KHAITAN PUBLIC SCHOOL, SAHIBABAD

WORKSHEET- MCQ
1. The direction ratios of a line are Its direction cosines are

(a) (b) (c) (d)

2. A line makes angles with the positive directions of x-axis, y-axis and
z-axis respectively. Its direction cosines are

(a) (b) (c) (d)

3. The direction cosines of the vector

(a) (b) (c) (d) none of these

4. The direction cosines of the y-axis are

(a) (b) (c) (d) none of these

5. The angle which the vector makes with the x-axis is

(a) (b) (c) (d)

6. The line with direction ratios inclined with z-axis at an angel

(a) (b) (c) (d)

7. The direction cosines of the two lines are . The

angle between these lines is
(a) (b) (c) (d)

8. The direction cosines of the two lines are and

respectively. These lines are

(a) coincident (b) parallel (c) perpendicular (d) none of these

9. The direction cosines of the lines segment joining the points

are

(a) (b) (c) (d) none of

these

10. The angle between the lines whose direction ratios are is

(a) (b) (c) (d)

11. If a line makes angles with x-axis, y-axis and z-axis respectively, then
 (a) (b) (c) (d) none of these

12. If are the direction ratios of two parallel lines, then

(a) (b)

(c) (d)

13. The angle which the vector make with the z-axis, is

(a) (b) (c) (d)

14. The angle between the vectors is

(a) (b) (c) (d)

15. A line passes through the points and The equations of line
are

(a) (b)

(c) (d) none of these

16. The vertices of a are Then

(a) (b) (c) (d)

17. The direction ratios of the line are

(a) (b) (c) (d) none of these

18. The line meets the plane at the point

(a) (b) (c) (d) none of these

19. The angle between the lines is

(a) (b) (c) (d)

20. The angle between the lines and

is

(a) (b) (c) (d)

21. The angle between the lines is

(a) (b) (c) (d) none of these

22. If the lines are perpendicular to each

other, then

(a) (b) (c) (d)

23., If and are rowed square matrices such that

(a) (b) (c) (d)

24.If

(a) (b) (c) (d) none of these

25.If

(a) (b) (c) (d) none of these

26.If

(a) (b) (c) (d) none of these

27.If

(b) (b) (c) (d) none of these

28.If

(a) (b) (c) (d)

29.If
(b) (b) (c) (d)

30.If
(c) (b) (c) (d) none of these

31.If the matrix is singular, then

(d) (b) (c) (d)

32.If

(a) (b)

(c) (d) none of these

33.If

(a) (b) (c) (d)

34.If is singular, then

(a) (b) (c) (d) none of these

35.If then adj

(a) (b) (c) (d)

36.If

(a) (b) (c) (d)

37.If are square matrices of the same order, then

(a) (b)
(c) (d) none of these

38.If are square matrices of the same order, then

(a) (b)
(c) (d) none of these
40.If are square matrices of the same order, then
(a) (b)
(c) (d) none of these

41.If are symmetric matrices of the same order, then is always

(a) asymmetric matrix (b) a skew symmetric matrix
(c) a zero matrix (d) an identity matrix

42.Matrices are inverse of each other only when

(a) (b) (c) (d)

43.For square matrices of the same order, we have adj

(a) (b)

(c) (d) none of these

44.If is a rowed square matrix and then adj

(a) (b) (c) (d) none of these

45.If is a rowed square matrix and then adj

(a) (b) (c) (d) none of these

46.If is an invertible square matrix, then

(a) (b) (c) (d)

47.If are invertible matrices of the same order, then

(a) (b) (c) (d)

48.If are two non-zero square matrices of the same order such that then

(a) (b)

(c) (d) none of these

49.If is a square matrix such that

(a) (b) (c) (d)

50.If is not invertible, then

(a) (b) (c) (d)
51.If
(a) (b) (c) (d)

52.The matrix is
(a) idempotent (b) orthogonal (c) nilpotent (d) none of these

53.The matrix is
(a) non-singular (b) idempotent (c) nilpotent (d) orthogonal

54.If is singular, then

(a) a unit matrix (b) a null matrix
(c) a symmetric matrix (d) none of these

55.For any rowed square matrix then the value of is

(a) (b) (c) (d)

56.If then

(a) (b) (c) (d)

57.If then the values of adj are

(a) (b) (c) (d)

58.If

(a) (b) (c) (d) none of these

59.If is square matrix of order such that then

(a) (b) (c) (d) none of these

60.If are invertible square matrices of the same order, that

(a) (b) (c) (d)
61.If

(a) (b) (c) (d) none of these

62. If

(a) (b) (c) (d)

63. If is an invertible matrix and

A) (b) (c) (d) none of these

64.If
(a) (b) (c) (d)

65. If is a rowed square matrix and

(a) (b) (c) (d) none of these

66. If is an invertible square matrix and is a non-negative real number, then

(a) (b) (c) (d) none of these

67. If

(a) (b) (c) (d) none of these

68. If is a square matrix, then is

(a) a null matrix (b) an identity matrix
(c) a symmetric matrix (d) a skew symmetric matrix
69. If is a square matrix, then is
(a) a null matrix (b) an identity matrix
(c) a symmetric matrix (d) a skew symmetric matrix

70. If is a rowed square matrix and

71. Which one of the following is a scalar matrix?

(a) (b) (c) (d) none of these

72. If then
(a) (b) (c) (d) none of these
INTEGRATION
1..∫ x dx=¿ ?
6

x7
(a) 7 x 7 +C (b) +C (c) 6 x 5+ C (d) 6 x 7 +C
7

2..∫ x
5 /3
dx=¿ ?
3 8 8 /3 3 5
(a) x 2/ 3 + C (b) x + C (c) x 8 /3 +C (d) x 8 /3 + C
5 3 8 3

1
3.∫ dx =?
x3
−3 −1 −1 x
−2
(a) 2 + C (b) + C (c) + C (d) + C
x 2 x2 3 x2 2
4.∫ √ x dx =?
3

3 3/ 4 4 3/ 4 3 4
(a) x +C (b) x + C (c) x 4 /3 +C (d) x 4 /3 +C
4 3 4 3

1
5. ∫ 3 dx =?
√x
3 2/ 3 4 2 2 3/ 2
(a) x +C (b) 2 /3 + C (c) 2 /3 +C (d) x +C
2 2x 3x 3

