Problemns in Physi

38
Level
LEVEL 02 JEE Main
11 xln2x) =
Single Choice Correct Questions dx
(b) 1 + Inx
1 Cu+4)=
dx
(c) 0 (d) 2x + 4 (c) 1 + In2x (d)+In2x
(a) 2x2 (b) 2x 2

2
1 1
12 dxsinx)=
dx
1 1 (b) sinx
(a) 2x + -+ (b) 2x - , (a) x cosX
(c) x coSX + sinx (d) None of these
(d) None of these
(c) 2x -1 dy
1 1
+3. then dy is
13 y =xlnx +x,then dx is
3y =x0 y10
+
dx 1
X
(a) 1+In x+ (b) 1+ Inx +
(a) 10x +
10
+ Inx (b) 10x?
10
+ Inx 2/
x11 1 1
1 (c)x + Inx + (d) x + In x+
10
(c)10,9 10
+ Inx (d) 10x°-. 2Vr
x10
d
1 14 (xe* sinx) =
4 I6=, k s t h e n k e
d
dx (a) e* (xcoSX + XSinx + sinx)
(d) 2 (b) e (x cosx + sinx)
(a) 3 (b) 1
(c)e* xsinx + cosx)
(d) None of the above
5 Ify = tan x, then dy -1=
Vdx
(c) tanx (d) None of these 15 y=Inx +e*,then dx is
(a) sec'x (b) sec x
(a) X +e-* (b)-e (c)x+e* (a)+e'
6x-2
dx
sinx +3cosx) = X X

(a) 4x -2cosx +3sinx (b) 3x+2cosx +3sinx 16 Ify =2 tanx, find dy

(d) 4x-2coS X- 3sinx dx
(c) 4x+ 2cosx -3sinx tanx
d x+1 (a) 2sec² x (b). sec x (c) Wx sec?* (d)
7
dx x+1 da
17 Ifa = sec(3b), then will be
(a) ´+2x-1 x-2x +1 db
«+1)2 K+1)2 (a) 3sec(3b) tan(3b) (b) 3a sin (36)
x´+2x -1 x² +2x +1 (c) sec(3b)tan(3b) (d) 3sec(36)
(c) (d)
X +1 (x+1)2 dy
18 Ify = sin2x, then =

dy
8Ify =x' sinx, then will be, dx
(a) -2 (b) 2 (d) 1
(a) x cosx + 2x sinx (b) 2x sinx 2
(c) x cosx (d) 2x coS X dy
19 y= cos(3x) + sin(1-x), then dx
will be

w'e')=
dx (a) - sin(3) + cos(- 1) (b) sin(3x) + cos(1-x)
(a) 2xe* (b) x'e* + 2x (c) e +2x (d) e (x+ 2x) (c)-3sin(3x) - cos(1-x) (d) 3sin(3x)+ cos(1- X)

10I(1+x'le']= 20 y =esin 3x,then is

dx dx
(a) (x + 1)°e* (b) (x + 1)3e (a) e sin3x cos3x (b) 3e Sin3x cos3X
(c) (x? +1)'e* (d) None of these (c) 3e Sin3x (d) 3e Sin3x cosx
calculus in Physics 39

21 y=3tan then dy
dx
is 30 Find the derivative of y= sin (Inx).
(a) 2sin(Inx)cos(Inx)-1 (b)- 2cos(Inx)cos(Inx)
X X
-2sin(inx) cosx
(c) 2cos(lInx) (d)
X

