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JEE Main · Physics · Kinematics

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1
[JEE Main 2026, 8 Apr Shift 2, Q29] A gas balloon is going up with a constant velocity of 10 m/s. When this balloon reached a height of 75 m, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is ______ m. (Take g=10g=10 m/s2^2)
Not attempted
A
185185
B
150150
C
129129
D
125125
2
[JEE Main 2026, 8 Apr Shift 2, Q31] Two identical bodies, projected with the same speed at two different angles cover the same horizontal range R. If the time of flight of these bodies are 5 s and 10 s, respectively, then the value of R is ______ m. (Take g=10g=10 m/s2^2)
Not attempted
A
250250
B
2525
C
500500
D
125125
3
[JEE Main 2026, 8 Apr Shift 2, Q50] Two masses of 3.4 kg and 2.5 kg are accelerated from an initial speed of 5 m/s and 12 m/s, respectively. The distances traversed by the masses in the 5th5^{th} second are 104 m and 129 m, respectively. The ratio of their momenta after 10 s is x8\frac x8. The value of x is ______.
Not attempted
Your answer: —
Correct answer: 9
4
[JEE Main 2026, 5 Apr Shift 2, Q29] The velocity (v) versus time (t) plot of a particle is shown in the figure, for a time interval of 40 s. The total distance travelled by the particle and the average velocity during this period are, respectively ______.
Not attempted
A
25 m and zero
B
50 m and zero
C
100 m and zero
D
100 m and 2.5 m/s
5
[JEE Main 2026, 5 Apr Shift 1, Q47] From 18 m height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is ______ m. (Take g=10g=10 m/s2^2 and neglect the air resistance)
Not attempted
Your answer: —
Correct answer: 13
6
[JEE Main 2026, 4 Apr Shift 2, Q27] Two cars A and B are moving in the same direction along a straight line with speeds 100 km/h and 80 km/h, respectively such that car A is moving ahead of car B. A person in car B throws a stone with a speed v so that it hits the car A with a speed of 5 m/s. The value of v is ______ km/h.
Not attempted
A
1818
B
2828
C
3838
D
4848
7
[JEE Main 2026, 4 Apr Shift 2, Q29] If x and y coordinates of a projectile as a function of time (t) are given as 24t24t and 43.6t−4.9t243.6t-4.9t^2, respectively, then the angle (in degrees) made by the projectile with horizontal when t=2t=2 s is ______.
Not attempted
A
6060
B
4545
C
3030
D
7575
8
[JEE Main 2026, 4 Apr Shift 2, Q47] A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is 6.4 m. The speed of the bullets from the gun is ______ m/s. (take g=10g=10 m/s2^2)
Not attempted
Your answer: —
Correct answer: 8
9
[JEE Main 2026, 4 Apr Shift 1, Q31] The two projectiles are projected with the same initial velocities at the 15∘15^\circ and 30∘30^\circ with respect to the horizontal. The ratio of their ranges is 1:x1:x. The value of x is
Not attempted
A
2\sqrt2
B
3\sqrt3
C
232\sqrt3
D
12\frac1{\sqrt2}
10
[JEE Main 2026, 2 Apr Shift 1, Q28] The velocity of a particle is given as v⃗=−xi^+2yj^−zk^\vec v=-x\hat i+2y\hat j-z\hat k m/s. The magnitude of acceleration at point (1,2,4)(1,2,4) is ______ m/s2^2.
Not attempted
A
6\sqrt6
B
99
C
33\sqrt{33}
D
00
11
[JEE Main 2026, 28 Jan Shift 2, Q44] A particle starts moving from time t=0t=0 and its coordinate is given as x(t)=4t3−3tx(t)=4t^3-3t. A. The particle returns to its original position (origin) 0.866 units later B. The particle is 1 unit away from origin at its turning point C. Acceleration of the particle is non-negative D. The particle is 0.5 units away from origin at its turning point E. Particle never turns back as acceleration is non-negative Choose the correct answer from the options given below:
Not attempted
A
C, E Only
B
A, C Only
C
A, B, C Only
D
A, C, D Only
12
[JEE Main 2026, 28 Jan Shift 1, Q28] Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is ____ m. (g=10 m/s2g=10\ \text{m/s}^2)
Not attempted
A
3.83.8
B
2.52.5
C
4.24.2
D
4.04.0
13
[JEE Main 2026, 24 Jan Shift 2, Q42] The velocity (v) - Distance (x) graph is shown in figure. Which graph represents acceleration (a) versus distance (x) variation of this system?
Not attempted
A
(A)
B
(B)
C
(C)
D
(D)
14
[JEE Main 2026, 24 Jan Shift 1, Q26] A boy throws a ball into air at 45∘45^\circ from the horizontal to land it on a roof of a building of height H. If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then value of H is ____ m. (g=10 m/s2g=10\ \text{m/s}^2)
Not attempted
A
1515
B
1010
C
2525
D
2020
15
[JEE Main 2026, 23 Jan Shift 2, Q28] A bead P sliding on a frictionless semi-circular string (ACB) and it is at point S at t=0t=0 and at this instant the horizontal component of its velocity is v. Another bead Q of the same mass as P is ejected from point A at t=0t=0 along the horizontal string AB, with the speed v, friction between the beads and the respective strings may be neglected in both cases. Let tPt_P and tQt_Q be the respective times taken by beads P and Q to reach the point B, then the relation between tPt_P and tQt_Q is
Not attempted
A
tP>1.25tQt_P>1.25t_Q
B
tP<tQt_P<t_Q
C
tP>tQt_P>t_Q
D
tP=tQt_P=t_Q
16
[JEE Main 2026, 23 Jan Shift 2, Q30] A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with 3 m/s23\ \text{m/s}^2. At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is 5 m/s. The initial height of the airplane is ____ m. (g=10 m/s2g=10\ \text{m/s}^2)
Not attempted
A
92.592.5
B
82.582.5
C
2020
D
62.562.5
17
[JEE Main 2026, 23 Jan Shift 1, Q45] An object is projected with kinetic energy K from a point A at an angle 60∘60^\circ with the horizontal. The ratio of the difference in kinetic energies at points B and C to that at point A (see figure), in the absence of air friction is :
Not attempted
A
2:32:3
B
1:41:4
C
3:43:4
D
1:21:2
18
[JEE Main 2026, 22 Jan Shift 1, Q42] A projectile is thrown upward at an angle 60∘60^\circ with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is 45∘45^\circ with the horizontal. The initial speed of the projectile is ____ m/s.
Not attempted
A
20320\sqrt3
B
4040
C
40240\sqrt2
D
20220\sqrt2
19
[JEE Main 2026, 21 Jan Shift 2, Q42] A river of width 200 m is flowing from west to east with a speed of 18 km/h. A boat, moving with speed of 36 km/h in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for this journey and also the displacement along the river bank are ____ and ____ respectively.
Not attempted
A
40 s and 0 m
B
40 s and 200 m
C
20 s and 100 m
D
40 s and 100 m
20
[JEE Main 2025, 8 Apr Shift 2, Q64] Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is 8 times higher than that of the second ball. T1T_1 and T2T_2 are the total flying times of first and second ball, respectively, then the ratio of T1T_1 and T2T_2 is
Not attempted
A
2 : 1
B
2:1\sqrt{2}:1
C
2 2:1\sqrt{2}:1
D
4 : 1
21
[JEE Main 2025, 7 Apr Shift 2, Q53] A helicopter flying horizontally with a speed of 360 km/h at an altitude of 2 km, drops an object at an instant. The object hits the ground at a point O, 20 s after it is dropped. Displacement of 'O' from the position of helicopter where the object was released is : (use acceleration due to gravity g = 10 m/ s2\mathrm{s}^{2} and neglect air resistance)
Not attempted
A
7.2 km
B
2 5\sqrt{5} km
C
2 2\sqrt{2} km
D
4 km
22
[JEE Main 2025, 7 Apr Shift 1, Q62] Two projectiles are fired from ground with same initial speeds from same point at angles (45∘+({45}^{\circ}+ α)\alpha ) and (45∘−α)({45}^{\circ}-\alpha ) with horizontal direction. The ratio of their times of flights is
Not attempted
A
1+tan⁡α1−tan⁡α\frac{1+\tan \alpha }{1-\tan \alpha }
B
1+sin⁡2α1−sin⁡2α\frac{1+\sin 2\alpha }{1-\sin 2\alpha }
C
1−tan⁡α1+tan⁡α\frac{1-\tan \alpha }{1+\tan \alpha }
D
1
23
[JEE Main 2025, 4 Apr Shift 2, Q57] The displacement x versus time graph is shown below. (A) The average velocity during 0 to 3 s is 10 m/s10\ m/s (B) The average velocity during 3 to 5 s is 0 m/s0\ m/s (C) The instantaneous velocity at t=2 st=2\ s is 5 m/s5\ m/s (D) The average velocity during 5 to 7 s and instantaneous velocity at t=6.5 st=6.5\ s are equal (E) The average velocity from t=0t=0 to t=9 st=9\ s is zero Choose the correct answer from the options given below :
Not attempted
A
(B), (C), (D) only
B
(B), (D), (E) only
C
(A), (D), (E) only
D
(B), (C), (E) only
24
[JEE Main 2025, 3 Apr Shift 2, Q53] A particle moves along the xx -axis and has its displacement xx varying with time t according to the equation: x=c0(t2−2)+c(t−2)2x=c_0(t^2-2)+c(t-2)^2 where c0c_0 and c are constants of appropriate dimensions. Then, which of the following statements is correct?
