
8
4
(Answer: b)
7.The value of the integral
(a) e sin x cos x c
sin x
cos xdx is
(b) e sin x c
(Answer: b)
8. The value of the integral
cos( x 3 ) dx is
(a)
1
sin( x 3 ) cos x c
3
1
3
3
(b) sin( x ) c (c)
1
sin( x 3 ) c
3
(d) 3 sin( x 3 ) c
(Answer: c)
9.The value of the integral
2x 1
1 x
dx is
a) log( x 2 1) tan 1 x c
(Answer: a)
10.The value of the integral
1
c
log(log x)
a)
x log x dx
is
(b) log(log x ) c
(Answer: d)
11. The value of the integral
1
dx is
3x 2
a) log( x 2) log( x 1) c
(Answer: b)
12. The value of the integral
7x 6
dx is
3x 2
a) 8 log( x 2) log( x 1) c
(c) 8 log( x 2) log( x 1) c
(Answer: a)
13.
log xdx is
x3
x3
log x
c
3
9
a)
(c)
x3
x3
log x
c
3
9
(Answer: c)
(b) x 3 log x
(d)
x3
c
9
x3
log x x 3 c
3
2 x 3x dx
2
(a) 12
(b) 11
(c) 10
(d) 9
(Answer: a)
15.
cos x
1 sin
(a)
dx
(b) 0
(c)
(d) 1
(Answer: a)
1
2
2x
16. x e dx
0
(a)
e2 1
4
(b)
e2 1
4
(c)
4
e 1
2
(d)
4
e 1
2
(Answer: b)
2
xdx
is
3
2
(b)
1
2
(c)
3
2
(c)
e2 1
e
(d)
1 e2
e
(c)
280
351
(d)
351
280
(d)
1
2
(Answer: c)
1
1
e
(Answer: a)
(a)
(b)
1 e2
e
3
4
19. x 1 x dx
0
(a)
280
351
(Answer: d)
1
20.
0
x2
dx
x2 1
(b)
351
280
4
4
(a)
(b)
4
4
(Answer: b)
1
x 2 2 x 1 dx is
(b) 1
(c) 1
(a) 1
(d) 1
(Answer: a)
22.
cos xdx
0
(a) 1
(b) 0
(c)
(d) 1
(Answer: d)
23.
cos x dx is
0
a)
(b)
(c)
1
2
(d) 1
(Answer: d)
24.
sin 2 x dx is
0
a)
(b) 1
(c)
1
2
(d)
(Answer: b)
25.
cos 2 x dx is
0
a)
(Answer: c)
2
25. sin 3 xdx
(b) 1
(c) 0
(d)
(b) x sin 6 x
a) x sin 6 x
(c) x sin 6 x
12
(d) x sin 6 x
2
12
(Answer: d)
DIFFICULT
1.
2 3 sin x
2
cos x
dx
(a) 2 3 3 (b)
(Answer: a)
2.
2 3 3
(c)
(d)
23 3
23 3
2 cos 5 x sin 3x dx is
0
(c)
a) 1 (b) 1
(d)
(Answer: b)
3.
sin x
dx is
sin x cos x
a)
(b)
(c)
(d) 1
(Answer: a)
4.
tan
xdx is
a)
1
log 2
4 2
(b)
1
log 2
4 2
(c)
1
log 2
4 2
(Answer: b)
5.
tan x sec
x dx is
a)
(Answer: c)
(b)
(c)
1
2
(d)
1
3
(d) log 2
6.
cos x
1 sin
a)
dx is
(b) 1
(c) 0
(d)
(Answer: a)
7.The value of
e x dx
is
(a) 12
(b) 48
(c) 24
(d) 6
(Answer: c)
8.
cos
xdx
a)
cos 3x 3 cos x
sin 3 x 3 sin x
(b)
12
4
12
4
sin 3 x 3 sin x
12
4
(Answer: b)
9.
9x
dx
2
4
a)
1
3x
tan 1
6
2
(b)
1
3x
tan 1
6
2
(b)
3
1 2
3 x a 2 2
3x
3x
1
(c) tan
1
(d) 6 tan
(Answer: a)
10. x
x 2 a 2 dx
a) 3 x 2 a 2
3
2
(c)
3
1 2
3 x a 2 2 (d) x 2 a 2
3
2
(Answer: c)
(a) true
(b) row
(Answer: b)
3. A column matrix is a matrix with only one -----(a) column
(b) row
(Answer: a)
4.A square matrix is one in which the number of row is ------ to the number of columns.
(a) not equal
(Answer: d)
5. If
A 0,
(a) idompotent
(Answer: c)
6. If
A 0
(a) idompotent
(b) unit
(c) singular
(Answer: d)
7. A square matrix A whose elements below the principal diagonal are all zero is called ------matrix
(a) upper triangular
(b) diagonal
(d) unit
(Answer: a)
8. A square matrix A whose elements above the principal diagonal are all zero is called ------matrix
(a) upper triangular
(b) diagonal
(d) unit
(Answer: c)
9. A square matrix all of whose elements except those in the leading diagonal, are zero is called a
--------- matrix
(a) upper triangular
(b) diagonal
(d) unit
(Answer: b)
10.A diagonal matrix whose all the leading diagonal elements are equal is called a ------ matrix.
(a) upper triangular
(Answer: d)
(b) diagonal
(c) unit
(d) scalar
MODERATRLY EASY
1. A diagonal matrix of order n which has unity for all its diagonal elements, is called a -----matrix of order n.
(a) null
(b) diagonal
(c) unit
(d) scalar
(Answer: c)
2.If all the elements of a matrix are zero, it is called a ------ matrix.
(a) null
(d) scalar
(Answer: a)
3.A square matrix A = [aij] is said to be -------- when aij = aji for all i and j.
(a) skew symmetric
(b) real
(c) scalar
(d) symmetric
(Answer: d)
4.If aij = -aji for all i and j so that all the leading diagonal elements are zero, then the matrix is
called a -------- matrix.