6. √3 x 2 dx =?
5 5/ 3 3 5/ 3 5 3/ 5 3
(a) x +C (b) x +C (c) x +C (d) x 3/ 5 +C
3 5 3 5

7.∫ 3 dx=¿ ?
x

3
x
log 3
(a) 3 x (log 3 ⁡)+ C (b) 3 x +C (c) +C (d) x +C
log 3 3

8.∫ 2
logx
dx=¿ ?
2logx−1 x log2 +1
(a) +C (b) +C
(logx+1) ( log 2+1)
logx logx
2 2
(b) (c) +C (d) +C
( log 2) 2
9.∫ cosecx (cosecx + cotx)dx =¿?
(a) cotx - cosecx +C (b)- cotx -cosecx +C

(c) cot + cosecx +C (d) -cotx-cosecx +C

secx
10.∫ dx =?
( secx+tanx)
(a) tanx + secx +c (b) tanx - secx +c
(c)- tanx + secx +c (d) -tanx - secx +c

(1−cos 2 x)
11.∫ dx =?
(1+ cos 2 x )
(a) tanx + x +c (b) tanx - x +c
(c)- tanx + x +c (d) -tanx - x +c
1
12.∫ 2 dx =?
sin x cos 2 x
(a) tanx + cotx +c (b)- tanx + cotx +c
(c)tanx - cotx +c (d) none of these
cos 2 x
13.∫ 2 dx =?
sin x cos 2 x
(a) - cotx –tanx +c (b) - cotx +tanx +c
(c) cotx –tanx +c (d) cotx +tanx +c
( cos 2 x−cos 2 α )
14.∫ dx =?
(cosx−cosα )
(a) 2sinx +2x cosα +c (b) 2sinx -2x cosα +c
(c)- 2sinx +2x cos +c α (d) -2sinx -2x cosα +c
15.∫ √ 1+cos 2 x dx=?
(a)√ 2cosx +C (b)√ 2sinx +C (c)−√ 2cosx +C (d)−√ 2sinx +C
16.∫ √1+sin 2 x dx=?
(a)sinx +cosx +C (b)-sinx +cosx +C
(c)sinx -cosx +C (d)-sinx -cosx +C
cos 2 x
17.∫ 2 dx =?
sin x cos 2 x
(a) cotx +tanx +c (b) - cotx +tanx +c
(c) cotx –tanx +c (d)- cotx -tanx +c
dx
18.∫ =?
(1−cos 2 x)
1
(a) cotx + C (b) 2cotx + C
2

1
(c)- cotx+C (d)-2cotx + C
2
sin 2 x
19.∫ dx =?
sinx
1 1
(a) 2sinx +c (b) sinx + C (c) 2cosx +c (d) cosx + C
2 2
(1−sinx)
20.∫ 2 dx =?
cos x
(a) tanx + secx +C (b) tanx - secx +C
(c)-tanx + secx +C (d) -tanx - secx +C
21.∫ cot x dx=¿ ?
2

(a) – cotx−x +C (b) cotx−x +C

(c) – cotx+ x +C (d)cotx+ x+C

22.∫ secx (secx +tanx)dx=¿ ?
(a) tanx−secx+C (b) – tan+ secx+C

(c)tanx+ secx +C (d)−tanx−secx +C

2
sec x
23.∫ dx =?
co sec 2 x
(a) tanx +x +C (b) tanx -x +C
(c) tanx +secx +C (d)−tanx−secx +C
2
sin x
24.∫ dx =?
1+cosx
(a) x + sinx +c (b) x - sinx +c
(c)sinx -x +c (d) -sinx - x +c
cotx
25.∫ dx =?
( cosecx−cotx)
(a) -cosecx-cotx-x +c (b) cosecx-cotx-x +c
(c)- cosecx+cotx-x +c (d) cosecx+cotx-x +c
sinx
26.∫ dx =?
(1+ sinx)
(a) secx+tanx+x +c (b) secx-tanx+x +c
(c) -secx+tanx+x +c (d) none of these
(1+ sinx)
27.∫ dx =?
(1−sinx)
(a) 2tanx+2secx+x+c (b) 2tanx+2secx-x+c
(c) tanx+secx-x+c (d) none of these
1
28.∫ dx =?
1+cosx
(a) –cotx+cosecx +c (b) cotx-cosecx +c
(c) cotx+cosecx +c (d) none of these
29.∫ sin ¿ ¿ ?
−1

2 2 2
πx x πx x x πx
(a) cosecx+C (b) + +C (c) − +C (d) − +C
2 2 2 2 2 2

30.∫ tan−1
1
√
1−cos 2 x
1+cos 2 x
dx=¿ ?
1 1 x
2
(a) +C (b) +C (c) +C (d) +C
1+ x2 √1+ x 2 √1−x2 2

34.∫ tan ¿ ¿ ?
−1

x2 −x 2
(a) +C (b) +C
4 4

x2 −x 2
(c) +C (d) +C
2 2

35.∫
(( ))
( x 4 +1 )
x 2+ 1
3
dx=?
3
x x
(a) + x - tan−1 x +C (b) - x -2 tan −1 x +C
3 3
3
x
(c) + x -2 tan −1 x +C (d)none of these
3
36.∫ ( )
( ax+ b )
( cx +d )
dx=¿ ?
ax a
(a) +log |cx+ d|+C (b) +log |cx+ d|+C
c c

ax (bc−ad)
(c) + log|cx +d|+C (d)none of these
c c
2

sin2 x+ cos3 x
37.∫ dx =?
sin 2 x co s 2 x
(a) sinx -cosx +c (b) tanx -cosx +c
(c) secx -cosecx +c (d)none of these
sinx
38.∫ dx =?
sin ⁡( x−α )
(a) xcosα +(sinα ¿ log|sin(x-α )|+c
(b) xsinα +(sinα ¿ log|sin(x-α )|+c
(c) xcosα -(sinα ¿ log|sin(x-α )|+c
(d) xsinα +(sinα ¿ log|sin(x-α )|+c
39.∫ sin 3 xsin 2 x dx=¿ ?
1 1 1
(a) - cos 5 x +C (b) sinx + sin 5 x −C
5 2 10