Not attempted
A
the acceleration of the particle is 2(c+c0)2(c+c_0)
B
the acceleration of the particle is 2c02c_0
C
the acceleration of the particle is 2 c
D
the initial velocity of the particle is 4c4c
25
[JEE Main 2025, 3 Apr Shift 2, Q67] A particle is projected with velocity uu so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as nu225g\frac{nu^2}{25g} , where value of nn is: (Given, ' gg ' is the acceleration due to gravity.)
Not attempted
A
6
B
12
C
18
D
24
26
[JEE Main 2025, 3 Apr Shift 1, Q54] The angle of projection of a particle is measured from the vertical axis as ϕ\phi and the maximum height reached by the particle is hmh_m . Here hmh_m as function of ϕ\phi can be presented as
Not attempted
A
(A)
B
(B)
C
(C)
D
(D)
27
[JEE Main 2025, 3 Apr Shift 1, Q66] Which of the following curves possibly represent one-dimensional motion of a particle? \text{Which of the following curves possibly represent one-dimensional motion of a particle? } Choose the correct answer from the options given below :
Not attempted
A
A, B and C only
B
A, C and D only
C
A, B and D only
D
A and B only
28
[JEE Main 2025, 2 Apr Shift 2, Q58] A sportsman runs around a circular track of radius rr such that he traverses the path ABABABAB . The distance travelled and displacement, respectively, are
Not attempted
A
πr,3r\pi r,3r
B
2r,3πr2r,3\pi r
C
3πr,2r3\pi r,2r
D
3πr,πr3\pi r,\pi r
29
[JEE Main 2025, 2 Apr Shift 1, Q54] A river is flowing from west to east direction with speed of 9 km h−19\ \mathrm{km}{\ h}^{-1} . If a boat capable of moving at a maximum speed of 27 km h−127\ \mathrm{km}{\ h}^{-1} in still water, crosses the river in half a minute, while moving with maximum speed at an angle of 150∘{150}^{\circ} to direction of river flow, then the width of the river is :
Not attempted
A
112.5 m
B
75 m
C
300 m
D
112.5×3 m112.5\times \sqrt{3}\ m
30
[JEE Main 2025, 2 Apr Shift 1, Q75] A person travelling on a straight line moves with a uniform velocity v1v_1 for a distance xx and with a uniform velocity v2v_2 for the next 32x\frac{3}{2}x distance. The average velocity in this motion is 507 m/s\frac{50}{7}\ m/s . If v1v_1 is 5 m/s5\ m/s then v2=v_2= __________ m/sm/s .
Not attempted
Your answer: —
Correct answer: 10
31
[JEE Main 2025, 29 Jan Shift 2, Q72] Two cars P and Q are moving on a road in the same direction. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time t = 0, for the first time. The maximum possible number of crossing(s) (including the crossing at t = 0) is ________.
Not attempted
Your answer: —
Correct answer: 3
32
[JEE Main 2025, 29 Jan Shift 1, Q58] Two projectiles are fired with same initial speed from same point on ground at angles of (45∘−α)({45}^{\circ}-\alpha ) and (45∘+α)({45}^{\circ}+\alpha ) , respectively, with the horizontal direction. The ratio of their maximum heights attained is :
Not attempted
A
1+sin⁡α1−sin⁡α\frac{1+\sin \alpha }{1-\sin \alpha }
B
1+sin⁡2α1−sin⁡2α\frac{1+\sin 2\alpha }{1-\sin 2\alpha }
C
1−tan⁡α1+tan⁡α\frac{1-\tan \alpha }{1+\tan \alpha }
D
1−sin⁡2α1+sin⁡2α\frac{1-\sin 2\alpha }{1+\sin 2\alpha }
33
[JEE Main 2025, 29 Jan Shift 1, Q68] The maximum speed of a boat in still water is 27 km/h. Now this boat is moving downstream in a river flowing at 9 km/h. A man in the boat throws a ball vertically upwards with speed of 10 m/s. Range of the ball as observed by an observer at rest on the bank is __________ cm. (Take g=10g=10 m/ s2)\mathrm{s}^{2}\mathrm{)}
Not attempted
Your answer: —
Correct answer: 2000
34
[JEE Main 2025, 28 Jan Shift 2, Q55] The velocity-time graph of an object moving along a straight line is shown in the figure. What is the distance covered by the object between t=0t=0 to t=4st=4s ?
Not attempted
A
11 m
B
30 m
C
13 m
D
10 m
35
[JEE Main 2025, 24 Jan Shift 2, Q67] The position vector of a moving body at any instant of time is given as r⃗=(5t2i^−5tj^)m\vec{r}=(5t^2\hat{i}-5t\hat{j})m . The magnitude and direction of velocity at t=2st=2s is,
Not attempted
A
517 m/s5\sqrt{17}\ m/s , making an angle of tan⁡−14{\tan}^{-1}4 with - ve Y axis
B
515 m/s5\sqrt{15}\ m/s , making an angle of tan⁡−14{\tan}^{-1}4 with + ve XX axis
C
517 m/s5\sqrt{17}\ m/s , making an angle of tan⁡−14{\tan}^{-1}4 with + ve XX axis
D
515 m/s5\sqrt{15}\ m/s , making an angle of tan⁡−14{\tan}^{-1}4 with −- ve YY axis
36
[JEE Main 2025, 23 Jan Shift 2, Q58] A ball having kinetic energy KE, is projected at an angle of 60∘{60}^{\circ} from the horizontal. What will be the kinetic energy of ball at the highest point of its flight?
Not attempted
A
(KE)2\frac{(\mathrm{KE})}{2}
B
(KE)8\frac{(\mathrm{KE})}{8}
C
(KE)4\frac{(\mathrm{KE})}{4}
D
(KE)16\frac{(\mathrm{KE})}{16}
37
[JEE Main 2025, 23 Jan Shift 1, Q67] The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is ̱_______ km .
Not attempted
A
12
B
6
C
3
D
9
38
[JEE Main 2025, 22 Jan Shift 2, Q68] A ball of mass 100 g is projected with velocity 20 m/s20 \mathrm{~m} / \mathrm{s} at 60∘60^{\circ} with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is
Not attempted
A
20 J
B
5 J
C
15 J
D
zero
39
[JEE Main 2025, 22 Jan Shift 1, Q74] A particle is projected at an angle of 30∘{30}^{\circ} from horizontal at a speed of 60 m/s60\ m/s . The height traversed by the particle in the first second is h0h_0 and height traversed in the last second, before it reaches the maximum height, is h1h_1 . The ratio h0:h1h_0:h_1 is __________. [Take, g=10 m/s2g=10\ m/s^2 ]
Not attempted
Your answer: —
Correct answer: 5
40
[JEE Main 2024, 9 Apr Shift 2, Q63] Two cars are travelling towards each other at speed of 20 m s−120\ m{\ s}^{-1} each. When the cars are 300 m300\ m apart, both the drivers apply brakes and the cars retard at the rate of 2 m s−22\ m{\ s}^{-2} . The distance between them when they come to rest is :
Not attempted
A
25 m
B
100 m
C
50 m
D
200 m
41
[JEE Main 2024, 9 Apr Shift 1, Q69] A particle moving in a straight line covers half the distance with speed 6 m/s6\ m/s . The other half is covered in two equal time intervals with speeds 9 m/s9\ m/s and 15 m/s15\ m/s respectively. The average speed of the particle during the motion is :
Not attempted
A
9.2 m/s
B
8.8 m/s
C
10 m/s
D
8 m/s
42
[JEE Main 2024, 8 Apr Shift 2, Q75] The angle of projection for a projectile to have same horizontal range and maximum height is :
Not attempted
A
tan⁡−1(12){\tan}^{-1}(\frac{1}{2})
B
tan⁡−1(2){\tan}^{-1}(2)
C
tan⁡−1(14){\tan}^{-1}(\frac{1}{4})
D
tan⁡−1(4){\tan}^{-1}(4)
43
[JEE Main 2024, 8 Apr Shift 2, Q90] A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a distance of 100 m100\ m from the foot of the tower. A body of mass 2 M2\ M thrown at a velocity v2\frac{v}{2} from the top of the tower of height 4H4H will touch the ground at a distance of _______ m.
Not attempted
Your answer: —
Correct answer: 100
44
[JEE Main 2024, 8 Apr Shift 1, Q66] A clock has 75 cm,60 cm75\ \mathrm{cm},60\ \mathrm{cm} long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel xx distance more than the tip of minute hand. The value of xx in meter is nearly (Take π=3.14\pi =3.14 ) :
Not attempted
A
118.9
B
140.5
C
139.4
D
220.0
45
[JEE Main 2024, 6 Apr Shift 2, Q61] A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in t1t_1 . If it is projected vertically downwards from the same point with the same speed, it reaches the ground in t2t_2 . Time required to reach the ground, if it is dropped from the top of the tower, is :
Not attempted
A
t1+t2\sqrt{t_1+t_2}
B
t1t2\sqrt{t_1t_2}
C
t1t2\sqrt{\frac{t_1}{t_2}}
D
t1−t2\sqrt{t_1-t_2}
46
[JEE Main 2024, 6 Apr Shift 2, Q85] A particle moves in a straight line so that its displacement xx at any time tt is given by x2=1+t2x^2=1+t^2 . Its acceleration at any time tt is x−nx^{-n} where n=n= _________.