(a) skew symmetric
(b) real
(c) scalar
(d) symmetric
(Answer: a)
5.If ----- , then the matrix A is called idempotent.
(a) A3 = A
(b) A2 = A
(c) AT = A
(d) A = 0
(Answer: b)
6. If rows and columns are interchanged in a matrix A, we obtain in a second matrix that is
called the ------- matrix.
(a) det
(d) scalar
(Answer: c)
7.If A is a square matrix and I is the unit matrix of the same order, then AI = IA =
(a) I
(b) I
(c) A
(d) -A
(Answer: c)
8.The trace of the product of two or more matrices is independent of the order of -------(a) multiplication
(b) addition
(c) subtraction
(d) commutative
(Answer: a)
9. If A is m x n matrix and B is an n x p matrix, then (AB)T =
(a) (AB)T =- BTAT
(Answer: d)
10. If A is m x n matrix then AT is an ----- matrix.
(a) m x n
(b) n x m
(c) m x m
(d) n x n
(Answer: b)
1
(a) 2 x 3
2
3
3
4
14
(b) 3 x 2
4
1
is
(c) 3 x 4
(d) 4 x 3
(Answer: c)
1
(a) 3
(b) 4
3
14
4
1
1 is
2
(c) 12
(d) 14
(Answer: b)
13.If two matrices are equal, then their difference is a ------- matrix
(a) unit
(b) zero
(c) adjoint
(d) scalar
(Answer: b)
14. If A is a square matrix and A is the transpose of its conjugate, such a matrix is called a -----matrix
(a) skew symmetric
(b) real
(c) hermitian
(d) symmetric
(Answer: c)
15.If A is skew symmetric and has order n, then
(a)
(b) 0
(c) 1
(d)
(Answer: b)
1
0
0
0
(a) Unit
0
1
is a __________ matrix.
(b) Diagonal
(c) Zero
(d) Rectangle
(Answer:b)
17.The matrix A is equivalent to the matrix B is symbolically denoted by ----(a) A+ B
(b) A - B (c) A
~B
(Answer:c )
18. If A and B are two matrices of the same order then
(d) A B
(a) A B B A
(b) A + B = B + A (c) A B B A
(d) A B B A
(Answer: b)
1
19. The product of the matrix is 2 is
3
(a) 1 2
(b) 1
1
(c) 2
3
(Answer: b)
20. The order of the matrix A is 3 x 3 and the order of the matrix B is 3 x 2. What is the order of
the matrix A x B?
(a) 3 x 2
(b) 3 x 3
(c) 2 x 2
(d) 2 x 3
(Answer: a)
1
21. Let A = 2
1
0
1
1
(a) 1
1
0 .Cofactor of A32 =
1
(b) -4
(c) 2
(d) -2
(Answer: c)
1
22 . Let A = 2
1
0
1
1
(a) 1
1
0 .Cofactor of A33 =
1
(b) -4
(c) 2
(d) -2
(Answer: a)
23. A 1
1
1
adj. of A (c)
(a) A det . of A (b)
A
1
cofactor of A
A
(d)
1
adj. of A
A
(Answer: d)
24. The solution of the equations 2x + y = 3, 7x - 3= 4 is
a) x = 1, y = -1
b) x = 1, y = 1
c) x = -1, y = 2
d) x = 1, y = 0
(Answer: b)
25. The solution of the equations 11x + 3y = 17, 2x +7y= 16 is
a) x = 2, y = 1
b) x = 2, y = 1
c) x = -1, y = 2
d) x = 1, y = 2
(Answer: d )
26. The solution of the equations 4x - 3y = 11, 3x +2y= 4 is
a) x = 2, y = 1
b) x = 2, y = -1
c) x = -1, y = 2
d) x = 1, y = 2
answer b
MODERATE
1. If A =
1
3
2
4
, then 2A =
2
6
(a)
2 4 4
(b)
2
6
4
8
4
(c)
2
6
4
8
4
(d)
2
(Answer: d)
2
2.If A = 3
4
1
1
0
13
(a) 1
1
13
1
3
2 , B =
1
3
10
9
3
10
9
5
90
16
1
2
2
2
1
13
(b) 1
1
4
3
0
3
10
9
then AB =
5
13
90 (c) 1
1
16
5
90
16
(Answer: d)
2
3.If A = 3
4
1
1
0
3
2 , B =
1
1
2
2
2
1
4
3
0
then BA =
3
10
9
5
90
16
(d)
6
4
8
4
24
(a) 2
3
24
2
5
5
3
4
11
24
(b) 2
3
24
(c) 2
3
11
3
4
5
5
3
4
2
5
5
(d)
11
5
5
3
4
11
(Answer: a)
2
4. If A = 1
5
1
(a) 6
4
4
6
9
1
21
8
7
17
and B =
then AB is
1 2 1
1
(b) 6
4
8
7
17
(c) 6
4
9
1
21
8
7
17
9
1
21
(d) 6
4
(Answer: b)
2
5. If A = 1
5
4
6
18
(a)
1
and B =
then BA is
1 2 1
28
11
18
18
(b)
28 11
(c)
11
28
1
28
(d)
18 11
(Answer: a)
3
6. Given
5
2
2
+ 2X =
1
1
3
(a)
0
3
1
2
, then X =
4
3
(b)
3
0
1
3
1
(d) 2
2
5
3
2
(d) 3
5
7
3
2
3
(c)
0
(Answer: d)
4
7. Given
2
(a) 3
7
1
3
+ 3A =
1
5
5
3
2
(Answer: b)
(b) 3
7
4
, then A =
1
5
3
2
(c) 3
7
8
7
17
9
1
21
2 y 5
1
4 x 5 = 4
2 w 5
3w 1
w 2
5
2 x 1 is
20
(c) x = -2, y = 5, z = 8, w = -7