31 y=sin(cos² (e), then dy dx

22 y =sinx+sin 3x,then is (a)-2e* sin(e")cosle")x cos(cos (e))
dx
(a) 3sin x +3cos3x (b) 3sin xcoSX +3cos3x (b) e* sin(e")cosle")x sin(cos(e))
(c) 3sin xcOSX + Cos 3x (d) 3sinx cosx +3cos3x (c) e sine cose xcos(cos (e*))
(d) None of the above
23 Find the derivative for the function y =xsin x.
(a) sinx(2x+ sinx) (b)sinx(X COSX + sinx) 32 y =log, (tan(x), find dx
(c) (2x cosx + sinx) (d) xsin2x + sin x
(a) 3x? seclr) (b) x² sec ()
24 2x+3) =
d
tan(x°)
(a)
1
(b
2x (c) 3x secx) (d) None of these
tan(x)
2/2x +3 2x +3
1 d
(c) (d) None of these 33 dx
1+ sin2x) =
J2x +3
(a) cos X (b) cosx+ sinx
25 Calculate the rate of change for the function (c) cosx - sinx (d)sinx
y=x+2 w.r.t. x. d |1- cos2x
2x 34
(6 dy
1
dx V1+ cos2x
Jx²+2 dx
Jx2+2 (a) tanx (b) sec x
X
(d dy X
(c) tan x (d) None of these
dx 2.x'+2 dx x? +2 dy will be
35 Ify = sinx andx=3t, then
26 Calculate the rate of change for the function dt
(a) 3cos(3x) (b) cosx (c) 3cos(3t) (d)- cosx
dy 1 V2x dy 2
eV2r 36 For what values of x is the derivative of the function
la) e (b) 3
2x --equal to 14?
dy =kevr X
(c) dx V2x
e (d)
dx (a) 1
3 3
27 y= esinl 3-x) then find y'.
37 Find derivative of x+ 4x +5with respect to 2x +7.
(a) e sin(3- x) cos(3 -x) (b) - esin(3 - x cos(3 - x)
(a) x + 4 (b) x +2 (c) 2x + 4 (d) 4x +8
(c) e sin(3 -x) (d) -e sin3-x)
38 Suppose u and v are functions of x that are
28(x-3x
dx
+3x 1100 = differentiable at x=0and that
u0) =5, u(0)= -3, v0) = -1, v(0) =2
(a) 30(X - 1)2 (b) 300 (x - 1) d
(c) 300 (x - 1)29 (d) 100 (x - 1)9 Find-(v)
dx
at x =0.
29 f(x) =(x +6x? +12x - 13)0, then f'(x)= (a) 7 (b) 10 (c) 13 (d)-5
(a) 100 (x +6x? +12x - 13" 39 The slope of curve y =2 secx - tanx at x = will be
(b) 300 (x +2) (x + 6x? + 12x - 13)* 6
(a) 0 (b)1
(c) 100x 99 8
(d) None of the above (c) (d) None of these
 Problems in Physi
40