Not attempted
Your answer: —
Correct answer: 3
47
[JEE Main 2024, 6 Apr Shift 1, Q78] A train starting from rest first accelerates uniformly up to a speed of 80 km/h80\ \mathrm{km}/h for time tt , then it moves with a constant speed for time 3t3t . The average speed of the train for this duration of journey will be (in km/h\mathrm{km}/h ) :
Not attempted
A
70
B
40
C
30
D
80
48
[JEE Main 2024, 5 Apr Shift 2, Q67] A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius 9 m9\ m and completes 120 resolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (in m/s2m/s^2 ) :
Not attempted
A
4π2 ms−24{\pi}^2{\ \mathrm{ms}}^{-2}
B
16π2 ms−216{\pi}^2{\ \mathrm{ms}}^{-2}
C
57600π2 ms−257600{\pi}^2{\ \mathrm{ms}}^{-2}
D
Zero
49
[JEE Main 2024, 5 Apr Shift 2, Q86] The maximum height reached by a projectile is 64 m64\ m . If the initial velocity is halved, the new maximum height of the projectile is ______ mm .
Not attempted
Your answer: —
Correct answer: 16
50
[JEE Main 2024, 5 Apr Shift 1, Q88] A body moves on a frictionless plane starting from rest. If SnS_n is distance moved between t=n−1t=n-1 and t=nt=n and Sn−1S_{n-1} is distance moved between t=n−2t=n-2 and t=n−1t=n-1 , then the ratio Sn−1 Sn\frac{S_{n-1}}{{\ S}_n} is (1−2x)(1-\frac{2}{x}) for n=10n=10 . The value of xx is __________.
Not attempted
Your answer: —
Correct answer: 19
51
[JEE Main 2024, 4 Apr Shift 2, Q71] A cyclist starts from the point PP of a circular ground of radius 2 km2\ \mathrm{km} and travels along its circumference to the point SS . The displacement of a cyclist is:
Not attempted
A
8\sqrt{8} km
B
4 km
C
6 km
D
8 km
52
[JEE Main 2024, 4 Apr Shift 2, Q83] A bus moving along a straight highway with speed of 72 km/h72\ \mathrm{km}/h is brought to halt within 4s4s after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is ________ mm .
Not attempted
Your answer: —
Correct answer: 40
53
[JEE Main 2024, 4 Apr Shift 1, Q69] A body travels 102.5 m102.5\ m in nth n^{\text{th }} second and 115.0 m115.0\ m in (n+2)th (n+2)^{\text{th }} second. The acceleration is :
Not attempted
A
6.25 m/s26.25\ m/s^2
B
5 m/s25\ m/s^2
C
12.5 m/s212.5\ m/s^2
D
9 m/s29\ m/s^2
54
[JEE Main 2024, 4 Apr Shift 1, Q71] The co-ordinates of a particle moving in xx - yy plane are given by : x=2+4t,y=3t+8t2x=2+4t,y=3t+8t^2 . The motion of the particle is :
Not attempted
A
uniform motion along a straight line.
B
non-uniformly accelerated.
C
uniformly accelerated having motion along a straight line.
D
uniformly accelerated having motion along a parabolic path.
55
[JEE Main 2024, 4 Apr Shift 1, Q87] Two forces Fˉ1{\bar{F}}_1 and Fˉ2{\bar{F}}_2 are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between F⃗1{\vec{F}}_1 and F⃗2{\vec{F}}_2 is cos⁡−1(1n){\cos}^{-1}(\frac{1}{n}) . The value of ∣n∣|n| is _______.
Not attempted
Your answer: —
Correct answer: 6
56
[JEE Main 2024, 1 Feb Shift 2, Q71] Train A is moving along two parallel rail tracks towards north with speed 72 km/h72\ \mathrm{km}/h and train B is moving towards south with speed 108 km/h108\ \mathrm{km}/h . Velocity of train B with respect to A and velocity of ground with respect to B are (in ms−1{\mathrm{ms}}^{-1} ):
Not attempted
A
-50 and -30
B
-50 and 30
C
-30 and 50
D
50 and -30
57
[JEE Main 2024, 1 Feb Shift 2, Q83] A particle initially at rest starts moving from reference point x=0x=0 along xx -axis, with velocity vv that varies as v=4x m/sv=4\sqrt{x}\ m/s . The acceleration of the particle is __________ ms−2{\mathrm{ms}}^{-2} .
Not attempted
Your answer: —
Correct answer: 8
58
[JEE Main 2024, 1 Feb Shift 1, Q78] A particle moving in a circle of radius RR with uniform speed takes time TT to complete one revolution. If this particle is projected with the same speed at an angle θ\theta to the horizontal, the maximum height attained by it is equal to 4R4R . The angle of projection θ\theta is then given by :
Not attempted
A
sin⁡−1[2gT2π2R]12{\sin}^{-1}{[\frac{2{\mathrm{gT}}^2}{{\pi}^2R}]}^{\frac{1}{2}}
B
sin⁡−1[π2R2gT2]12{\sin}^{-1}{[\frac{{\pi}^2R}{2{\mathrm{gT}}^2}]}^{\frac{1}{2}}
C
cos⁡−1[πR2gT2]12{\cos}^{-1}{[\frac{\pi R}{2{\mathrm{gT}}^2}]}^{\frac{1}{2}}
D
cos⁡−1[2gT2π2R]12{\cos}^{-1}{[\frac{2{\mathrm{gT}}^2}{{\pi}^2R}]}^{\frac{1}{2}}
59
[JEE Main 2024, 1 Feb Shift 1, Q84] A particle is moving in one dimension (along xx axis) under the action of a variable force. It's initial position was 16 m16\ m right of origin. The variation of its position (x)(x) with time (t)(t) is given as x=−3t3+18t2+16tx=-3t^3+18t^2+16t , where xx is in mm and tt is in ss . The velocity of the particle when its acceleration becomes zero is _________ m/sm/s .
Not attempted
Your answer: —
Correct answer: 52
60
[JEE Main 2024, 31 Jan Shift 2, Q67] If two vectors A⃗\vec{A} and B⃗\vec{B} having equal magnitude RR are inclined at angle θ\theta , then
Not attempted
A
∣A⃗+B⃗∣=2Rcos⁡(θ2)|\vec{A}+\vec{B}|=2R\cos (\frac{\theta }{2})
B
∣A⃗−B⃗∣=2Rcos⁡(θ2)|\vec{A}-\vec{B}|=2R\cos (\frac{\theta }{2})
C
∣A⃗−B⃗∣=2Rsin⁡(θ2)|\vec{A}-\vec{B}|=\sqrt{2}R\sin (\frac{\theta }{2})
D
∣A⃗+B⃗∣=2Rsin⁡(θ2)|\vec{A}+\vec{B}|=2R\sin (\frac{\theta }{2})
61
[JEE Main 2024, 31 Jan Shift 1, Q65] The relation between time ' tt ' and distance ' xx ' is t=αx2+βxt=\alpha x^2+\beta x , where α\alpha and β\beta are constants. The relation between acceleration (a)(a) and velocity (v)(v) is :
Not attempted
A
a=−5αv5a=-5\alpha v^5
B
a=−3αv2a=-3\alpha v^2
C
a=−2αv3a=-2\alpha v^3
D
a=−4αv4a=-4\alpha v^4
62
[JEE Main 2024, 31 Jan Shift 1, Q85] A body starts falling freely from height HH hits an inclined plane in its path at height hh . As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of Hh\frac{H}{h} for which the body will take the maximum time to reach the ground is __________.
Not attempted
Your answer: —
Correct answer: 2
63
[JEE Main 2024, 30 Jan Shift 1, Q88] The displacement and the increase in the velocity of a moving particle in the time interval of tt to (t+1)s(t+1)s are 125 m125\ m and 50 m/s50\ m/s , respectively. The distance travelled by the particle in (t+2)ths(t+2)^{\mathrm{th}}s is _________ m.
Not attempted
Your answer: —
Correct answer: 175
64
[JEE Main 2024, 29 Jan Shift 2, Q74] A particle is moving in a straight line. The variation of position ' xx ' as a function of time ' tt ' is given as x=(t3−6t2+20t+15)mx=(t^3-6t^2+20t+15)m . The velocity of the body when its acceleration becomes zero is :
Not attempted
A
6 m/s
B
10 m/s
C
8 m/s
D
4 m/s
65
[JEE Main 2024, 29 Jan Shift 2, Q88] A particle is moving in a circle of radius 50 cm50\ \mathrm{cm} in such a way that at any instant the normal and tangential components of it's acceleration are equal. If its speed at t=0t=0 is 4 m/s4\ m/s , the time taken to complete the first revolution will be 1α[1−e−2π]s\frac{1}{\alpha }[1-e^{-2\pi}]s , where α=\alpha = _________.
Not attempted
Your answer: —
Correct answer: 8
66
[JEE Main 2024, 29 Jan Shift 1, Q77] A body starts moving from rest with constant acceleration covers displacement S1S_1 in first (p−1)(p-1) seconds and S2S_2 in first pp seconds. The displacement S1+S2S_1+S_2 will be made in time :
Not attempted
A
(2p+1)s(2p+1)s
B
(2p−1)s(2p-1)s
C
(2p2−2p+1)s(2p^2-2p+1)s
D
(2p2−2p+1)s\sqrt{(2p^2-2p+1)}s
67
[JEE Main 2024, 29 Jan Shift 1, Q89] A ball rolls off the top of a stairway with horizontal velocity uu . The steps are 0.1 m0.1\ m high and 0.1 m0.1\ m wide. The minimum velocity uu with which that ball just hits the step 5 of the stairway will be x ms−1\sqrt{x}{\ \mathrm{ms}}^{-1} where x=x= __________ [use g=10 m/s2g=10\ m/s^2 ].