(d) x = 2, y = 5, z = -8, w = -7
(Answer: a)
2
1
1
,B=
1
2
9. Given A =
4
3
14
(a)
3 16
8
4
2
1
,C=
1
1
3
0
3
16
(b)
14
8
4
2
4
3
0
then A(B + C) =
5
8
4
14
(c)
3 16
(d)
3
14
16
8
4
(Answer: c)
10.If A is of order 3 x 3 and B is of order 3 x 2 then AB is
(a) 2 x 2
(b) 3 x 3
(c) 2 x 3
(d) 3 x 2
(Answer: d)
2
11. If A = 0
0
1
1
0
3 , then AI =
1
(a) 0
(b) -A
(c) A
(d) I
(Answer: c)
1
12.The product of the matrix is 2
3
4
(a) 8
12
5
10
15
12
18
(b) 5
6
6 is
5
8
10
15
12
12
18
(c) 10
15
4
8
12
12
18
(d) 8
12
5
10
15
(Answer: a)
1
14. Let A =
2
6
(a)
2
3
10
5
21
(Answer: d)
4
7
1
5
and B =
0
1
(b)
5
5
21
2
11
6
2
3
then A + B is
12
6
(c)
2
5 1
21 5
(d)
2
5
21
1
5
6
18
15
15. Given A = 3
5
(a) 3
15
5
3
15
2
4 ; B =
6
0
1
10
20
6
3
4
2
3
1
2 then 3A 4B =
6
1
0
(b) 3
15
(c 3
15
10
20
6
3
4
1
2
6
3
4
(d)
10
20
6
3
4
(Answer: a)
1
0
3
and B =
1
1
16. Given A =
0
2
7
1
(a)
0
(b)
7
0
1
7
then (A + B)T =
2
2
(c)
7
0
1
(d)
7
0
1
(Answer: c)
2
17.Given A = 5
4
3
(a) 7
11
7
11
5
9
4
1 and B =
5
3
2
6
3
5
9
10
3
1
1
2
(b) 3
10
7
5
3
4
30
3
11
9
1
7
8 then (A + B)T =
4
3
10
3
7
(c)
1 11
3
5
9
(d)
10
3
1
(Answer: a)
18. The value of the determinant is unaltered by changing rows into columns and vice versa. Say
true or false.
a) false
b) true
(Answer: b)
19. The value of the determinant changes in sign by altering the elements of any 2 consecutive
rows or columns. Say true or false.
a) false
b) true
(Answer: b)
20. The value of the determinant is not equal to zero when any 2 rows or columns are identical.
Say true or false
a) false
b) true
(Answer: a)
21.When every element of a row (or column) is multiplied by a constant then the value of the
determinant is also multiplied by the same constant. Say true or false
a) false
b) true
22. Given A =
2
5
then
4
(a) 1
(b) 18
(Answer: b)
is
(c) -18
(d) 12
(Answer: b)
3
23.Given A = 1
1
1
3
1
(a) 8
1
1 then
2
(b) -8
is
(c) -18
(d) 12
(Answer: a)
24. If A is a square matrix of order n, then
(a)
(b)
(c)
adjA
n 1
(d)
is
A
(Answer:c )
25.A skew symmetrical determinant of odd order is ----(a) I
(b) 1
(c) -1
(d) 0
(Answer: d)
26.A skew symmetrical determinant of an even order is a ----(a) I
(d) 0
(Answer: b)
27. If C = AB and A is of order 1 x 3 and the order of the matrix B is p x 2, then what is the
value of p?
(a) 2
(b) 1
(c) 3
(d) 4
(Answer: c)
(b) I
(c) 0
(d) -1
(Answer:c )
29.Crammars rule is applicable only (with three unknowns) when
(a) 0
(c) 0 , x 0 (d) x y z 0
(b) 0
(Answer: a )
x
4
0. The value of x is
x
30. Given
4
(b) 4i (c) 2
(a) 16
(d) 4
(Answer: d )
MODERATELY DIFFICULT
1.If A =
3
2
, then A2 =
4
10
(a)
15 22
(b)
15
10
22
(c)
10
5
22
(Answer: b)
1
, then A2 =
0
2.Given A =
1
1
(a)
0
0
1
(b)
0
0
1
(c)
0
0
1
(Answer: c)
2i
3 2i
3.If A =
, then A =
2 3i 4 3i
2i
3 2i
(a)
2 3i 4 3i
2i
(b)
2 3i
3 2i
4 3i
(d)
1
1
0
10
(d)
15
7
22
2i
3 2i
(c)
2 3i 4 3i
2i
(d)
2 3i
3 2i
4 3i
(Answer: b)
5
(a) 76
(b) 100
2
1
7
(c) 14
3
5
9
(d) 340
(Answer: a)
5. (AT)-1 is equal to
(a) A-1
(b) AT
(c) A
(d) (A-1)T
(Answer:d)
6. If each element of a row (or column) of a determinant is the sum of 2 quantities, then the
determinant can be expressed as the sum of 2 determinant of the same order. Say true or false
a) false
b) true
(Answer: b)
7.A determinant is unaltered when the elements of any row (or column) are added to those of
several other rows (or columns) multiplied by constants. Say true or false
a) false
b) true
(Answer: b)
8. In a given determinant if 2 rows (or columns) are identical for x = a, then ----- is a factor of
the given determinant.
(a) x -a
(b) x + a
(c) -x + a
(d) x-a
(Answer: d)