tangent to the curve

47 The charge flowing through aconductor beginnin
40 Find points at which the parallel to the X-axis with time t=0is given by the formula
y=x-3x -9x+7 is q=2t -3t + 1(coulomb). Find the current
(3, 20) and (1, 12)
(a) (3,- 20) and (-1,12) (b) i= dg/ dt at t =5 s.
(d)None of these
(c) (3,- 10) and(1, 12) (a) 36 (b) 17
curvex+4=y. The (d) 40
41 Aparticle moves alongthe (c) 20
the y-coordinates
point on the curve at which
X-COordinate, is
48 The momentum of amoving particle given by
changes twice as fast as the P=tlnt. Net force acting on this particle is define
(a) (1, 5) (b) (5, 29) dp
(d) None of these byequation F = The net force acting on the
(c) (2, 8) dt
level field is particle is zero at time
42 Ahot air balloon rising straight up from a
lift-off
tracked by a range finder 500 ft from the (a) t=0 (b)t= (d) None of thes
elevation
point. At the moment the range finder's
angle is the angle is increasing at the rate of 0.14 49 Find the point of minima for the function
4
y =2x -9x+100.
rad/min. How fast is the balloon rising at the (a) 0 (b) 1 (c) 2 (d) 3
moment?
(a) 50 ft/min (b) 70 ft/min 50 Ify = V3sinx + coSx, then there will be maxima
(c) 100 ft/min (d) 140 ft/min corresponding to
(d)
43 The sides of a certain closed cube are increasing at a (a) O b)
3 2
constant rate uniformly such that at the instant
when the side-length is 25 cm, the rate of change for 51 Minimum value of function x -2x+3 is
the volume enclosed within the cube is exactly equal (a) 1 (b) 2 (c) -2 (d) 3
to 3 cc/s. The rate of change for the total surface
area of the cube is 52 Find the minimum value of the function
(b) 0.12 cm'/s y=x -7x +8x +5.
(a) 12 cm? /s (c)- 11 (d)-5
(d) 0.48 cm'/s (a) -7 (b) 4
(c) 4.8 cm'/s
53 A2m wide truck is moving with a uniform speed ofl
44 A stone is dropped into a quiet lake and waves move m/s along a straight horizontal road. Apedestrian
when
in circles at the speed of 5 cm/s. At the instant starts crossing the road at an instant when the truck
the radius of the circular wave is &cm,how fast is is 4m away from him. The minimum constant
the enclosed area increasing? velocity with which he should run to avoid an
(a) 80 T cm/s (b) 90 Cm/s accident is
(c) 85 T cm/s (d) 89 n cm/s
2m: Truck
45 Aladder 5m long is leaning against a wall. The foot of
the ladder is pulled out along the ground away from
K.
4m
the wall at a rate of 2 m/s. How fast is the height of
(a) 16V5 m/s (b) 1.2/5 m/s
ladder on the wall decreasing at the instant when
(c) 1.2/7 m/s (d) 1.6/7 m/s
the foot of the ladder is 4 m away from the wall?
3
(a) 10 m/s (b) m/s
2 54 (5x°dx =
8 (a) x +C (b)x+C
(c) m/s (d) None of these (d) x +c
3 (c) x +c
46 A kite is 120 m high and 130 m of string is out. If the 55
kite is moving away horizontally at the rate of
52 m/s, find the rate at which the string is being (a) x + +2x +C (b)
1
+ 2x +C
pulled out. 2x3 2x3
(a) 20 m/s (b) 30 m/s 2 +2x +C
(c) 40m/s (d) 50 m/s + 2x +C (d)
3 X 3
Calculus in Physics 41

56
3x+7x-11
dx = 64 [(3x -4)° dx =
3 7 11 (a)
(3x - 4)4 +C
(b) Br+4)*
+C
(a) - -+
X 2x2
+C (b) 3in|x-411 +C 12 12
2x2 (3x-4)
3 7, 22 (c) +C ld).(3x +4) +C
+C (d) 3I n x + . 2 2 +C 4
2
65 /1+x dx =
la)(1+*)"
3 +c (b)1+x)
2
+c
x? 1
4
-In|x 3 (d) (1+
3 x) +c
dx
X
+In|x|+ 1 66
4 2
1 1
1 (a) -+C (b)
4 2
+In| x-+C
2y2
43x + 1)*
1
X 1 (c) - +C (d) -
+In|x -+C 18(3x + 1)6
4 2 2x2 5
67
-1)2
dx =
,3

1
(a)in|
3
3x -7|+C (b) En| 5x -7| +C
-Inx + C (b)-+ 2Inx +C (c) ln| 5x -7|+C 3
2 2x (0 5 n| 3x-7| +c
x 1
- 2lnx + C (d) None of these
2 2x? 68 ( d X

(a) In(x)+C (6) nc

3
(c nx
2
+C (d) - In(x) +C
la)x2 +2Vx +C (6)2-2/ +c 69 1=(+2sinx dx; then I is equal to
3 3 cosx
(a) tanX + secx+C (b) tanx- secx +C
(c)x2
3
+2Vx +C (a) x2
3
2Vx +C (c) tanx -2 secx +C (d) tanx +2secx +C
60 Calculate the indefinite integral | (xVx+2)d. 70 cos ydy
sin2y sin2y
(b).
la)xvx +2x +C (b)xN t2+C +C +C
5
2 2 2 4
5 sin2y +C y sin2y
x'x +2x +C ()x +2x² +c lc) 4 4
+C
5 4
5
71 cos(*).x² dx willbe
61
(a) sin(x) +C (b) cosx) +C
(a) - cos(x /2) + C (b) cos(x /2) +C 3
ld)Sintr9)
(c) 2cosk /2)+C
62 cosec²x dx
(d) -2 cos(x/2) + C (c) sinaC
3 3
+C