Not attempted
Your answer: —
Correct answer: 2
68
[JEE Main 2024, 27 Jan Shift 2, Q71] A bullet is fired into a fixed target looses one third of its velocity after travelling 4 cm4\ \mathrm{cm} . It penetrates further D×10−3 mD\times {10}^{-3}\ m before coming to rest. The value of DD is :
Not attempted
A
23
B
32
C
42
D
52
69
[JEE Main 2024, 27 Jan Shift 2, Q85] A body falling under gravity covers two points AA and BB separated by 80 m80\ m in 2 s2\ s . The distance of upper point A from the starting point is _________ mm (use g=10 ms−2g=10{\ \mathrm{ms}}^{-2} ).
Not attempted
Your answer: —
Correct answer: 45
70
[JEE Main 2024, 27 Jan Shift 1, Q61] Position of an ant ( SS in metres) moving in YY - ZZ plane is given by S=2t2j^+5k^S=2t^2\hat{j}+5\hat{k} (where tt is in second). The magnitude and direction of velocity of the ant at t=1 st=1\ s will be :
Not attempted
A
16 m/s16\ m/s in yy -direction
B
4 m/s4\ m/s in xx -direction
C
9 m/s9\ m/s in zz -direction
D
4 m/s4\ m/s in yy -direction
71
[JEE Main 2024, 27 Jan Shift 1, Q81] A particle starts from origin at t=0t=0 with a velocity 5i^ m/s5\hat{i}\ m/s and moves in x−yx-y plane under action of a force which produces a constant acceleration of (3i^+2j^)m/s2(3\hat{i}+2\hat{j})m/s^2 . If the xx -coordinate of the particle at that instant is 84 m84\ m , then the speed of the particle at this time is α m/s\sqrt{\alpha }\ m/s . The value of α\alpha is _________.
Not attempted
Your answer: —
Correct answer: 673
72
[JEE Main 2023, 15 Apr Shift 1, Q46] The position of a particle related to time is given by x=(5t2−4t+5)mx=(5t^2-4t+5)m . The magnitude of velocity of the particle at t=2st=2s will be :
Not attempted
A
14 ms−114{\ \mathrm{ms}}^{-1}
B
16 ms−116{\ \mathrm{ms}}^{-1}
C
10 ms−110{\ \mathrm{ms}}^{-1}
D
06 ms−106{\ \mathrm{ms}}^{-1}
73
[JEE Main 2023, 15 Apr Shift 1, Q55] A vector in x−yx-y plane makes an angle of 30∘{30}^{\circ} with yy -axis. The magnitude of yy -component of vector is 232\sqrt{3} . The magnitude of xx -component of the vector will be :
Not attempted
A
3\sqrt{3}
B
2
C
6
D
13\frac{1}{\sqrt{3}}
74
[JEE Main 2023, 13 Apr Shift 2, Q44] The distance travelled by an object in time tt is given by s=(2.5)t2s=(2.5)t^2 . The instantaneous speed of the object at t=5 st=5\ s will be:
Not attempted
A
5 ms−15{\ \mathrm{ms}}^{-1}
B
12.5 ms−112.5{\ \mathrm{ms}}^{-1}
C
62.5 ms−162.5{\ \mathrm{ms}}^{-1}
D
25 ms−125{\ \mathrm{ms}}^{-1}
75
[JEE Main 2023, 13 Apr Shift 2, Q61] A passenger sitting in a train A moving at 90 km/h90\ \mathrm{km}/h observes another train BB moving in the opposite direction for 8 s8\ s . If the velocity of the train B is 54 km/h54\ \mathrm{km}/h , then length of train B is:
Not attempted
A
80 m
B
200 m
C
120 m
D
320 m
76
[JEE Main 2023, 13 Apr Shift 1, Q57] Two trains 'A' and 'B' of length ' ll ' and ' 4l4l ' are travelling into a tunnel of length ' LL ' in parallel tracks from opposite directions with velocities 108 km/h108\ \mathrm{km}/h and 72 km/h72\ \mathrm{km}/h , respectively. If train 'A' takes 35 s35\ s less time than train 'B' to cross the tunnel then. length ' LL ' of tunnel is : (Given L=60lL=60l )
Not attempted
A
900 m
B
1200 m
C
1800 m
D
2700 m
77
[JEE Main 2023, 12 Apr Shift 1, Q56] A ball is thrown vertically upward with an initial velocity of 150 m/s150\ m/s . The ratio of velocity after 3 s3\ s and 5 s5\ s is x+1x\frac{x+1}{x} . The value of xx is ___________. { take, g=10 m/s2}\{\text{ take, }g=10\ m/s^2\}
Not attempted
A
−5-5
B
10
C
5
D
6
78
[JEE Main 2023, 11 Apr Shift 2, Q54] A projectile is projected at 30∘{30}^{\circ} from horizontal with initial velocity 40 ms−140{\ \mathrm{ms}}^{-1} . The velocity of the projectile at t=2 st=2\ s from the start will be : (Given g=10 m/s2g=10\ m/s^2 )
Not attempted
A
203 ms−120\sqrt{3}{\ \mathrm{ms}}^{-1}
B
Zero
C
20 ms−120{\ \mathrm{ms}}^{-1}
D
403 ms−140\sqrt{3}{\ \mathrm{ms}}^{-1}
79
[JEE Main 2023, 11 Apr Shift 2, Q57] When vector A⃗=2i^+3j^+2k^\vec{A}=2\hat{i}+3\hat{j}+2\hat{k} is subtracted from vector B⃗\vec{B} , it gives a vector equal to 2j^2\hat{j} . Then the magnitude of vector B⃗\vec{B} will be :
Not attempted
A
3
B
33\sqrt{33}
C
6\sqrt{6}
D
5\sqrt{5}
80
[JEE Main 2023, 11 Apr Shift 1, Q63] From the v−tv-t graph shown, the ratio of distance to displacement in 25 s25\ s of motion is:
Not attempted
A
1
B
35\frac{3}{5}
C
12\frac{1}{2}
D
53\frac{5}{3}
81
[JEE Main 2023, 11 Apr Shift 1, Q69] A projectile fired at 30∘{30}^{\circ} to the ground is observed to be at same height at time 3 s3\ s and 5 s5\ s after projection, during its flight. The speed of projection of the projectile is ___________ m s−1m\ s^{-1} . (Given g=10 ms−2g=10{\ \mathrm{ms}}^{-2} )
Not attempted
Your answer: —
Correct answer: 80
82
[JEE Main 2023, 10 Apr Shift 2, Q39] A person travels xx distance with velocity v1v_1 and then xx distance with velocity v2v_2 in the same direction. The average velocity of the person is vv , then the relation between v,v1v,v_1 and v2v_2 will be.
Not attempted
A
V=V1+V2\mathbf{V}={\mathbf{V}}_1+{\mathbf{V}}_2
B
V=v1+V22V=\frac{v_1+V_2}{2}
C
1v=1v1+1v2\frac{1}{v}=\frac{1}{v_1}+\frac{1}{v_2}
D
2 V=1v1+1v2\frac{2}{\ V}=\frac{1}{v_1}+\frac{1}{v_2}
83
[JEE Main 2023, 10 Apr Shift 2, Q45] Two projectiles are projected at 30∘{30}^{\circ} and 60∘{60}^{\circ} with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:
Not attempted
A
1:31:\sqrt{3}
B
3:1\sqrt{3}:1
C
1 : 3
D
2:32:\sqrt{3}
84
[JEE Main 2023, 10 Apr Shift 1, Q53] The range of the projectile projected at an angle of 15 ∘{}^{\circ} with horizontal is 50 m. If the projectile is projected with same velocity at an angle of 45 ∘{}^{\circ} with horizontal, then its range will be
Not attempted
A
50 2\sqrt{2} m
B
100 m
C
100 2\sqrt{2} m
D
50 m
85
[JEE Main 2023, 10 Apr Shift 1, Q59] The position-time graphs for two students A and B returning from the school to their homes are shown in figure. (A) A lives closer to the school (B) B lives closer to the school (C) A takes lesser time to reach home (D) A travels faster than B (E) B travels faster than A Choose the correct answer from the options given below :
Not attempted
A
(A), (C) and (D) only
B
(A) and (E) only
C
(A), (C) and (E) only
D
(B) and (E) only
86
[JEE Main 2023, 8 Apr Shift 2, Q47] Given below are two statements Statement I : Area under velocity- time graph gives the distance travelled by the body in a given time. Statement II : Area under acceleration- time graph is equal to the change in velocity- in the given time. In the light of given statements, choose the correct answer from the options given below.
Not attempted
A
Both Statement I and Statement II are False.
B
Both Statement I and Statement II are true.
C
Statement I is incorrect but Statement II is true.
D
Statement I is correct but Statement II is false.
87
[JEE Main 2023, 8 Apr Shift 2, Q55] The trajectory of projectile, projected from the ground is given by y=x−x220y=x-\frac{x^2}{20} . Where xx and yy are measured in meter. The maximum height attained by the projectile will be.
Not attempted
A
10 m
B
5 m
C
200 m
D
10 2\sqrt{2} m
88
[JEE Main 2023, 8 Apr Shift 1, Q56] Two forces having magnitude AA and A2\frac{A}{2} are perpendicular to each other. The magnitude of their resultant is:
Not attempted
A
5A2\frac{5A}{2}
B
5A4\frac{\sqrt{5}A}{4}
C
5A2\frac{\sqrt{5}A}{2}
D
5A22\frac{\sqrt{5}A^2}{2}
89
[JEE Main 2023, 8 Apr Shift 1, Q59] Two projectiles A and B are thrown with initial velocities of 40 m/s40\ m/s and 60 m/s60\ m/s at angles 30∘{30}^{\circ} and 60∘{60}^{\circ} with the horizontal respectively. The ratio of their ranges respectively is (g=10 m/s2)(g=10\ m/s^2)
Not attempted
A
4:94:9
B
2:32:\sqrt{3}
C
3:2\sqrt{3}:2
D
1:11:1
90
[JEE Main 2023, 6 Apr Shift 2, Q45] A particle starts with an initial velocity of 10.0 ms−110.0{\ \mathrm{ms}}^{-1} along xx -direction and accelerates uniformly at the rate of 2.0 ms−22.0{\ \mathrm{ms}}^{-2} . The time taken by the particle to reach the velocity of 60.0 ms−160.0{\ \mathrm{ms}}^{-1} is __________.