9. The transpose of the co-factor matrix is called the ------- matrix.
(a) determinant
(b) transpose
(c) diagonal
(Answer: d)
4
10. Let A = 2
1
1
3
0
(a) 2
(Answer: b)
2
4 .The minor of the element 2 =
7
(b) -2
(c) 3
(d) 4
(d) adjoint
11. Let A = 2
1
1
3
0
(a) -21
2
4 .The minor of the element -4 =
7
(b) 21
(c) 3
(d) 4
(Answer: a)
4
12. Let A = 2
1
1
3
0
(a) 4
2
4 .The minor of the element -1 =
7
(b) -10
(c) 7
(d) 10
(Answer: d)
4
13. Let A = 2
1
1
3
0
(a) -1
2
4 .The minor of the element -2 =
7
(b) -7
(c) 7
(d) 4
(Answer: c)
4
14. Let A = 2
1
1
3
0
(a) 26
2
4 .The minor of the element 3 =
7
(b) -26
(c) 30
(d) -30
(Answer: a)
4
15. Let A = 2
1
1
3
0
(a) 0
2
4 .The minor of the element 4 =
7
(b) -2
(c) 3
(d) 1
(Answer: d)
4
16. Let A = 2
1
(a) -1
1
3
0
2
4 .The minor of the element1 =
7
(b) -10
(c) 3
(d) 10
(Answer: b)
4
17. Let A = 2
1
1
3
0
(a) -4
2
4 .The minor of the element 0 =
7
(b) 10
(c) -10
(d) 4
(Answer: c)
4
18. Let A = 2
1
1
3
0
(a) 2
2
4 .The minor of the element -7 =
7
(b) -4
(c) 14
(d) -14
(Answer: d)
1
19. Let A = 2
1
0
1
1
(a) -1
1
0 .Cofactor of A11 =
1
(b) -4
(c) -3
(d) -2
(Answer: a)
1
20. Let A = 2
1
0
1
1
(a) 1
1
0 .Cofactor of A12 =
1
(b) -4
(c) -2
(d) 2
(Answer: d)
1
21. Let A = 2
1
0
1
1
(a) 1
1
0 .Cofactor of A13 =
1
(b) -4
(c) -3
(Answer: c)
1
22. Let A = 2
1
0
1
1
1
0 .Cofactor of A21 =
1
(d) -2
(a) 1
(b) -4
(c) -3
(d) -2
(Answer: a)
1
23. Let A = 2
1
0
1
1
(a) 1
1
0 .Cofactor of A22 =
1
(b) -4
(c) -3
(d) -2
(Answer: d)
1
24. Let A = 2
1
0
1
1
(a) 1
1
0 .Cofactor of A23 =
1
(b) -4
(c) -3
(d) -2
(Answer: a)
1
25. Let A = 2
1
0
1
1
(a) 1
1
0 .Cofactor of A31 =
1
(b) -1
(c) -3
(d) -2
(Answer: b)
DIFFICULT
1. The solution of the equations 5x - y = 9, 3x +y= 7 is
a) x = 2, y = 1
b) x = 2, y = -1
c) x = -1, y = 2
d) x = 2, y = 1
answer d
2. The solution of the equations 2x +y = 5, 5x -2y= 8 is
a) x = 2, y = 1
b) x = 2, y = -1
c) x = 2, y = 1
d) x = 1, y = 2
answer c
3.The solution of the equations 2x + y + 4z = 12, 4x + 11y z = 33, 8x 3y + 2z = 20 is
a) x = 1, y = 2, z = 1
b) x = 1, y = 2, z = 1 c) x = 3, y = 2, z = 1 d) x = 1, y = 2, z = 1
(Answer: c )
4.The solution of the equations x +2y + z = 3, 2x + 3y +3z = 10, 3x y + 2z = 13 is
a) x = 1, y = 2, z = 1 b) x = 1, y = 2, z = 1 c) x = 2, y = -1, z = 3 d) x = 1, y = 2, z = 1
(Answer: c )
5.The solution of the equations 2x + 3y - z = 5, 4x + 4y 3z = 3, 2x 3y + 2z = 2 is
a) x = 1, y = 2, z = 1 b) x = 1, y = 2, z = 3 c) x = 3, y = 2, z = 1 d) x = 1, y = 2, z = 1
(Answer: b )
6. The solution of the equations 3x - y +2z = 7, 2x + 3y z = 5, x +y + z = 6 is
a) x = 1, y = 2, z = 1 b) x = 1, y = 2, z = 3 c) x = 3, y = 2, z = 1 d) x = 1, y = 2, z = 1
(Answer: b )
7. The solution of the equations 2x + 3y = 1, 3x + 2z = 3, 4y + z = 7 is
a) x = 1, y = 2, z = 1 b) x = 1, y = 2, z = 3 c) x = -1, y = 1, z = 3 d) x = 1, y = 2, z = 1
(Answer: c)
8. The solution of the equations 3x - y +2z = 8, x - y + z = 2, 2x + y - z = 1 is
a) x = 1, y = 2, z = 1 b) x = 1, y = 2, z = 3 c) x = 3, y = 2, z = 1 d) x = 1, y = 3, z = 4
(Answer: d )
9. The solution of the equations x + y - z = 4, 3x - y +z = 4, 2x 7y + 3z = -6 is
a) x = 2, y = 1, z = -1 b) x = 1, y = 2, z = 3
c) x = 3, y = 2, z = 1 d) x = 1, y = 2, z = 1
(Answer: a )
10. The solution of the equations 3x + 5y - 7z = 13, 4x + y 12z = 6, 2x + 9y - 3z = 20 is
a) x = 1, y = 2, z = 1 b) x = 1, y = 2, z = 3 c) x = 1, y = 2, z = 0
(Answer: c )
d) x = 1, y = 2, z = 1
Tr 1
a) Tr 1 nC r x n r a
nC r x n a r
b) Tr nC r x n a n r
c) Tr 1 nC r x n r a r
d)
(Answer: c)
3.Binomial expansion contains ------ terms
a) n 2
b)
c) n 1
d) n 1
(Answer: d)
4. Binomial theorem for positive integral index (x - a)n =
n
n 1
n2 2
n r r
a) x nc1 x a nc 2 x a ..... nc r x a ..... a n
b) 1 x x 2 ..... x r
MODERATELY EASY
1.When n is even, the numerically coefficient in the expansion of (1+x)n is
a) nC r
b)
c)
nC n
d) n 1
(Answer: c)
2.When n is odd, the numerically coefficient in the expansion of (1+x)n is
a)
nC n 1
2
b)
c)
nC n
2
d) nC n 1
(Answer: a)
3. Binomial expansion of (1-x)-1 is
a) 1 x x 2 ..... x r
b) 1 x x 2 ..... x r
x x2 x3
1 2
3
(c) 1
(b) 1
x x 2 x3
1! 2! 3!
x x2 x3
1! 2!