1 1 1 1
(c) sinx− sin 5 x−C (d)- cos 3 x− sin 2 x−C
2 10 3 2
40.∫ cos 3 xsin 2 x dx=¿ ?
1 1 1 1
(a) cosx+ cos 5 x +C (b) - sinx + sin 5 x −C
2 10 2 10

−1 1
(c) cosx + sin 5 x−C (d)none of these
2 10
41.∫ cos 4 xcosx dx=¿ ?
1 1 1 1
(a) - sin 5 x+ sin3 x +C (b) cos 5 x + cos 3 x+ C
5 3 5 3

1 1
(c) sin 5 x+ sin 3 x +C (d)none of these
10 6
INTEGRATION SET -2
1. ∫ (2 x +3) dx =?
5

(2 x+ 3)6 (2 x+ 3)4 (2 x+ 3)6

(a) + C (b) + C (c) + C (d)none of these.
6 8 12
2. ∫ ( 3−5 x ) dx=?
7

(3−5 x )3
(a)−5(3−5 x)6 +C (b) +C
−40
8
5(3−5 x )
(c) +C (d)none of these
8
1
3.∫ dx=?
(2−3 x)4
1 1
(a) 5 + C (b) 3 + C
15(2−3 x ) −12(2−3 x)
1
(c) +C (d)none of these
9(2−3 x )3
4.∫ √ax +b dx =?
 3/ 2 3 /2
2(ax +b) 3(ax +b)
(a) + C (b) + C
3a 2a
1
(c) +C (d) none of these
2 √ ax +b

5.∫ sec (7-4x)ds=?

2

1 −1
(a) tan(7-4x) + C (b) tan(7-4x) + C
4 4
(c)4 tan(7-4x) + C (d)−4 tan(7-4x) + C
6.∫ cos 3 x dx =?
1 1
(a) - sin3x +C (b) sin3x +C (c)3sin3x+C (d)-3sin3x +C
3 3
7.∫ e
(5 −3 x)
dx = ?
(5−3 x) 1 (5−3 x)
e e(5−3 x)
(a) -3e + C (b) +C (c) +C (d)none of these
3 −3
8.∫ 2
(3 x+ 4)
dx =?
3 2(3 x+ 4)
(a) . 2(3 x+4 ) + C (b)
( log 2) 3 ( log 2 )+C
(3 x+4 )
2
(c) +C (d)none of these
2 ( log 3 )
2 x
9.∫ tan dx=?
2
x x
(a)tan - x +C (b)tan + x +C
2 2
x x
(c) 2tan + x +C (d) 2tan - x +C
2 2
10.√ 1−cosx dx=?
x x −1 x −1 x
(a) -√ 2 cos +C (b) (a) -2 √ 2 cos +C (c) cos +C (d) cos +C
2 2 2 2 2 √2
11.√ 1+sinx dx=?

(
(a) -√ 2 sin − +C )
π x
4 2 (
(b) √ 2 sin − +C
π x
4 2)
(
(c) -2 √ 2 sin − +C
π x
4 2) (d)none of these
12.sin 3 x dx=?
3 cos 3 x 3 cos 3 x
(a) - cosx + +C (b) cosx + +C
4 12 4 12
3 cos 3 x
(c) - cosx - +C (d)none of these
4 12
logx
13. ∫ dx = ?
x
1 1
(a) (logx)2 + C (b) - (logx)2 + C
2 2
2 −2
(c) 2 + C (d) 2 + C
x x
2
sec logx( )
14. ∫ dx=?
x
(a) log(tanx) + C (b) - log(tanx) + C
(c) tan(tanx) + C (d) –tan(logx) + C
1
15. ∫ dx=?
xlogx
 −2
(a)log |x| +C (b) 2 + C (c) (logx)2+ C (d) log |logx| +C
3
x
16. ∫ e x x2 dx=?
3 1 x 3 1 x 3

(a) e x + C (b) e + C (c) +C (d) none of these

3 6 e
e√x
17. ∫ dx = ?
√x
1
(a)e √ x + C (b) e √ x + C (c) 2e √ x + C (d) none of these
2
−1
tan x
e
18. ∫ =?
(1+ x 2)
−1

e tan x −1

(a) +C (b) e tan x

+ C (c) e x tan−1 x + C (d)none of these
x
sin √ x
19. ∫ dx= ?
√x
cos √ x
(a)2cox √x +C (b) - 2cox √x +C (c) – + C (d)none of these
2
20. ∫ (√sinx )cosx dx = ?
2 3
(a) (cosx)3 /2 + C (b) (cosx )3 /2 + C
3 2
2 3
(c) ( sinx)3/ 2 + C (d) (sinx)3/ 2 + C
3 2
1
21. ∫ dx = ?
( 1+ x ) √ tan−1 x
2

1
(a) log| tan−1 x | + C (b) 2 √ tan −1 x + C
2
1
(c) + C (d)none of these
2 √ tan x
−1

cotx
22. ∫ dx =?
log ⁡( sinx)
(a) log |cotx| +C (b) log |cotx cosecx| +C
(c) log |log sinx| + C (d)none of these
1
23. ∫ 2 dx = ?
x cos (1+ logx)
(a) tan(1+logx) + C (b) cot(1+logx) + C
(c) sec(1+logx) + C (d) none of these
2 −1 3
x tan x
24. ∫ 6 dx =?
(1+ x )
1
(a) ( tan−1 x 3)2 + C (b)log | tan−1 x 3| + C
3
1
(c) ( tan−1 x 3)2 + C (d) none of these
6
25. ∫ sec 5 xtanx dx =?
1 1
(a) tan 5x + C (b) 5
tan x + C
5 5
(c)5 log|cosx| +C (d)none of these
26. ∫ cosec3(2x+1)cot(2x+1)dx =?
1 1
(a) cosec4(2x+1) + C (b) - cosec3(2x+1) + C
4 3
1 1
(c) - cosec3(2x+1) + C (d) cosec(2x+1)cot(2x+1) + C
6 2
 tan(sin−1 x)
27. ∫ dx=?
√1− x2
(a) log|sec(sin-1x)| + C (b) log|cos(sin-1x)| + C
(c) tan(sin-1x) + C (d) none of these
tan ⁡(logx)
28. ∫ dx = ?
x
(a) xtan(log x) +C (b) log|tanx| +C
(c) log|cos(logx)| +C (d) –log|cos(logx)| + C
29. ∫ e x cot(e x ) dx =?
(a) cot(ex) + C (b)log|sin ex| + C
(c) log|cosec ex| + C (d)none of these
x
e
30. ∫ dx =?
√1+ e x
1
(a) 2√ 1+e x + C (b)
2
√ x
1+ e + C
1
(c) +C (d) none of these
√1+ e x
x
31.∫ dx =?
√1−x2
(a) sin −1 x + C (b)sin−1 √ x + C (c) √ 1−x 2 + C (d) -√ 1−x 2 + C
x
e (1+ x)
32. x dx =?
cos ( x e )
2