72
(a) cotx +C (b) cot'x+C
(c) - cotX +C (d) cotx +C (a) 24 (b) 21 (c) 18 (d) 15
63 e"dx is equal to 27

( 6 )e r
73 (9de
la) e2 +C +C
3r2
(c) 2e+C (d) 2e +C 2
(b)
2
(c) 2r? (d) 3r2
42
Problems in Physice
n/2
74 Ifl= sin2x dx, the value of lis 82(sin2x
Jo +cos2x) dx
(a) 2 (b) 1 (c) -2 (d)-1
(a) 1 (b) - 1 ld)1
2
4
83 xsinx' dx
75 (2cosx -dx (a) 1 (b) 2 (d) None of these
X=0

(a) 1/2 (b) V2 (c) 1 (d) 1//2 84 Area of curve y =2x°-3x+4 from x, =-1to
X, =1will be
76 dx = (a) 0 (b) 2 (c) 6 (d) 10
85 The area of region between y=sinx and X-axis in th
(a) 1 (b) -1 (d) 3
n/2
3
interval|o,wil be
77 Value of cos(3t) dt is (a) 3 (b) 0 (c) 1 (d)-1
86 Consider the parabola y =x
3
(b) The shaded area is

78 e dk 1, 1)
(a) 1 (b) O ’X
(c)-1 (d) None of these
X= T/8
(a) 1
79 [2cos2x dx
X=0
3 3

(a) 1/2 (b) V2 (c) 1 (d) 1/V2 Previous Year's Questions

X=T/4
JEE Advanced
80 (2 sin 4x dx
X=0 1 A
person of height 1.6 mis walking away from a
(a) 0 (b) W2 (c) 1 (d) None of these lamp post of height 4 m along a straight path on the
1/2 flat ground. The lamp post and the person are always
81 sinx dx = perpendicular to the ground. If the speed of the
person is 60 cm s, the speed of the tip of the
(b) (c). (d) person's shadow on -1the ground with respect to the
4 8 person is ... cm s [2023 Adv]
Level 2
Single Choice Correct Questions
1. (b) 2. (d) 3. (d) 4. (d) 5. (c)
6. (d) 7. (a) 8. (a) 9. (d) 10. (a)
11. (c) 12. (c) 13. (b) 14. (a) 15. (b)
16. (b) 17. (a) 18. (b) 19. (c) 20. (b)
21. (a) 22. (b) 23. (d) 24. (c) 25. (d)
26. (c) 27. (b) 28. (c) 29. (b) 30. (a)
31. (a) 32. (a) 33. (c) 34. (b) 35. (c)
36. (c) 37. (b) 38. (c) 39. (a) 40. (a)
41. (a) 42. (d) 43. (d) 44. (a) 45. (c)
46. (a) 47. (b) 48. (b) 49. (d) 50. (b)
51. (b) 52. (c) 53. (a) 54. (b) 55. (c)
56. (b) 57. (c) 58. (c) 59. (d) 60. (c)
61. (d) 62. (c) 63. (b) 64. (a) 65. (a)
66. (b) 67. (a) 68. (b) 69. (d) 70. (b)
71. (d) 72. (b) 73. (b) 74. (a) 75. (b)
76. (c) 77. (b) 78. (a) 79. (d) 80. (c)

81. (b) 82. (b) 83. (a) 84. (c) 85. (a)
86. (b)

Previous Year's Questions

JEE Advanced
1. (40)