3!
(d) 1 x x 2 x 3 .....
(Answer: c)
6.The exponential theorem for e-x is----(a) 1
x x2 x3
1 2
3
(c) 1
(b) 1
x x 2 x3
1! 2! 3!
x x2 x3
1! 2!
3!
(d) 1 x x 2 x 3 .....
(Answer: b)
7. The exponential series for e1 is----(a) 1
1 12 13
1! 2! 3!
1
1
(b) 1
12 13
2
3
(c) 1
1 12 13
1! 2! 3!
(d) 1 1 1 1.....
(Answer: a)
8. The exponential series for e-1 is----(a) 1
1 12 13
1! 2! 3!
1
1
(c) 1
12 13
2
3
1
1
(b) 1
(d) 1
12 13
2
3
1 12 13
1! 2! 3!
(Answer: d)
9.The exponential series for
e1 e 1
is----2
(a) 1
1 15
3! 5!
(c) 1
1 1
3 5
(b) 1
1 1
3! 5!
(d) 1 1 1
(Answer: b)
10.The exponential series for
e1 e 1
is----2
(a) 1
1 1
2! 4!
(c) 1
1 1
2 4
(b) 1
1
1
2! 4!
(d) 1 1 1
(Answer: a)
MODERATE
1. The exponential series for
(a) 1
e x ex
is----2
x2 x4
2!
4!
(b) 1
x2 x4
2! 4!
(c) 1
x2 x4
2
4
(d) 1
x2 x4
2
4
(Answer: b)
2. The exponential series for
e x ex
is----2
(a) x
x3 x5
3! 5!
(c) x
x3 x5
3! 5!
(b) x
(d) 1
x3 x5
3
5
x2 x4
2
4
(Answer: c)
3.If 1 x 1, then logarithmic series is given by
(a) log(1+x) = x
x2 x3
2
3
(c) log(1+x) = x x 2 x 3
(b) log(1+x) = x
(d) log(1+x) = x
(Answer: d)
4. log(1-x) =
(a) x
x2 x3
2
3
(c) x x 2 x 3
(b) x
x2 x3
2
3
(d) x
x2 x3
2
3
(Answer: a)
5. - log(1-x) =
(a) x
x2 x3
2
3
(c) x x 2 x 3
(Answer: b)
6. log
1 x
1 x
(b) x
x 2 x3
2
3
(d) x
x2 x3
2
3
x2 x3
2
3
x2 x3
2
3
(a) 2 x x 3 x 5
x3
x5
(b) x
3
5
x3 x5
2
x
(c)
3
5
x3 x5
2
x
(d)
3
5
(Answer: c)
7.How many terms are there in the expansion of (3x 2y)5?
(a) 4
(b) 5
(c) 7
(d) 6
(Answer: d)
8.Which is the middle term of (x2 + 2)14?
(a) 8th term
(Answer: a)
2
9. Which is the middle term of ( 2 x
y 9
) ?
x
(Answer: a)
10. How many terms are there in the expansion of (5x y) 7?
(a) 4
(b) 5
(c) 8
(d) 6
(Answer: c)
11. How many terms are there in the expansion of (9y 2)12?
(a) 12
(b) 13
(c) 11
(Answer: b)
12. How many terms are there in the expansion of (x2 3y)15?
(a) 13
(b) 14
(c) 16
(d) 15
(Answer: c)
13.The nth term of the series
5
7
9
is
1.2.3 3.4.5 5.6.7
2n 3
2n
(b) ( 2n 1) 2n( 2n 1)
(c)
2n 3
( 2n 1) 2n( 2n 1)
2n 3
(d) ( 2n 1) 2n( 2n 1)
(Answer: c)
14. The nth term of the series
(a)
1
1
1
is
1.2 3.4 5.6
n
1
1
(b)
c)
( 2n 1) 2n
( 2n 1)( 2n 2)
(2n 1)(2n 1)
(d)
1
( 2n 1) 2n
(Answer: d)
15. The nth term of the series
(a)
1
1
1
is
2.3 4.5 6.7
n
1
1
(b)
c)
( 2n 1) 2n
( 2n 1)( 2n 2)
2n( 2n 1)
(d)
1
( 2n 1) 2n
(Answer: c)
MODERATELY DIFFICULT
1
1. The general term in the expansion of x
2x
(a)
7C r x 7 2 r
2r
7C r x 7 2 r
(c)
2 r
(b)
is
7C r x 7 2 r
2r
(Answer: a)
2. 6th power of 11 is
(a) 17,71,551
(b) 18,71,561
(c) 17,61,561
(d) 17,71,561
(b) 108243216
(Answer: d)
3. 4th power of 102 is
(a) 118243216
(Answer: b)
4. The value of loge1 is
(a) 0 (b) 1 c)
(d)
(Answer: a)
5. The value of loge2 is
(a) 0.69317 (b) 0.69315 c) 0.79315
(d) 0.59315
(Answer: b)
DIFFICULT
1.Sum of the coefficients in the expansion of (1+x)n is
a) 2 n 1
b) 2 n
c) 2 n 1
d) 2 n 1 1
(Answer: a)
2.In the binomial expansion, the successive of the numerator are in ----- whose common
difference is the denominator of the index.
a) geometric progressio n
b) harmonic progressio n
c) arithmetical progressio n
d) none of these
(Answer: c)
3.In binomial expansion, in each term the index of x is the same as the number of factors in
the numerator or in the denominator. Say true or false.
a) true
1
Lt 1
4.Exponential limit
n
n
(a)
b) false
(Answer: a)
(b)
(c) 1
(Answer: b)
5. The value of e is calculated more than ----- decimal places
(d)
(a) 500
(b) 100
(c) 200
(d) 50
(Answer: a)
6.The value of e is ----(a) 2.91384 (b) 2.71356
(c) 3
(d) 2.71828
(Answer: d)
7. In the expansion of (1 + x)n, the sum of the coefficients of the odd terms is equal to the sum
of the coefficients of the even terms. Say true or false.
a) true
b) false
(Answer: a)
b) false
(Answer: a)
b) false
(Answer: a)
100.The sum to infinity of the binomial series for any given value of x for which is convergent
has
only one value. Say true or false.
a) true
b) false
(Answer: a)
(a) 0
(c)
(d) 1
(Answer: a)
2. The equation of the x axis is y =
(a) 0
(Answer: a)
(b)
(c)
(d) 1
3.If a straight line makes an angle with the positive direction of x axis m = ------ is called
the slope of the straight line.