(a)tan(xe x ) + C (b) cot(xe x ) + C (c) e x x tanx + C (d) none of these

dx
33. ∫ x − x dx=?
(e +e )
(a)cot −1(e x ) + C (b) tan−1 (e x ) + C
(c)log|e x +1| + C (d)none of these
x
2
34. ∫ dx = ?
1−4 x
(a)sin-1(2x) + C (b)(log e2)sin −1( 2x ) + C
(c) (log e2)cos−1 (2x ) + C (d)(log 2 e )sin−1(2x ) + C
dx
35. ∫ x =?
e −1
(a)log|ex -1| + C (b) log|1- e− x | + C
(c) log|e -1| + C
x
(d)none of these
1
36. ∫ dx = ?
√x+x
(a) log|1+ √x | + C (b) 2log|1+ √x | + C
1
(c) tan-1√ x + C (d)none of these
√x
dx
37.∫ =?
(1+ sinx)
(a)tanx + secx + C (b) tanx + secx + C
1 x
(c) tan + C (d)none of these
2 2
sinx
38. ∫ dx = ?
(1+ sinx)
(a) x+tanx-secx+C (b) x-tanx-secx+C
(c) x-tanx+secx+C (d) none of these
sinx
39. ∫ dx = ?
(1−sinx)
(a) -x+secx-tanx+C (b)x +cosx-sinx+C
 (c) –log|1-sinx| + C (d) none of these
dx
40. ∫ =?
(1+cosx )
1 x x
(a) tan + C (b) -cot +C
2 2 2
x
(c) tan + C (d)none of these
2
dx
41. ∫ =?
(1−cosx)
1
(a) +C (b)log|x-sinx| + C
( x−sinx)
x x
(c) log|tan | + C (d)-cot +C
2 2

{ }
x
1−tan ⁡( )
2
42. ∫ dx =?
x
1−tan ⁡( )
2
x x
(a) 2 log |sec | + C (b) 2 log |cos | + C
2 2
π x π x
(c) 2 log |sec( − )| + C (d) 2 log |cos( − )| + C
4 2 4 2
43. ∫ √ e dx=?
x

1
(a) √ e x +C (b) 2 √ e x +C (c) √ e x +C (d)none of these
2
cosx
44. ∫ dx =?
(1+cosx )
x x x
(a)x+tan + C (b) -x+tan + C (c) x-tan + C (d)none of these
2 2 2
45. ∫sec2x cosec2x dx=?
(a)tanx – cotx + C (b)tanx + cotx + C
(c)-tanx + cotx + C (d)none of these
(1−cos 2 x )
46. ∫ dx = ?
(1+cos 2 x )
(a)tanx + x + C (b)tanx –x + C (c) –tanx +x +C (d)none of these
(1+ cosx)
47. ∫ dx = ?
(1−cosx)
x x
(a)-2cot - x + C (b) -2cot + x + C
2 2
x
(c) 2cot + x + C (d)none of these
2
1
48. ∫ 2 2 dx= ?
sin x cos x
(a)tanx +cot x + C (c)tanx –cot x + C
(c)-tanx +cotx + C (d)none of these
cos 2 x
49. ∫ 2 2 dx= ?
cos xsin x
(a)cot x +tanx + C (c)–cot x +tanx + C
(c) cotx-tanx + C (d)-cotx –tanx +C
(cos 2 x−cos 2α )
50. ∫ dx=?
(cosx−cosα )
(a)sinx +xcosα + C (b)2sinx +xcosα +C
(c)2sinx +2xcos + C α (d)none of these
51. ∫ tan-1 {√ }
1−cos 2 x
1+ cox 2 x
dx=?

x2 2
(a)2x2 + C (b) + C (c) 2 + C (d) none of these
2 1+ x
52. ∫ tan-1(secx +tanx)dx = ?
πx x2 πx x2 1
(a) + + C (b) - + C (c) 2 + C (d)none of these
4 4 4 4 (1+ x )
(1+ sinx)
53. ∫ dx= ?
(1−sinx)
(a) 2tanx + x -2secx + C (b)2tanx –x +2secx + C
(c) 2tanx –x- 2secx +C (d) none of these
4
x
54. ∫ 2 dx =?
(1+ x )
3 3
x −x
(a) + x + tan-1x +C (b) + x - tan-1x +C
3 3
3
x
(c) - x + tan-1x +C (d)none of these
3
sin ⁡( x−α )
55.∫ dx=?
sin ⁡( x + α )
(a) xcos2α - sin2α - log|sin(x+α )| + C
(b) xcos2α + sin2α - log|sin(x+α )| + C
(c) xcos2α + sinα - log|sin(x+α )| + C
(d) none of these
1
56.∫ dx=?
√ x +3 – √ x +2
2 3 /2 2 3/ 2 2 3 /2 2 3/ 2
(a) ( x+3) - ( x+2) + C (b) ( x+3) + ( x+2) + C
3 3 3 3
3 3 /2
(c) ( x+3) - 2( x +2)3 / 2 + C (d)none of these
2
(1+tanx)
57.∫ dx=?
(1−tanx)
(a) –log|cosx-sinx|+ C (b) log|cosx-sinx|+ C
(b) log|cosx+sinx|+ C (d) none of these
2
3x
58. ∫ 6 dx=?
(1+ x )
(a)sin-1x3 + C (b) cos-1x3 + C
(c) tan-1x3 + C (d) cot-1x3 + C
dx
59. ∫ =?
x√ x
6−1