Not attempted
A
30s
B
6s
C
3s
D
25s
91
[JEE Main 2023, 6 Apr Shift 2, Q54] As shown in the figure, a particle is moving with constant speed π m/s\pi \ m/s . Considering its motion from AA to BB , the magnitude of the average velocity is :
Not attempted
A
π m/s\pi \ m/s
B
1.53 m/s1.5\sqrt{3}\ m/s
C
3 m/s\sqrt{3}\ m/s
D
23 m/s2\sqrt{3}\ m/s
92
[JEE Main 2023, 6 Apr Shift 1, Q43] A particle is moving with constant speed in a circular path. When the particle turns by an angle 90∘{90}^{\circ} , the ratio of instantaneous velocity to its average velocity is π:x2\pi :x\sqrt{2} . The value of xx will be -
Not attempted
A
1
B
7
C
5
D
2
93
[JEE Main 2023, 6 Apr Shift 1, Q46] Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R Assertion A : When a body is projected at an angle 45∘{45}^{\circ} , it's range is maximum. Reason R : For maximum range, the value of sin⁡2θ\sin 2\theta should be equal to one. In the light of the above statements, choose the correct answer from the options given below:
Not attempted
A
Both A\mathbf{A} and R\mathbf{R} are correct and R\mathbf{R} is the correct explanation of A\mathbf{A}
B
A\mathbf{A} is true but R\mathbf{R} is false
C
A\mathbf{A} is false but R\mathbf{R} is true
D
Both A\mathbf{A} and R\mathbf{R} are correct but R\mathbf{R} is NOT the correct explanation of A\mathbf{A}
94
[JEE Main 2023, 1 Feb Shift 2, Q59] For a body projected at an angle with the horizontal from the ground, choose the correct statement.
Not attempted
A
Gravitational potential energy is maximum at the highest point.
B
The vertical component of momentum is maximum at the highest point.
C
The horizontal component of velocity is zero at the highest point.
D
The Kinetic Energy (K.E.) is zero at the highest point of projectile motion.
95
[JEE Main 2023, 1 Feb Shift 2, Q72] For a train engine moving with speed of 20 ms−120{\ \mathrm{ms}}^{-1} , the driver must apply brakes at a distance of 500 mm before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed x ms−1\sqrt{x}{\ \mathrm{ms}}^{-1} . The value of xx is ____________. (Assuming same retardation is produced by brakes)
Not attempted
Your answer: —
Correct answer: 200
96
[JEE Main 2023, 1 Feb Shift 1, Q52] An object moves with speed v1,v2v_1,v_2 and v3v_3 along a line segment AB, BC and CD respectively as shown in figure. Where AB = BC and AD = 3AB, then average speed of the object will be:
Not attempted
A
v1v2v33(v1v2+v2v3+v3v1)\frac{v_1v_2v_3}{3(v_1v_2+v_2v_3+v_3v_1)}
B
(v1+v2+v3)3\frac{(v_1+v_2+v_3)}{3}
C
(v1+v2+v3)3v1v2v3\frac{(v_1+v_2+v_3)}{3v_1v_2v_3}
D
3v1v2v3(v1v2+v2v3+v3v1)\frac{3v_1v_2v_3}{(v_1v_2+v_2v_3+v_3v_1)}
97
[JEE Main 2023, 1 Feb Shift 1, Q53] A child stands on the edge of the cliff 10 m10\ m above the ground and throws a stone horizontally with an initial speed of 5 ms−15{\ \mathrm{ms}}^{-1} . Neglecting the air resistance, the speed with which the stone hits the ground will be ms−1{\mathrm{ms}}^{-1} (given, g=10 ms−2g=10{\ \mathrm{ms}}^{-2} ).
Not attempted
A
20
B
25
C
30
D
15
98
[JEE Main 2023, 31 Jan Shift 2, Q62] A body is moving with constant speed, in a circle of radius 10 m10\ m . The body completes one revolution in 4 s4\ s . At the end of 3rd second, the displacement of body (in mm ) from its starting point is :
Not attempted
A
15π15\pi
B
30
C
10210\sqrt{2}
D
5π5\pi
99
[JEE Main 2023, 31 Jan Shift 2, Q66] Two bodies are projected from ground with same speeds 40 ms−140{\ \mathrm{ms}}^{-1} at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of 60∘{60}^{\circ} , with horizontal then sum of the maximum heights, attained by the two projectiles, is mm . (Given g=10 ms−2g=10{\ \mathrm{ms}}^{-2} )
Not attempted
Your answer: —
Correct answer: 80
100
[JEE Main 2023, 31 Jan Shift 1, Q48] The initial speed of a projectile fired from ground is uu . At the highest point during its motion, the speed of projectile is 32u\frac{\sqrt{3}}{2}u . The time of flight of the projectile is :
Not attempted
A
ug\frac{u}{g}
B
2ug\frac{2u}{g}
C
u2g\frac{u}{2g}
D
3ug\frac{\sqrt{3}u}{g}
101
[JEE Main 2023, 31 Jan Shift 1, Q68] The speed of a swimmer is 4 km h−14\ \mathrm{km}{\ h}^{-1} in still water. If the swimmer makes his strokes normal to the flow of river of width 1 km1\ \mathrm{km} , he reaches a point 750 m750\ m down the stream on the opposite bank. The speed of the river water is ___________ km h−1\mathrm{km}\ h^{-1}
Not attempted
Your answer: —
Correct answer: 3
102
[JEE Main 2023, 30 Jan Shift 2, Q45] A vehicle travels 4 km4\ \mathrm{km} with speed of 3 km/h3\ \mathrm{km}/h and another 4 km4\ \mathrm{km} with speed of 5 km/h5\ \mathrm{km}/h , then its average speed is
Not attempted
A
3.75 km/h3.75\ \mathrm{km}/h
B
4.25 km/h4.25\ \mathrm{km}/h
C
3.50 km/h3.50\ \mathrm{km}/h
D
4.00 km/h4.00\ \mathrm{km}/h
103
[JEE Main 2023, 30 Jan Shift 2, Q70] A stone tied to 180 cm180\ \mathrm{cm} long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is 1936xms−2\frac{1936}{x}ms^{-2} . The value of xx ________. (Take π=227\pi =\frac{22}{7} )
Not attempted
Your answer: —
Correct answer: 125
104
[JEE Main 2023, 30 Jan Shift 1, Q55] Match Column-I with Column-II : Column-I (x-t graphs)Column-II (v-t graphs)A.graph A in figureI.graph I in figureB.graph B in figureII.graph II in figureC.graph C in figureIII.graph III in figureD.graph D in figureIV.graph IV in figure\displaystyle\begin{array}{|l|l|l|l|}\hline & \text{Column-I (} x \text{-t graphs)} & & \text{Column-II (} v \text{-t graphs)} \\ \hline \text{A.} & \text{graph A in figure} & \text{I.} & \text{graph I in figure} \\ \hline \text{B.} & \text{graph B in figure} & \text{II.} & \text{graph II in figure} \\ \hline \text{C.} & \text{graph C in figure} & \text{III.} & \text{graph III in figure} \\ \hline \text{D.} & \text{graph D in figure} & \text{IV.} & \text{graph IV in figure} \\ \hline \end{array} Choose the correct answer from the options given below:
Not attempted
A I B II C III D IV
A
A- II, B-III, C-IV, D-I
B
A- II, B-IV, C-III, D-I
C
A- I, B-III, C-IV, D-II
D
A- I, B-II, C-III, D-IV
105
[JEE Main 2023, 30 Jan Shift 1, Q64] A horse rider covers half the distance with 5 m/s5\ m/s speed. The remaining part of the distance was travelled with speed 10 m/s10\ m/s for half the time and with speed 15 m/s15\ m/s for other half of the time. The mean speed of the rider averaged over the whole time of motion is x7 m/s\frac{x}{7}\ m/s . The value of xx is ___________.
Not attempted
Your answer: —
Correct answer: 50
106
[JEE Main 2023, 29 Jan Shift 2, Q55] An object moves at a constant speed along a circular path in a horizontal plane with center at the origin. When the object is at x=+2 mx=+2\ m , its velocity is −4j^-4\hat{j} m/s. The object's velocity (v) and acceleration (a) at x=−2 mx=-2\ m will be
Not attempted
A
v=4i^ m/s,a=8j^ m/s2v=4\hat{i}\ m/s,a=8\hat{j}\ m/s^2
B
v=4j^ m/s,a=8i^ m/s2v=4\hat{j}\ m/s,a=8\hat{i}\ m/s^2
C
v=−4i^ m/s,a=−8j^ m/s2v=-4\hat{i}\ m/s,a=-8\hat{j}\ m/s^2
D
v=−4j^ m/s,a=8i^ m/s2v=-4\hat{j}\ m/s,a=8\hat{i}\ m/s^2
107
[JEE Main 2023, 29 Jan Shift 2, Q67] A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of 54 km/hr is t(1−e−π/2)st(1-e^{-\pi /2})s . The value of t is ____________.