(a) cos
(c) sin
(b) tan
(d) tan
(Answer: d)
4.Equation of straight line which makes an angle with the positive direction of x axis and
cuts off an intercept c on the y axis is ----(a) y m cx
(b) x my c
(c) y mx c
(d) y mx c
(Answer: c)
5.If two lines are parallel then
(a) -1
(b) 1
(c)
(d) 0
(Answer: d)
6. If two lines are perpendicular then
(a) -1
(b) 1
(c)
(d) 0
(Answer: c)
7.The slope of the line a1x + b2y +c1 = 0 is
(a) b1/a1
(b) -b1/a1
(c) -a1/b1
(d) a1/b1
(Answer: c)
8. The condition for two lines to be perpendicular is that the product of their slopes is equal
to ----(a) -1
(b) 1
(c)
(d) 0
(Answer: a)
9. If the lines are parallel then ----(a) m1 =- m2
(b) m1 x m2 = 0
(c) m1 = m2
(d) m1 x m2 = 1
(Answer: c)
10. If the lines are perpendicular then ----(a) m1 =- m2
(b) m1 x m2 = 0
(c) m1 = m2
(d) m1 x m2 = -1
(Answer: d)
MODERATELY EASY
1.The distance between the points (4, 7) and (-2, 5) is
(a)
40 units
(b)
(c)
40 units
35 units
(d)
25 units
(Answer: a)
2.The points (4, 3), (-1, 2) and (3,-1) are the vertices of an isosceles triangle. Say true or
false.
(a) true
(b) false
(Answer: a)
3. The points (2, -2), (7, -1) and (9,3) are the vertices of an isosceles triangle. Say true or
false.
(a) true
(b) false
(Answer: a)
4. The points (6, 6), (2, 3) and (4, 7) are the vertices of right angled triangle. Say true or
false.
(a) true
(b) false
(Answer: a)
5.The area of the triangle whose vertices (4, 7), (7, 5), and (-1,3) is
(a) 21
(b) 19
(c) 20
(d) 18
(Answer: a)
6. The area of the triangle whose vertices are (2, 3), (7, 5) and (6, 3) =
(a) 18
(b) 17
(c) 19
(Answer: c)
7. The area of the triangle whose vertices are (4, 7), (7, 2) and (2, 3) =
(d) 20
(a) 12
(c) 13
(b) 11
(d) 14
(Answer: b)
8. The slope of the line joining the points (2, 3) and (4, -5) is
(a) 2
(b) 4
(c) 3
(d) -4
(Answer: d)
9.The slope of the line joining the points (4, 3) and (2, 5) is
(a) -2
(b) 1
(c) 2
(d) -1
(Answer: c)
10.The slope of the line joining the points (1, 4) and (9, -2) is
(a) -1
(b) 2
(c) 1
(d) -2
(Answer: a)
11.The slope of the line joining the points (6, 5) and (15, -1) is
(a) 3/2
(b) 2/3
(c) 1/3
(d) -2/3
(Answer: d)
12. The slope of the line 2x 3y +7 = 0 is -----(a) 3/2
(b) 2/3
(c) 1/3
(d) -2/3
(Answer: b)
13. The slope of the line 3x - 4y = 12 is -----(a) 4/3
(b) 2/3
(c) 3/4
(d) -3/4
(Answer: c)
14. The slope of the line 3x - 2y = 1 is -----(a) 3/2
(b) 2/3
(c) 3/4
(d) -3/4
(Answer: a)
15.The slope of the line 7x + 2y = 9 is -----(a) 2/7
(b) 7/2
(c) -2/7
(d) -7/2
(Answer: d)
16. The slope of the line 5y 4x = 1 is -----(a) -5/4
(b) 4/5
(c) 5/4
(d) -4/5
(Answer: b)
17. The slope of the line 8x - 11y = 33 is -----(a) 11/8
(b) -8/11
(c) 8/11
(d) -11/8
(Answer: c)
18.The points A(1, 1), B(5, -9) and C(-1, 6) are collinear. Say true or false.
(a) true
(b) false
(Answer: a)
19. A quadrilateral in which the opposite sides are equal and diagonals are equal is a rectangle.
Say true or false.