1 1
(a) sec-1x3 + C (b) cosec-1x3 + C
3 3
1
(c) cot-1x3 + C (d)none of these
3
60. ∫ {(2 x+1) √ x 2 + x+1 }dx=?
3 2
(a) (x2 + x +1)3/2 + C (b) (x2 + x +1)3/2 + C
2 3
3
(c) ( 2x +1)3/2 + C (d)none of these
2
dx
61. ∫ =?
( √ 2 x +3+ √ 2 x−3)
1 1 1 1
(a) (2x+3)3/2 + (2x-3)3/2 + 1 (b) (2x+3)3/2 - (2x-3)3/2 + 1
18 18 18 18
 1 1
(c) (2x+3)3/2 - (2x-3)3/2 + 1 (d)none of these
12 12
62. ∫ tanx dx=?
(a) log |cosx| +C (b) - log |cosx| +C
(c) log |sinx| +C (d) - log |sinx| +C
63. ∫ secx dx =?
(a) log|secx-tanx| + C (b) - log|secx+tanx| + C
(c) log|sec+-tanx| + C (d) none of these
64. ∫ cosecx dx =?
(a) log|cosecx-cotx| + C (b) - log|cosecx - cotx| + C
(c) log|cosec+cotx| + C (d) none of these
(1+ sinx)
65. ∫ dx=?
(1+cosx )
x x x x
(a)tan + 2log|cos | + C (b) - tan + 2log|cos | + C
2 2 2 2
x x
(c) tan - 2log|cos | + C (d) none of these
2 2
tanx
66. ∫ dx=?
( secx+cosx)
(a) tan-1(cosx) +C (b) -tan-1(cosx) +C
-1
(c) cot (cosx) +C (d) none of these
67. ∫
√ 1+ x
1−X
dx ?
(a) sin-1x + √ 1−x 2 (b) sin-1x + (1+ x2) +C
(c) sin-1x - √ 1−x 2 (d) none of these
1
68. ∫ 2 e-1/x dx= ?
x
−1/ x
e
(a) e-1/x + C (b)-e-1/x +C (c) + C (d) none of these
x
3
x
69. ∫ 8 dx =?
(1+ x )
1
(a) tan-1x4 + C (b) 4tan-1x4 + C (c) tan-1x4 + C (d)none of these
4
( x +1)(x +logx)2
70. ∫ dx =?
x
2
1 x
(a) (x+ logx)3 + C (b) + x + C
3 2
3 2
x x
(c) + +x+C (d) none of these
3 3
−1 2
2 x tan x
71. ∫ 4 dx =?
(1+ x )
(a) (tan-1x2)2 + C (b) 2tan-1x2 + C
1
(c) (tan-1x2)2 + C (d) none of these
2
dx
72. ∫ =?
(2−3 x )
1
(a) -3log|2-3x| + C (b) - log|2-3x| + C
3
(c) –log|2-3x| + C (d) none of these
73. ∫ x√ x −1 dx
2

2 1
(a) ( x 2−1)3/2 + C (b) ( x 2−1)3/2 + C
3 3
 1
(c) +C (d)none of these
√(5-3x)
2
x −1
74. ∫ 3 dx= ?
(5−3 x)
−3 3(4−3 x)
(a) +C (b) +C
3(log 3) (log 3)
(c) -3(5-3x) log3 + C (d)none of these
75. ∫ etanxsec2x dx =?
(a) etanx +tanx + C (b) etanx .tanx + C
(c) e + C
tanx
(d) none of these
2
cos x
76. ∫ e sin2x dx=?
2 2 2
cos x
(a) e +C (b) −e cos x + C (c) e sin x + C (d) none of these
77. ∫ x sin3x2cosx2x = dx
1 1 1
(a) sin4x2 + C (b) sin4x2 + C (c) sin4x2 + C (d) none of these
4 8 2
√x √x
e cos ⁡(e )
78. ∫ dx =?
√x
1
(a) sin(e √ x ) +C (b) sin(e √ x ) +C (c) 2sin(e √ x ) +C (d)none of these
2
79. ∫ x2sinx3 dx = ?
1
(a) cosx3 + C (b) -cosx3 + C (c) - cosx3 + C (d) none of these
3
x
( x +1)e
80. ∫ 2 x dx=?
cos ( xe)
(a) tan(xex) + C (b) -tan(xex) + C (c) cot(xex) + C (d)none of these
1
81. ∫ dx=?
x √ x −1
4

1
(a) sec-1x2 + C (b) sec-1x2 + C (c) cosec-1x2 + C (d)none of these
2
82. ∫ x√ x−1 dx = ?
2 3 /2 2 5 /2
(a) ( x−1) + C (b) ( x −1) + C
3 5
2 5 /2 2 5 /2
(c) (x −1) + ( x −1) +C (d)none of these
5 5
83. ∫ x√ x 2−x dx =?
1 2 3 /2 2 2 3 /2
(a) ( x −1) + C (b) ( x −1) + C
3 3
1
(c) +C (d)none of these
√ x 2−1
dx
84. ∫ =?
(1+ √ x)
(a)√ x -log |1+√ x | + C (b)√ x + log |1+√ x | + C
(c)2 √ x + 2log |1+√ x | + C (d)none of these
85. ∫ √ e x −1 dx =?
3 x 3/ 2 1 x 1 /2
(a) ( e −1) + C (b) (a) ( e −1) + C
2 2
2 x 3/ 2
(c) (e −1) + C (d)none of these
3
sinx
86. ∫ dx =?
( sinx−cosx )
1 1 1 1
(a) x - log|sinx-cosx| + C (b) x + log|sinx-cosx| + C
2 2 2 2
(c) log|sinx-cosx| + C (d) none of these
 dx
87. ∫ =?
(1−tanx)
1 1 1
(a) log|sinx-cosx| + C (b) x + log|sinx-cosx| + C
2 2 2
1 1
(c) x - log|sinx-cosx| + C (d) none of these
2 2
dx
88. ∫ =?
(1−cotx)
1
(a) log|sinx-cosx| + C (b) log|sinx-cosx| + C
2
1 1 1 1
(c) x - log|sinx-cosx| + C (d) x + log|sinx-cosx| + C
2 2 2 2
2
sec x
89. ∫ dx=?
√1−tan2 x
(a) sin −1 ( tanx ) +C (b) cos−1 ( sinx ) +C
(c) tan−1 ( cosx )+ C (d) tan−1 ( sinx ) +C
( x ¿¿ 2+1)
90. ∫ ¿ dx =?
( x ¿¿ 4 +1) ¿
1 1 1 1
(a) tan−1 ( x− ) + C (b) cot −1( x− ) + C
√2 x √2 x
(c)
1
√2
tan−1
6
{ 1
√2 } 1
( x− ) + C
x
(d)none of these