Not attempted
Your answer: —
Correct answer: 40
108
[JEE Main 2023, 29 Jan Shift 1, Q55] A stone is projected at angle 30∘{30}^{\circ} to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be -
Not attempted
A
1 : 4
B
1 : 2
C
4 : 3
D
4 : 1
109
[JEE Main 2023, 29 Jan Shift 1, Q73] A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height 5.0 m. Ball comes in contact with the floor for 0.2s. The average acceleration during contact is ___________ ms −2{}^{-2} . (Given g = 10 ms −2{}^{-2} )
Not attempted
Your answer: —
Correct answer: 120
110
[JEE Main 2023, 25 Jan Shift 2, Q49] The distance travelled by a particle is related to time t as x=4t2x=4t^2 . The velocity of the particle at t=5s is :-
Not attempted
A
25 ms−125\ {\mathrm{ms}}^{-1}
B
20 ms−120\ {\mathrm{ms}}^{-1}
C
8 ms−18\ {\mathrm{ms}}^{-1}
D
40 ms−140\ {\mathrm{ms}}^{-1}
111
[JEE Main 2023, 25 Jan Shift 2, Q55] Two objects are projected with same velocity 'u' however at different angles α\alpha and β\beta with the horizontal. If α+β=90∘\alpha +\beta ={90}^{\circ} , the ratio of horizontal range of the first object to the 2nd object will be :
Not attempted
A
1 : 1
B
2 : 1
C
1 : 2
D
4 : 1
112
[JEE Main 2023, 25 Jan Shift 1, Q55] A car travels a distance of ' xx ' with speed v1v_1 and then same distance ' xx ' with speed v2v_2 in the same direction. The average speed of the car is :
Not attempted
A
v1v22(v1+v2)\frac{v_1v_2}{2(v_1+v_2)}
B
2v1v2v1+v2\frac{2v_1v_2}{v_1+v_2}
C
2xv1+v2\frac{2x}{v_1+v_2}
D
v1+v22\frac{v_1+v_2}{2}
113
[JEE Main 2023, 24 Jan Shift 2, Q46] The velocity time graph of a body moving in a straight line is shown in the figure. The ratio of displacement to distance travelled by the body in time 0 to 10s is :
Not attempted
A
1 : 1
B
1 : 3
C
1 : 4
D
1 : 2
114
[JEE Main 2023, 24 Jan Shift 1, Q58] The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is :
Not attempted
A
136 m
B
272 m
C
68 m
D
192 m
115
[JEE Main 2022, 29 July Shift 2, Q50] A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach is
Not attempted
A
g/2n
B
g/n
C
2gn
D
g/ 2n2\mathrm{2n}^{2}
116
[JEE Main 2022, 29 July Shift 2, Q55] A ball is released from a height h. If t1t_1 and t2t_2 be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between t1t_1 and t2t_2 .
Not attempted
A
t1=(2)t2t_1=(\sqrt{2})t_2
B
t1=(2−1)t2t_1=(\sqrt{2}-1)t_2
C
t2=(2+1)t1t_2=(\sqrt{2}+1)t_1
D
t2=(2−1)t1t_2=(\sqrt{2}-1)t_1
117
[JEE Main 2022, 29 July Shift 1, Q49] A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height h3\frac{h}{3} while going up and coming down respectively.
Not attempted
A
2−12+1\frac{\sqrt{2}-1}{\sqrt{2}+1}
B
3−23+2\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}
C
3−13+1\frac{\sqrt{3}-1}{\sqrt{3}+1}
D
13\frac{1}{3}
118
[JEE Main 2022, 29 July Shift 1, Q50] If t=x+4t=\sqrt{x}+4 , then (dx dt)t=4{(\frac{dx}{\ dt})}_{t=4} is :
Not attempted
A
4
B
zero
C
8
D
16
119
[JEE Main 2022, 29 July Shift 1, Q67] An object is projected in the air with initial velocity u at an angle θ\theta . The projectile motion is such that the horizontal range R, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be _________ degree.
Not attempted
Your answer: —
Correct answer: 15
120
[JEE Main 2022, 28 July Shift 2, Q41] At time t=0t=0 a particle starts travelling from a height 7z^ cm7\hat{z}\ \mathrm{cm} in a plane keeping z coordinate constant. At any instant of time it's position along the x^\hat{x} and y^\hat{y} directions are defined as 3t3t and 5t35t^3 respectively. At t = 1s acceleration of the particle will be
Not attempted
A
−30y^-30\hat{y}
B
30y^30\hat{y}
C
3x^+15y^3\hat{x}+15\hat{y}
D
3x^+15y^+7z^3\hat{x}+15\hat{y}+7\hat{z}
121
[JEE Main 2022, 28 July Shift 2, Q57] A ball is thrown vertically upwards with a velocity of 19.6 ms−119.6{\ \mathrm{ms}}^{-1} from the top of a tower. The ball strikes the ground after 6 s6\ s . The height from the ground up to which the ball can rise will be (k5)m(\frac{k}{5})m . The value of kk is __________. (use g=9.8 m/s2g=9.8\ m/s^2 )
Not attempted
Your answer: —
Correct answer: 392
122
[JEE Main 2022, 28 July Shift 1, Q48] A NCC parade is going at a uniform speed of 9 km/h9\ \mathrm{km}/h under a mango tree on which a monkey is sitting at a height of 19.6 m19.6\ m . At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is: (Given g=9.8 m/s2g=9.8\ m/s^2 )
Not attempted
A
5 m
B
10 m
C
19.8 m
D
24.5 m
123
[JEE Main 2022, 27 July Shift 2, Q42] A body of mass 10 kg10\ \mathrm{kg} is projected at an angle of 45∘{45}^{\circ} with the horizontal. The trajectory of the body is observed to pass through a point (20,10)(20,10) . If TT is the time of flight, then its momentum vector, at time t=T2t=\frac{T}{\sqrt{2}} , is _____________. [Take g=10 m/s2g=10\ m/s^2 ]
Not attempted
A
100i^+(1002−200)j^100\hat{i}+(100\sqrt{2}-200)\hat{j}
B
1002i^+(100−2002)j^100\sqrt{2}\hat{i}+(100-200\sqrt{2})\hat{j}
C
100i^+(100−2002)j^100\hat{i}+(100-200\sqrt{2})\hat{j}
D
1002i^+(1002−200)j^100\sqrt{2}\hat{i}+(100\sqrt{2}-200)\hat{j}
124
[JEE Main 2022, 27 July Shift 2, Q45] The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is :
Not attempted
A
2.0
B
1.0
C
0.5
D
1.5
125
[JEE Main 2022, 27 July Shift 2, Q65] Two inclined planes are placed as shown in figure. A block is projected from the Point A of inclined plane AB along its surface with a velocity just sufficient to carry it to the top Point B at a height 10 m. After reaching the Point B the block slides down on inclined plane BC. Time it takes to reach to the point C from point A is t(2+1)t(\sqrt{2}+1) s. The value of t is ___________. (use  g=10 m/s2\ g=10\ m/s^2 )
Not attempted
Your answer: —
Correct answer: 2
126
[JEE Main 2022, 27 July Shift 1, Q48] A bullet is shot vertically downwards with an initial velocity of 100 m/s100\ m/s from a certain height. Within 10 s, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time t=20 st=20\ s will be: (Take g = 10 m/ s2)\mathrm{s}^{2}\mathrm{)} .
Not attempted
A
(A)
B
(B)
C
(C)
D
(D)
127
[JEE Main 2022, 27 July Shift 1, Q72] A ball of mass m is thrown vertically upward. Another ball of mass 2 m2\ m is thrown at an angle θ\theta with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is 1x\frac{1}{x} . The value of x is _____________.
Not attempted
Your answer: —
Correct answer: 1
128
[JEE Main 2022, 26 July Shift 2, Q40] Two projectiles are thrown with same initial velocity making an angle of 45∘{45}^{\circ} and 30∘{30}^{\circ} with the horizontal respectively. The ratio of their respective ranges will be :
Not attempted
A
1:21:\sqrt{2}
B
2:1\sqrt{2}:1
C
2:32:\sqrt{3}
D
3:2\sqrt{3}:2
129
[JEE Main 2022, 26 July Shift 2, Q58] If A⃗=(2i^+3j^−k^)m\vec{A}=(2\hat{i}+3\hat{j}-\hat{k}) m and B⃗=(i^+2j^+2k^)m\vec{B}=(\hat{i}+2\hat{j}+2\hat{k}) m . The magnitude of component of vector A⃗\vec{A} along vector B⃗\vec{B} will be ____________ mm .
Not attempted
Your answer: —
Correct answer: 2
130
[JEE Main 2022, 26 July Shift 1, Q62] Two projectiles thrown at 30∘{30}^{\circ} and 45∘{45}^{\circ} with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is :
Not attempted
A
1:21:\sqrt{2}
B
2:12:1
C
2:1\sqrt{2}:1
D
1:21:2
131
[JEE Main 2022, 26 July Shift 1, Q64] If the initial velocity in horizontal direction of a projectile is unit vector i^\hat{i} and the equation of trajectory is y=5x(1−x)y=5x(1-x) . The yy component vector of the initial velocity is ______________ j^\hat{j} . ( Take\mathrm{Take} g=10 m/s2)g=10\ m/s^2)
Not attempted
Your answer: —
Correct answer: 5
132
[JEE Main 2022, 25 July Shift 2, Q60] A ball is projected from the ground with a speed 15 ms−1\mathrm{ms}^{-1} at an angle θ\theta with horizontal so that its range and maximum height are equal, then 'tan θ\theta ' will be equal to :
Not attempted
A
14\frac{1}{4}
B
12\frac{1}{2}
C
2
D
4
133
[JEE Main 2022, 25 July Shift 2, Q63] A particle is moving in a straight line such that its velocity is increasing at 5 ms−1\mathrm{ms}^{-1} per meter. The acceleration of the particle is _____________ ms−2\mathrm{ms}^{-2} at a point where its velocity is 20 ms−1\mathrm{ms}^{-1} .