(a) true
125 units
(b)
120 units
(c)
130 units
(c)
175 units
(d)
130 units
(Answer: c)
2. The distance between the points (-2, -5) and (4, 7) is
(a)
185 units
(b)
180 units
(d)
180 units
(Answer: d)
3.The coordinates of the points which divide the line joining two given points (x1, y1), (x2, y2)
internally in the given ratio m: n is
mx 2 nx1 my 2 ny1
,
mn
mn
mx1 nx 2 my1 ny 2
,
mn
mn
(a)
mn
mn
(c)
(b)
mx1 nx 2 my1 ny 2
,
mn
mn
(d)
(Answer: c)
4. The coordinates of the points which divide the line joining two given points (x1, y1), (x2, y2)
externally in the given ratio m: n is
mx 2 nx1 my 2 ny1
,
mn
mn
mx1 nx 2 my1 ny 2
,
mn
mn
(a)
mn
mn
(c)
(b)
mx1 nx 2 my1 ny 2
,
mn
mn
(d)
(Answer: a)
5. The coordinates of the points which divide the line joining two given points (2, 3), (-4, 7)
internally in the ratio 3: 2 is
8 27
,
5
5
(a)
8 27
,
5 5
(b)
5 5
,
8 27
(c)
5 5
,
8 27
(d)
(Answer: b)
6. The coordinates of the points which divide the line joining two given points (2, 3), (-4, 7)
externally in the ratio 3: 2 is
(a) 16,12
(b) 16, 15
16, 15
(Answer: c)
(c) 16,15
(d)
7. The coordinates of the points which divide the line joining two given points (2, 3), (4, -5)
internally in the ratio 2: 3 is
14 1
,
(a) 5 5
14 1
,
(b) 5
5
14 1
,
5
5
(c)
(d)
14,
(Answer: a)
8. The coordinates of the points which divide the line joining two given points (2, 3), (4, -5)
(b) 2, 19
2, 19
(c) 2, 19
(d)
(Answer: d)
9. The coordinates of the points which divide the line joining two given points (4, -7), (3, -6)
internally in the ratio 3: 2 is
17 32
,
5
5
(a)
17 32
,
5
5
17 32
,
5
5
(b)
(c)
17 32
,
5
5
(d)
(Answer: b)
10. The coordinates of the points which divide the line joining two given points (4, -7), (3, -6)
externally in the ratio 3: 2 is
(a) 1, 4
(b) 1, 4
(c) 1, 4
(d) 1, 4
(Answer: c)
11.The mid point of the line joining the points (x1, y1), (x2, y2) is
x1 y1 x 2 y 2
,
2
2
(b)
x1 y1 x 2 y 2
,
2
2
(d)
(a)
(c)
x1 x 2 y1 y 2
,
2
2
x1 x 2 y1 y 2
,
2
2
(Answer: b)
12.The centroid of the triangle whose vertices (x1, y1), (x2, y2) and (x3, y3) are
x1 x 2 x3 y1 y 2 y 3
,
3
3
(a) x1 x 2 x3 , y1 y 2 y 3
(b)
(c) x1 x 2 x3 , y1 y 2 y 3
(d)
x1 x 2 x3 y1 y 2 y 3
,
3
3
(Answer: c)
13. Let A(x1, y1), B(x2, y2) and C(x3, y3) be the vertices of the ABC .Then the area of ABC
=
(a)
1
( y 2 y3 ) ( y3 y1 ) ( y1 y 2 )
2
(b)
1
x1 ( y 2 y3 ) x2 ( y3 y1 ) x3 ( y1 y 2 )
2
(c)
1
x1 ( y 2 y3 ) x 2 ( y 3 y1 ) x3 ( y1 y 2 )
2
(d)
1
x1 ( y 2 y3 ) x2 ( y3 y1 ) x3 ( y1 y 2 )
2
(Answer: d)
14. Equation of the straight line which cuts off intercepts a and b on the x and y axes is ----(a)
x y
1
a b
(b)
x y
1
a b
(c)
a b
x y
1
1 (d)
x y
a b
(Answer: b)
15. Equation of the straight line with given slope m and passing through the given point (x1, y1)
is -------(a) y-y1 = m(x-x1) (b) y-y1 = m(x+x1) (c) x-x1 = m(y-y1)
(d) y-y1 =
1
m(x-x1)
m
(Answer: a)
16. The equation of the straight line passing through two given points (x1, y1) and (x2, y2) is ----(a)
y y1 y1 y 2
x x1 x1 x 2
(c)
y y1 y1 y 2
x x1 x1 x 2
(b)
y y1 y1 y 2
x x1 x1 x 2
(d)
y y1 y1 y 2
x x1 x1 x 2
(Answer: d)
17. The equation of a straight line in terms of the perpendicular P from the origin to the line
and the angle that perpendicular makes with x axis is ----(a) x cos y sin 0
(Answer: c)
18.Let (x1, y1) be the point of intersection of the two lines a1x + b1y + c1 =0 and
a2x + b2y + c2 =0. Then the point of intersection is ------ b1c 2 b2 c1 c1 a 2 c 2 a1
,
(a)
a1b2 a 2 b1 a1b2 a 2 b1
b1c 2 b2 c1 c1 a 2 c 2 a1
,
(b)
a1b2 a 2 b1 a1b2 a 2 b1
b1c 2 b2 c1 c1 a 2 c 2 a1
,
(c)
a1b2 a 2 b1 a1b2 a 2 b1
b1c 2 b2 c1 c1a 2 c 2 a1
,
(d)
a1b2 a 2 b1 a1b2 a 2 b1
(Answer: b)
19.Angle between two lines is ----- m1 m 2
1 m1 m 2
m1 m 2
1 m1 m 2
1
(a) tan
1
(b) tan
m1 m2
1 m1 m2
1
(c) tan
1 m1 m 2
m1 m 2
1
(d) tan
(Answer: a)
20.The acute angle between the lines is ----- m1 m 2
1 m1 m 2
1
(a) tan
1
(b) tan
m1 m2
1 m1 m 2
1
(c) tan
m1 m 2
1 m1 m 2
1 m1 m 2
m1 m 2
1
(d) tan
(Answer: c)
21. The perpendicular distance from (x1, y1) on the line ax + by +c = 0 is
(a) p
(c) p
ax1 by1 c
a b
2
ax1 by1 c
(Answer: b)
a b
2
(b) p
ax1 by1 c
a2 b2
(d) p
ax1 by1 c
a2 b2
c
a b
2
(b) p
c
a b
(c) p
c
a b
2
(d) p
a2 b2
c
(Answer: c)
23.The length of the perpendicular from the origin to the line 2x 3y + 4 = 0 is
(a)
2
13
(b)
(c)
13
3
13
(d)
5
13
(Answer: b)
24. The length of the perpendicular from the origin to the line 5x + 12y = 15 is
(a) 15/13
(b) 13/15
(c) 14/13
(d)12/13
(Answer: a)
25. The length of the perpendicular from (3, -1) to the line 2x + 3y + 9 = 0 is
(a)
13
13
(b)
11
13
(c)
10
13
(d)
12
13
(Answer: d)