sin x
91. ∫ dx= ?
cos8 x
1 1
(a) tan7x + C (b) sec7x + C
7 7
(c) log|cos6x| + C (d)none of these
92. ∫ sec5x tanx dx=?
1 1
(a) tan5x + C (a) sec5x + C
5 5
(c)5log|cosx| + C (d)none of these
93. ∫ tan5x dx =?
1
(a) tan6x + C
6
1 1
(b) tan4x + tan2x + log|secx| + C
4 2
1 1
(c) tan4x - tan2x + log|secx| + C
4 2

(d) none of these

94.∫ sin3xcos3x dx=?
1 1 1 1
(a) - cos4x + cos6x + C (b) sin4x - sin6x + C
4 6 4 6
1 1
(c) sin4x + cos6x + C (d)none of these
4 6
4
95. ∫ sec x tanx dx =?
1 1 1 1
(a) sec2x + sec4x + C (b) tan2x + tan4x + C
2 4 2 4
1
(c) secx +log|secx + tanx| + C (d) none of these
2
log tanx
96. ∫ dx=?
sinx cosx
 1
(a) log{ log ⁡(tanx ) } + C (b) (logtanx)2 + C
2
(c) log(sinxcosx) + C (d) none of these
97. ∫sin3(2x+1) dx= ?
1
(a) sin4(2x+1) + C
8
1 1
(b) cos(2x+1) + cos3(2x+1) + C
2 3
1 1
(c)- cos(2x+1) + cos3(2x+1) + C
2 6
(d) none of these
98. ∫
√tanx dx= ?
sinxcosx
(a) 2 √ tanx + C (b) 2 √ cotx + C (c) 2 √ secx + C (d) none of these
(cosx + sinx)
99. ∫ dx =?
(1−sin 2 x )
1
(a) log |sinx – cosx | + C (b) +C
(cosx −sinx )
(c) log |cosx +sinx| + C (d)none of these
100. ∫√ e x −1 dx = ?
2 1 ex
(a) (e x −1)3 /2 + C (b) . +C
3 2 √ e x −1
(c) 2√ e x −1 - 2tan-1√ e x −1 + C (d) none of these
dx
101. ∫ =?
√sin 3 x cos x
−2
(a) 2 √ tanx + C (b) 2 √ cotx + C (c) -2 √ tanx + C (d) +C
√tanx
cosx
102. . ∫ =?
(1+sin 2 x)
(a) –tan-1 (sinx ) + C (b) tan-1 (cosx ) + C
(b) tan (cosx ) + C
-1
(d) - tan-1 (cosx ) + C
dx
103. .∫ 2 =?
(2 x + x +3)
1 ( 4 x+1) 1 ( x +1)
(a) tan-1 +C (b) tan-1 +C
√23 √23 √23 √ 23
2 ( 4 x+1)
(c) tan-1 +C (d) none of these
√ 23 √23
2
sec x
104. dx=?
√ tan2 x −4
(a) log |tanx -√ tan 2 x−4| + C (b) log |tanx+√ tan 2 x−4| + C
1
(c) log |tanx +√ tan 2 x−4| + C (d) none of these
2
INTEGRATION SET-3
4

1. ∫ x √ x dx=?
0
(a) 12.8 (b) 12.4 (c) 7 (d) none of these
2

2. ∫ √6 x +4 dx=?
0
64 56
(a) (b) 7 (c) (d)none of these
9 9
 1
dx
3. ∫ =?
0 √ 5 x +3
2 2 2
(a) (√ 8− √ 3 ) (b) (√ 8+ √ 3) (c) (√ 8) (d) none of these
5 5 5
1
dx
4. ∫ 2 =?
0 (1+ x )
π π π
(a) (b) (c) (d) none of these
2 3 4
2
dx
5.∫ dx =?
0 √ 4−x 2
−1 1 ❑
(a) 1 (b) sin (c) 4 (d) none of these
2
√8
6.∫ x √ 1+ x dx =?
2

√3
19 19 38 9
(a) (b) (c) (d)
3 6 3 4
1
x3
7. ∫ 8
dx =?
0 (1+ x )
❑ ❑ ❑ ❑
(a) 2 (b) 4 (c) 8 (d) 16
e

8. ∫ ¿ ¿ ¿ =?
1
1 1 3 1
(a) (b) e (c) ¿ - 1) (d) ¿
3 3 3
❑
2

9.∫ cotx dx =?
❑
2
1
(a) log 2 (b) 2 log 2 (c) log2 (d) none of these
2
❑
2
10. ∫ tan 2 x dx =?
0
❑ ❑ ❑ ❑
(a) (1- 4 ) (b) (1+ 4 ) (c) (1- 2 ) (d) (1+ 2 )
❑
2
11. ∫ cos 2 x dx =?
0
❑ ❑
(a) 2 (b)  (c) 4 (d) 1
❑
2