Not attempted
Your answer: —
Correct answer: 100
134
[JEE Main 2022, 25 July Shift 1, Q43] A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is 60 m60\ m , then the magnitude of displacement would be : (Given cos⁡135∘=−0.7)\cos {135}^{\circ}=-0.7)
Not attempted
A
42 m
B
47 m
C
19 m
D
40 m
135
[JEE Main 2022, 25 July Shift 1, Q61] A car is moving with speed of 150 km/h150\ \mathrm{km}/h and after applying the break it will move 27 m27\ m before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling ___________ m distance.
Not attempted
Your answer: —
Correct answer: 3
136
[JEE Main 2022, 30 June Shift 1, Q42] At t = 0, truck, starting from rest, moves in the positive x-direction at uniform acceleration of 5 ms−2\mathrm{ms}^{-2} . At t = 20 s, a ball is released from the top of the truck. The ball strikes the ground in 1 s after the release. The velocity of the ball, when it strikes the ground, will be : (Given g = 10 ms−2)\mathrm{ms}^{-2}\mathrm{)}
Not attempted
A
100i^−10j^100\hat{i}-10\hat{j}
B
10i^−100j^10\hat{i}-100\hat{j}
C
100i^100\hat{i}
D
−10j^-10\hat{j}
137
[JEE Main 2022, 30 June Shift 1, Q45] Two projectiles P1\mathrm{P}_{1} and P2\mathrm{P}_{2} thrown with speed in the ratio 3\sqrt{3} : 2\sqrt{2} , attain the same height during their motion. If P2\mathrm{P}_{2} is thrown at an angle of 60 ∘{}^{\circ} with the horizontal, the angle of projection of P1\mathrm{P}_{1} with horizontal will be :
Not attempted
A
15 ∘{}^{\circ}
B
30 ∘{}^{\circ}
C
45 ∘{}^{\circ}
D
60 ∘{}^{\circ}
138
[JEE Main 2022, 30 June Shift 1, Q60] A person starts his journey from centre 'O' of the park and comes back to the same position following path OPQO as shown in the figure. The radius of path taken by the person is 200 m and he takes 3 min 58 sec to complete his journey. The average speed of the person is _____________ ms−1\mathrm{ms}^{-1} . (take π\pi = 3.14)
Not attempted
Your answer: —
Correct answer: 3
139
[JEE Main 2022, 29 June Shift 2, Q44] A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10m in t s, the distance travelled by the toy in the next t s will be :
Not attempted
A
10 m
B
20 m
C
30 m
D
40 m
140
[JEE Main 2022, 29 June Shift 2, Q61] A person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?
Not attempted
A
25 m
B
50 m
C
100 m
D
200 m
141
[JEE Main 2022, 29 June Shift 1, Q42] Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is thrown vertically down with an initial velocity 'u' at t = 2 s. After a certain time, both balls meet 100 m above the ground. Find the value of 'u' in ms−1\mathrm{ms}^{-1} . [use g = 10 ms−2]\mathrm{ms}^{-2}\mathrm{]} :
Not attempted
A
10
B
15
C
20
D
30
142
[JEE Main 2022, 29 June Shift 1, Q53] Two vectors A⃗\vec{A} and B⃗\vec{B} have equal magnitudes. If magnitude of A⃗\vec{A} + B⃗\vec{B} is equal to two times the magnitude of A⃗\vec{A} −- B⃗\vec{B} , then the angle between A⃗\vec{A} and B⃗\vec{B} will be :
Not attempted
A
sin⁡−1(35){\sin}^{-1}(\frac{3}{5})
B
sin⁡−1(13){\sin}^{-1}(\frac{1}{3})
C
cos⁡−1(35){\cos}^{-1}(\frac{3}{5})
D
cos⁡−1(13){\cos}^{-1}(\frac{1}{3})
143
[JEE Main 2022, 28 June Shift 2, Q77] A car covers AB distance with first one-third at velocity v1\mathrm{v}_{1} ms−1\mathrm{ms}^{-1} , second one-third at v2\mathrm{v}_{2} ms−1\mathrm{ms}^{-1} and last one-third at v3\mathrm{v}_{3} ms−1\mathrm{ms}^{-1} . If v3\mathrm{v}_{3} = 3v1\mathrm{3v}_{1} , v2\mathrm{v}_{2} = 2v1\mathrm{2v}_{1} and v1\mathrm{v}_{1} = 11 ms−1\mathrm{ms}^{-1} then the average velocity of the car is _____________ ms−1\mathrm{ms}^{-1} .
Not attempted
Your answer: —
Correct answer: 18
144
[JEE Main 2022, 28 June Shift 1, Q45] Motion of a particle in x-y plane is described by a set of following equations x=4sin⁡(π2−ωt)mx=4\sin (\frac{\pi }{2}-\omega t) m and y=4sin⁡(ωt)my=4\sin (\omega t) m . The path of the particle will be :
Not attempted
A
circular
B
helical
C
parabolic
D
elliptical
145
[JEE Main 2022, 27 June Shift 2, Q47] When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :
Not attempted
A
19.6 m
B
29.4 m
C
39.2 m
D
73.5 m
146
[JEE Main 2022, 27 June Shift 1, Q42] A projectile is launched at an angle ' α\alpha ' with the horizontal with a velocity 20 ms−1\mathrm{ms}^{-1} . After 10 s, its inclination with horizontal is ' β\beta '. The value of tan β\beta will be : (g = 10 ms−2)\mathrm{ms}^{-2}\mathrm{)} .
Not attempted
A
tan α\alpha + 5sec α\alpha
B
tan α\alpha −- 5sec α\alpha
C
2tan α\alpha −- 5sec α\alpha
D
2tan α\alpha ++ 5sec α\alpha
147
[JEE Main 2022, 27 June Shift 1, Q43] A girl standing on road holds her umbrella at 45 ∘{}^{\circ} with the vertical to keep the rain away. If she starts running without umbrella with a speed of 15 2\sqrt{2} kmh−1\mathrm{kmh}^{-1} , the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is :
Not attempted
A
30 kmh−1\mathrm{kmh}^{-1}
B
252\frac{25}{\sqrt{2}} kmh−1\mathrm{kmh}^{-1}
C
302\frac{30}{\sqrt{2}} kmh−1\mathrm{kmh}^{-1}
D
25 kmh−1\mathrm{kmh}^{-1}
148
[JEE Main 2022, 26 June Shift 2, Q64] A ball is projected vertically upward with an initial velocity of 50 ms−1\mathrm{ms}^{-1} at t = 0s. At t = 2s, another ball is projected vertically upward with same velocity. At t = __________ s, second ball will meet the first ball (g = 10 ms−2)\mathrm{ms}^{-2}\mathrm{)} .
Not attempted
Your answer: —
Correct answer: 6
149
[JEE Main 2022, 26 June Shift 1, Q44] An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?
Not attempted
A
Momentum
B
Potential Energy
C
Acceleration
D
Force
150
[JEE Main 2022, 26 June Shift 1, Q59] A fighter jet is flying horizontally at a certain altitude with a speed of 200 ms−1\mathrm{ms}^{-1} . When it passes directly overhead an anti-aircraft gun, a bullet is fired from the gun, at an angle θ\theta with the horizontal, to hit the jet. If the bullet speed is 400 m/s, the value of θ\theta will be ___________ ∘{}^{\circ} .
Not attempted
Your answer: —
Correct answer: 60
151
[JEE Main 2022, 26 June Shift 1, Q60] A ball of mass 0.5 kg is dropped from the height of 10 m. The height, at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity, is ________ m. [Use g = 10 m/ s2]\mathrm{s}^{2}\mathrm{]}
Not attempted
Your answer: —
Correct answer: 5
152
[JEE Main 2022, 25 June Shift 2, Q46] Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Two identical balls A and B thrown with same velocity 'u' at two different angles with horizontal attained the same range R. IF A and B reached the maximum height h1\mathrm{h}_{1} and h2\mathrm{h}_{2} respectively, then R=4h1h2R=4\sqrt{h_1h_2} Reason R : Product of said heights. h1h2=(u2sin⁡2θ2g).(u2cos⁡2θ2g)h_1h_2=(\frac{u^2{\sin}^2\theta }{2g}) . (\frac{u^2{\cos}^2\theta }{2g}) Choose the correct answer :
Not attempted
A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is NOT the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.
153
[JEE Main 2022, 25 June Shift 2, Q47] Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by XP(t)=αt+βt2X_P(t)=\alpha t+\beta t^2 and XQ(t)=ft−t2X_Q(t)=ft-t^2 . At what time, both the buses have same velocity?