MODERATELY DIFFICULT
1.The locus of the point which is equidistant from the two given points (2, 3) and (4, -1) is
(a) 3x + y = -1
(b) 3x- y = 1
(c) 3x + y = 0
(d) 3x + y = 1
(Answer: d)
2. The locus of the point which is equidistant from the two given points (4, 5) and (-3, 7) is
(a) 14x -4y = 17
(b) 14x +4y = -17 (c) 14x -4y = -17 (d) -14x -4y = -17
(Answer: c)
3. The locus of the point which moves from the point (4, 3) keeping a constant distance of 5
units from it ----(a) x2 +y2 + 8x +6y =0
(b) x2 +y2 8x 6y =0
(c) x2 +y2 8x + 6y =0
(d) x2 +y2 + 8x 6y =0
(Answer: b)
4.The equation of the straight line making an angle of 135o with the positive direction of x
axis and cutting an intercept 5 on the y axis is ----(a) x + y = 5
(b) x - y = 5
(c) x + y = -5
(d) - x + y = 5
(Answer: a)
5. The equation of the straight line cutting off intercepts 2 and -5 on the axes =
(a) -5x + 2y = 20
(b) 5x - 2y = -20
(c) 5x + 2y = 20
(d) 5x - 2y = 20
(Answer: d)
6. The equation of the straight line which cuts off equal intercepts on the coordinate axes and
which passes through the point (3, 5) =
(a) x - y = 8
(b) x + y = 8
(c) -x + y = 8
(d) x + y = -8
(Answer: b)
7. The equation of the straight line which cuts off intercepts on the axes equal in magnitude
but opposite in sign and passing through the point (4, 7) =
(a) x - y = 3
(b) x + y = 3
(c) x - y = -3
(d) -x + y = 3
(Answer: c)
8. The equation of the straight line which cuts off intercepts on the axes equal in magnitude
but opposite in sign and passing through the point (4, -3) =
(a) x - y = 7
(b) x + y = 7
(c) x - y = -7
(d) -x + y = 7
(Answer: a)
9. The equation of the straight line which passes through the point (3, 2) if the portion of the
line intercepted between the axes is bisected at the point is ----(a) 2x - 3y = 12 (b) 2x + 3y = 12
(Answer: b)
(c) -2x + 3y = 12
(d) 2x + 3y = -12
10. The equation of the straight line passing through the point (3, 5), such that its intercept on
the y axis is ---(a) x - 2y = -13
(b) x - 2y = 13
(c) -x +2y = 13
(d) x + 2y = 13
(Answer: d)
11.If the lines 2x 3y = 7 and 3x ay = 13 are to be parallel, then the value of a is
(a)
2
9
(b)
2
9
(c)
9
2
(d)
9
2
(Answer: d)
12. The two lines 3x + 2y 1 = 0 and 6x + 4y 9 = 0 are parallel. Say true or false.
(a) true
(b) false
(Answer: a)
13. The two lines x + 3y 7 = 0 and 21x - 7y 3 = 0 are perpendicular. Say true or false.
(a) true
(b) false
(Answer: a)
5
2
(b)
5
2
(c)
2
5
(d)
2
5
(Answer: c)
15. The slope of the line perpendicular to 7x 9y + 2 = 0 is
(a)
5
2
(b)
7
9
(c)
2
5
(d)
9
7
(Answer: d)
16. The acute angle between the lines 3x + 6y = 8 and 2x + y = 5 is
(a) tan
4
3
(b) tan
3
4
(c) tan
1
2
(d) tan 1
(Answer: b)
17. The acute angle between the lines 2x - 3y = 1 and 5y - x = 3 is
(a) tan
7
17
(b) tan
8
17
(c) tan
1
2
(d) tan 1
(Answer: a)
18. The acute angle between the lines 3x - y = -1 and x 3y = -7 is
(a) tan
3
1
(b) tan
4
2
(c) tan
4
3
(d) tan 1
(Answer: c)
19. The slope of the line perpendicular to the line joining the points (3, 5) and (-4, 2) is
(a)
3
7
(b)
7
3
(c)
3
7
(d)
7
3
(Answer: d)
20. The inclination of the line y =
(a) 60 o
(b) 45 o
7 is
(c) 30 o
(d) 90 o
(Answer: c)
DIFFICULT
1.Two of the vertices of a triangle are (4, 7) and (-1, 2) and the centroid is at the origin. The
third vertex is
(a) 3, 9
3, 9
(b) 3, 9
(c) 3, 9
(d)
(Answer: b)
2. If the centroid of the triangle is (4, 6) and two of its vertices are (7, 1) and (-4, 10).The
third vertex is
(a) 9, 7
(b) 9, 7
(c) 9, 7
(d) 9, 7
(Answer: c)
3. If the centroid of the triangle is (2, 1) and two of its vertices are (1, -2) and (-5, 3).The
third vertex is
(a) 10, 2
10, 2
(b) 10, 2
(c) 10, 2
(d)
(Answer: a)
4. The centroid of the triangle whose vertices are (4, 7), (2, -5) and (-5, 6) =
1 8
,
3
3
1 8
,
3 3
(a)
1 8
(b)
(c) ,
3 3
(d)
1 8
,
3 3
(Answer: d)
5.The angle between the lines y =
(a) 30o
(b) 60o
x +4 and y =
1
3
(c) 45o
x +2 is ----(d) 90o
(Answer: a)
6. The ratio in which the line joining the points (4,7), (-3, 2) is divided by the y axis is ---(a) 3:2
(b) 4:3
(c) 2:3
(d) 3:4
(Answer: b)
7. (4, 3) is the centre of the circle which passes through the points (9, 3), (7, -1) and (1, -1).
Its radius is
(a) 3
(b) 4
(c) 2
(d) 5
(Answer: d)
8. The length of the perpendicular from (2, 1) to the line 3x +2y + 1 = 0 is
(a)
2
13
(b)
4
13
(c)
9
13
(d)
5
13
(Answer: c)
9. The length of the perpendicular from the origin to the line 5x + 9y + 7 = 0 is
(a)
9
106
(b)
7
106
(c)
(d)
106
8
106
(Answer: b)
10. The inclination to the x axis of the line y =
(a) 60 o
(b) 45 o
(Answer: a)
(c) 30 o
x + 1 is
(d) 90 o