12.∫ cosecx dx =?
❑
3
1 1
(a) log2 (b) log3 (c) –log2 (d) none of these
2 3
❑
2
13. ∫ cos 3 x dx =?
0
3 2
(a)1 (b) (c) (d) none of these
4 3
 ❑
4 tanx
14. ∫ e dx= ?
2
0 cos x
1 1
(a) (e-1) (b) (e+ 1) (c) ( +1) (d) ( −1)
e e
❑
2
15. ∫ cosx dx= ?
2
0 (1+sin x )
❑ ❑
(a) 2 (b) 4 (c)  (d) none of these
2
❑
sin ⁡( 1/x )
16.∫ 2 dx =?
1 x
❑
1 3
(a)1 (b) (c) (d) none of these
2 2
❑
dx
17.∫ ?
0 (1+ sinx)
1
(a) (b) 1 (c) 2 (d) 0
2
❑
2
18.∫ ( √ sinx cosx )3dx=?
0
2 2 8 5
(a) (b) (c) (d)
9 15 45 2
1
xe x
19.∫ 2 dx=?
0 (1+ x )
e
(a) -1 (b)(e-1) (c)e(e-1) (d)none of these
2
❑
2
20. ∫ e x ( (1+sinx) ) dx= ?
0 (1+ cosx )
❑
(a)0 (b) 4 (c) e/2 (d) e/2 -1
❑
2
21. ∫ √1+sin 2 x dx
0
(a)0 (b) 1 (c) 2 (d) √ 2
❑
2
22. ∫ √1+cos 2 x dx
0
3
(a)√ 2 (b) (c) √ 3 (d) 2
2
1
(1−x )
23. ∫ ( ) dx= ?
0 (1+ x)
1 1
(a) log2 (b) (2 log 2+1) (c) (2 log 2−1) (d) log2 -1
2 2
❑
2
24. ∫ sin 2 x dx =?
0
❑ ❑ ❑ 2
(a) 3 (b) 4 (c) 2 (d)
3
❑
6
25. ∫ cosxcos2 x dx =?
0
 1 5 1 7
(a) (b) (c) (d)
4 12 3 12
❑
2
26. ∫ sinxsin 2 x dx =?
0
2 3 5 3
(a) (b) (c) (d)
3 4 6 5
❑

27. ∫ sin 2 xcos3 x dx =?

0
4 −4 5 12
(a) (b) (c) (d) -
5 5 12 5
1
dx
28. ∫ −x =?
x
0 (e +e )
❑ −4 5 12
(a) 1− 4 (b) (c) (d) -
5 12 5
9
dx
29. ∫ =?
0 (1+ √ x )
(a) (3−2 log 2) (b) (3+2 log 2) (c) (6−2 log 4) (d) (6+ 2 log 4)
❑
2
30. ∫ xcosx dx =?
0
❑ ❑ ❑
(a) 2 (b) 2 -1 (c) 2 +1 (d)none of these
1
dx
31. ∫ 2 =?
0 (1+ x + x )
❑ ❑ ❑
(a) 3 (b) 3 (c) ) 3 3 (d) none of these
√ √

√
1
1−x
32.∫ dx= ?
0 1+ x
❑ ❑ ❑
(a) 2 (b) 2 -1 (c) 2 +1 (d)none of these
1
(1−x )
33. ∫ ( ) dx= ?
0 (1+ x)
(a) (log2 +1) (b) (log 2−1) (c) (2 log 2−1) (d) (2log2 +1)

√
1
a−x
34.∫ dx= ?
0 a+ x
a
(a)a (b) (c) 2a (d)none of these
2
√2
35. ∫ √2−x 2 dx =?
0
❑
(a) (b) 2 (c) 2 (d)none of these
2

36. ∫ ¿ x∨¿ ¿ dx =?
−2
(a)4 (b) 3.5 (c) 2 (d)0
1

37. ∫ ¿ 2 x−1∨¿ ¿ dx =?
0
1
(a)2 (b) (c) 1 (d)0
2
 1

38. ∫ ¿ 2 x+ 1∨¿ ¿ dx =?
0
5 7 4
(a) (b) (c) (d)4
2 2 2
1

39. ∫ ¿ x∨ ¿ ¿ dx =?
−2 x
(a)3 (b)2.5 (c)1.5 (d) none of these
a

40. ∫ x| x| dx=?
−a
2 a3
(a) 0 (b) 2a (c) (d) none of these
3
π

41. ∫|cosx|dx=?
0
3
(a) 2 (b) (c) 1 (d) 0
2
2π

42. ∫|sinx|dx=?
0
(a) 2 (b) 4 (c) 1 (d) none of these
π /2
sinx
43. ∫ (sinx+cosx )
dx=?
0
π π
(a) π (b) (c) 0 (d)
2 4
π /2
√ cosx
44. ∫ (√ cosx + √ sinx)
dx=?
0
π π
(a) (b) (c) π (d) 0
2 4
π /2
sin 4 x
45. ∫ 4 4
dx=?
0 (sin x +cos x)
π π
(a) (b) (c) 1 (d) 0
4 2
π /2 1/4
cos x
46. ∫ 1/ 4 1/ 4
dx=?
0 (sin x +cos x)
π
(a)0 (b)1 (c) (d) none of these
4
π /2 n
47. ∫ (sin nsin x
x +cos n x )
dx=?
0
π π
(a) (b) (c)1 (d) none of these
2 4
π /2
√ cotx
48. ∫ (√ cotx+ √tanx)
dx=?
0
π π
(a)0 (b) (c) (d) none of these
2 4
π /2 3
√tanx
49. ∫ 3 3
dx=?
0 ( √ tanx+ √ cotx)
π π
(a)0 (b) (c) (d) π
4 2
π /2
1
50. ∫ (1+tanx) dx =?
0
 π π
(a) 0 (b) (c) (d) π
2 4
π /2

51. ∫ (1+√1cotx) dx =?
0
π π
(a) 0 (b) (c) (d) π
4 2
π /2
1
52. ∫ (1+ tan 3
x)
dx=?
0
π π
(a) (b) 0 (c) (d) none of these
4 2
π /2 5
53. ∫ ( sec5 xsec x
+cosec 5 x)
dx=?
0
π π
(a) (b) 0 (c) (d) π
2 4
π /2

54. ∫ (1+√√cotx
cotx)
dx =?
0
π π
(a) (b) (c) 0 (d) 1
4 2
π /2
tanx
55. ∫ (1+tanx) dx =?
0
π
(a) 0 (b) 1 (c) (d) π
4
π

56. ∫ x 4 sinx dx=?

−π
(a) 2π (b) π (c)0 (d) none of these
π

57. ∫ x 3 cos 3 x dx=?

−π
π
(a) π (b) (c) 2π (d) 0
4
π

58. ∫ sin x dx =?
5

−π
3π 5π
(a) (b) 2π (c) (d) 0
4 16
−2

59. ∫ x (1−x ) dx=?

3 2

−1
40 40 5
(a) - (b) (c) (d) 0
3 3 6
α
a−x
60. ∫ log ⁡( )dx= ?
−α a+ x
(a) 2a (b) a (c) 0 (d) 1
π

61. ∫ ( sin x + x ) dx =?
61 123

−π
π
(a) 2π (b) 0 (c) (d) 125π
2
π

62. ∫ tanx dx =?
−π
1
(a) 2 (b) (c) -2 (d) 0
2
 1

63. ∫ log ( x + √ x +1 ) dx =?
2

−1
1 1
(a) log (b) log2 (c) log2 (d) 0
2 2
π /2

64. ∫ cosx dx=?

−π / 2
(a) 0 (b) 2 (c) -1 (d) none of these
π

65. ∫
√x dx= ?
0 √ x+ √a−x
(a)
a
(b) 2a (c)
2a
(d)
√a
2 3 2
π /4

66. ∫ log ( 1+ tanx ) dx=?

0
π π π
(a) (b) log2 (c) log2 (d) 0
4 4 8
α

67. ∫ f ( x ) dx=?
−α
α α

(a) 2∫ { f ( x )+ f (−x )} dx (a) 2∫ { f ( x )−f (−x) } dx

0 0
α

(c) ∫ { f ( x )+ f (−x )} dx (d) none of these

0
68. Let [x] denote the greatest integer less than or equal to x.
15

Then, ∫ [ x ] dx=?
0
1 1
(a) (b) (c) 2 (d) 3
2 2
69. Let [x] denote the greatest integer less than or equal to x.
Then, ∫ −1 [ x ] dx=?
−¿¿
1
(a) -1 (b) 0 (c) (d) 2
2
2

70. ∫ ¿ x −3 x +2∨¿ ¿ dx= ?

2

1
−1 1 1 2
(a) (b) (c) (d)
6 6 3 3
2π

71. ∫ |sinx|dx=?
π
(a) 0 (b) 1 (c) 2 (d) none of these
1 /√ 2 −1
sin x
72. ∫ (1−x 2)3 /2
=?
0
1 π
(a) (π – log2) (b) ( – 2log2)
2 2
π 1
(c) ( – log2) (d) none of these
4 2
1
2x
73. ∫ sin (
−1
)
2 dx= ?
0 1+ x
1 π
(a) (π – log2) (b) ( −log 2) (c) (π – 2log2) (d) none of these
2 2
VECTORS
1. If be two vector such that then angle between
is

(a) (b) (c) (d)

2. If be two vector such that then angle between

is

(a) (b) (c) (d) none of these

3. The angle between the vectors is

(a) (b) (c) (d) none of these

4. If be such that
(a) (b) (c) (d)

5. If then the angle between is

(a) (b) (c) (d)

6. If then the angle between

is

(a) (b) (c) (d) none of these

7. If are unit vectors such that , then

(a) (b) (c) (d)

8. If then

(a) (b) (c) (d) none of these

9. What is the projection of then

(a) (b) (c) (d) none of these

10. If is the angle between tow unit vector

(a) (b) (c) (d) none of these

11. If
 (a) (b) (c) (d) none of these

12. If
(a) (b) (c) (d)

13. If then the angel between is

(a) (b) (c) (d)

14. If
(a) (b) (c) (d)

15. Two adjacent sides of a If are represented by the vectors

The area of the is

(a) sq units (b) sq units (c) sq units (d) none of these

16. The diagonals of are represented by the vectors

The area of the is

(a) sq units (b) sq units (c) sq units (d) none of these

17. Two adjacent sides of a triangle are represented by the vectors

The area of the triangle is

(a) sq units (b) sq units (c) sq units (d) none of these

18. If the vectors are perpendicular to each other,

then
(a) (b) (c) (d)

19. The unit vector normal to the plane containing is

(a) (b) (c) (d)

20. If are mutually perpendicular unit vectors, then

(a) (b) (c) (d)

21. If are mutually perpendicular unit vectors, then

(a) (b) (c) (d)
DIFFERENTIAL EQUATIONS
1. The solution of the D.E. is
(a) (b) (c) (d) none of these

2. The solution of the D.E. is

(a) (b) (c) (d) none of these

3. The solution of the D.E. is

(a) (b)

(c) (d) none of these

4. The solution of the D.E. is

(a) (b) (c) (d) none of these

5. The solution of the D.E. is

(a) (b) (c) (d) none of these

6. The solution of the D.E. is

(a) (b)

(b) (c) (d) none of these

7. The solution of the D.E. is

(a) (b)

(c) (d) none of these

8. The solution of the D.E. is

(a) (b)

(c) (d) none of these

9. The solution of the D.E. is

(a) (b)
(c) (d) none of these

10. The solution of the D.E. is

(a) (b)
(c) (d) none of these
11. The solution of the D.E. is

(a) (b) (c) (d) none of these

12. The solution of the D.E. is

(a) (b)
(c) (d) none of these

13. The solution of the D.E. is

(a) (b)

(c) (d) none of these

14. The solution of the D.E. is

(a) (b)
(c) (d) none of these

15. The general solution of the D.E. is

(a) (b) (c) (d) none of these

16. The general solution of the D.E. is

(a) (b)
(c) (d) none of these

17. The general solution of the D.E. is

(a) (b) (c) (d) none of these

18. The general solution of the D.E. is

(a) (b)
(c) (d) none of these

19. The general solution of the D.E. is

(a) (b) (c) (d) none of these

20. The general solution of the D.E. is

(a) (b)

(c) (d) none of these

21. The general solution of the D.E. is

(a) (b) (c) (d) none of these

22. The general solution of the D.E. is
(a) (b) (c) (d) none of these

23. The general solution of the D.E. is

(a) (b)

(c) (d) none of these

24. The general solution of the D.E. is

(a) (b) (c) (d) none of these

25. The general solution of the D.E. is

(a) (b)
(c) (d) none of these

26. The general solution of the D.E. is

(a) (b)

(c) (d) none of these

27. The general solution of the D.E. of is

(a) (b) (c) (d) none of these