Not attempted
A
α−f1+β\frac{\alpha -f}{1+\beta }
B
α+f2(β−1)\frac{\alpha +f}{2(\beta -1)}
C
α+f2(1+β)\frac{\alpha +f}{2(1+\beta )}
D
f−α2(1+β)\frac{f-\alpha }{2(1+\beta )}
154
[JEE Main 2022, 25 June Shift 2, Q52] For a particle in uniform circular motion, the acceleration a⃗\vec{a} at any point P(R, θ\theta ) on the circular path of radius R is (when θ\theta is measured from the positive x-axis and v is uniform speed) :
Not attempted
A
−v2Rsin⁡θi^+v2Rcos⁡θj^-\frac{v^2}{R}\sin \theta \hat{i}+\frac{v^2}{R}\cos \theta \hat{j}
B
−v2Rcos⁡θi^+v2Rsin⁡θj^-\frac{v^2}{R}\cos \theta \hat{i}+\frac{v^2}{R}\sin \theta \hat{j}
C
−v2Rcos⁡θi^−v2Rsin⁡θj^-\frac{v^2}{R}\cos \theta \hat{i}-\frac{v^2}{R}\sin \theta \hat{j}
D
−v2Ri^+v2Rj^-\frac{v^2}{R}\hat{i}+\frac{v^2}{R}\hat{j}
155
[JEE Main 2022, 25 June Shift 1, Q45] A⃗\vec{A} is a vector quantity such that ∣A⃗∣|\vec{A}| = non-zero constant. Which of the following expression is true for A⃗\vec{A} ?
Not attempted
A
A⃗.A⃗=0\vec{A} . \vec{A}=0
B
A⃗×A⃗<0\vec{A}\times \vec{A}<0
C
A⃗×A⃗=0\vec{A}\times \vec{A}=0
D
A⃗×A⃗>0\vec{A}\times \vec{A}>0
156
[JEE Main 2022, 25 June Shift 1, Q46] Which of the following relations is true for two unit vector A^\hat{A} and B^\hat{B} making an angle θ\theta to each other?
Not attempted
A
∣A^+B^∣=∣A^−B^∣tan⁡θ2|\hat{A}+\hat{B}|=|\hat{A}-\hat{B}|\tan \frac{\theta }{2}
B
∣A^−B^∣=∣A^+B^∣tan⁡θ2|\hat{A}-\hat{B}|=|\hat{A}+\hat{B}|\tan \frac{\theta }{2}
C
∣A^+B^∣=∣A^−B^∣cosθ2|\hat{A}+\hat{B}|=|\hat{A}-\hat{B}|cos\frac{\theta }{2}
D
∣A^−B^∣=∣A^+B^∣cos⁡θ2|\hat{A}-\hat{B}|=|\hat{A}+\hat{B}|\cos \frac{\theta }{2}
157
[JEE Main 2022, 24 June Shift 2, Q56] An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to : [Use g = 10 ms−2]\mathrm{ms}^{-2}\mathrm{]} .
Not attempted
A
1 : 1
B
2\sqrt{2} : 3\sqrt{3}
C
3\sqrt{3} : 2\sqrt{2}
D
2 : 3
158
[JEE Main 2022, 24 June Shift 2, Q65] A body is projected from the ground at an angle of 45 ∘{}^{\circ} with the horizontal. Its velocity after 2s is 20 ms−1\mathrm{ms}^{-1} . The maximum height reached by the body during its motion is __________ m. (use g = 10 ms−2)\mathrm{ms}^{-2}\mathrm{)}
Not attempted
Your answer: —
Correct answer: 20
159
[JEE Main 2022, 24 June Shift 1, Q48] A projectile is projected with velocity of 25 m/s at an angle θ\theta with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of θ\theta will be : [use g = 10 m/ s2]\mathrm{s}^{2}\mathrm{]}
Not attempted
A
12sin⁡−1(5t24R)\frac{1}{2}{\sin}^{-1}(\frac{5t^2}{4R})
B
12sin⁡−1(4R5t2)\frac{1}{2}{\sin}^{-1}(\frac{4R}{5t^2})
C
tan⁡−1(4t25R){\tan}^{-1}(\frac{4t^2}{5R})
D
cot⁡−1(R20t2){\cot}^{-1}(\frac{R}{20t^2})
160
[JEE Main 2022, 24 June Shift 1, Q67] From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s. A second ball thrown vertically downward from the same position with the same speed reaches the ground in 1.5 s. A third ball released, from the rest from the same location, will reach the ground in ____________ s.
Not attempted
Your answer: —
Correct answer: 3
161
[JEE Main 2021, 1 September Shift 2, Q5] The ranges and heights for two projectiles projected with the same initial velocity at angles 42∘42^\circ and 48∘48^\circ with the horizontal are R1R_1, R2R_2 and H1H_1, H2H_2 respectively. Choose the correct option :
Not attempted
A
R1>R2R_1>R_2 and H1=H2H_1=H_2
B
R1=R2R_1=R_2 and H1<H2H_1<H_2
C
R1<R2R_1<R_2 and H1<H2H_1<H_2
D
R1=R2R_1=R_2 and H1=H2H_1=H_2
162
[JEE Main 2021, 31 August Shift 2, Q4] Statement I\textbf{Statement I} : Two forces (P⃗+Q⃗)(\vec P+\vec Q) and (P⃗−Q⃗)(\vec P-\vec Q) where P⃗⊥Q⃗\vec P\perp\vec Q, when act at an angle θ1\theta_1 to each other, the magnitude of their resultant is 3(P2+Q2)\sqrt{3(P^2+Q^2)}, when they act at an angle θ2\theta_2, the magnitude of their resultant becomes 2(P2+Q2)\sqrt{2(P^2+Q^2)}. This is possible only when θ1<θ2\theta_1<\theta_2. Statement II\textbf{Statement II} : In the situation given above. θ1=60∘\theta_1=60^\circ and θ2=90∘\theta_2=90^\circ In the light of the above statements, choose the most appropriate answer from the options given below :-
Not attempted
A
Statement-I is false but Statement-II is true
B
Both Statement-I and Statement-II are true
C
Statement-I is true but Statement-II is false
D
Both Statement-I and Statement-II are false.
163
[JEE Main 2021, 31 August Shift 2, Q24] A particle is moving with constant acceleration 'a'. Following graph shows v2v^2 versus x(displacement) plot. The acceleration of the particle is___m/s2^2.
Not attempted
1020300x (m)20406080v² (m²/s²)ABC
Your answer: —
Correct answer: 1
164
[JEE Main 2021, 31 August Shift 1, Q1] A helicopter is flying horizontally with a speed ′v′'v' at an altitude ′h′'h' has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?
Not attempted
A
2ghv2+1h2\sqrt{\dfrac{2ghv^2+1}{h^2}}
B
2ghv2+h2\sqrt{2ghv^2+h^2}
C
2v2hg+h2\sqrt{\dfrac{2v^2h}{g}+h^2}
D
2ghv2+h2\sqrt{\dfrac{2gh}{v^2}+h^2}
165
[JEE Main 2021, 27 August Shift 2, Q4] Water drops are falling from a nozzle of a shower onto the floor, from a height of 9.8 m9.8\ \text{m}. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor.
Not attempted
A
4.18 m4.18\ \text{m}
B
2.94 m2.94\ \text{m}
C
2.45 m2.45\ \text{m}
D
7.35 m7.35\ \text{m}
166
[JEE Main 2021, 27 August Shift 2, Q18] A player kicks a football with an initial speed of 25 ms−125\ \text{ms}^{-1} at an angle of 45∘45^\circ from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take g=10 ms−2g=10\ \text{ms}^{-2})
Not attempted
A
hmax=10 mT=2.5 sh_{max}=10\ \text{m}\quad T=2.5\ \text{s}
B
hmax=15.625 mT=3.54 sh_{max}=15.625\ \text{m}\quad T=3.54\ \text{s}
C
hmax=15.625 mT=1.77 sh_{max}=15.625\ \text{m}\quad T=1.77\ \text{s}
D
hmax=3.54 mT=0.125 sh_{max}=3.54\ \text{m}\quad T=0.125\ \text{s}
167
[JEE Main 2021, 27 August Shift 1, Q5] The resultant of these forces OP→\overrightarrow{OP}, OQ→\overrightarrow{OQ}, OR→\overrightarrow{OR}, OS→\overrightarrow{OS} and OT→\overrightarrow{OT} is approximately ...... N. [Take 3=1.7\sqrt3=1.7, 2=1.4\sqrt2=1.4 Given i^\hat i and j^\hat j unit vectors along xx, yy axis]
Not attempted
xx'yy'P 20 NQ 10 NR 20 NS 15 NT 15 N30°30°60°45°45°O
A
9.25i^+5j^9.25\hat i+5\hat j
B
3i^+15j^3\hat i+15\hat j
C
2.5i^−14.5j^2.5\hat i-14.5\hat j
D
−1.5i^−15.5j^-1.5\hat i-15.5\hat j
168
[JEE Main 2021, 27 August Shift 1, Q8] A huge circular arc of length 4.44.4 ly subtends an angle '4s4s' at the centre of the circle. How long it would take for a body to complete 44 revolution if its speed is 88 AU per second ? Given : 1 ly=9.46×10151\ \text{ly}=9.46\times10^{15} m, 1 AU=1.5×10111\ \text{AU}=1.5\times10^{11} m
Not attempted
A
4.1×108 s4.1\times10^{8}\ \text{s}
B
4.5×1010 s4.5\times10^{10}\ \text{s}
C
3.5×106 s3.5\times10^{6}\ \text{s}
D
7.2×108 s7.2\times10^{8}\ \text{s}
169
[JEE Main 2021, 27 August Shift 1, Q27] If the velocity of a body related to displacement xx is given by υ=5000+24x\upsilon=\sqrt{5000+24x} m/s, then the acceleration of the body is ...... m/s2\text{m/s}^2.
Not attempted
Your answer: —
Correct answer: 12
170
[JEE Main 2021, 26 August Shift 2, Q5] The angle between vector (A⃗)(\vec A) and (A⃗−B⃗)(\vec A-\vec B) is :
Not attempted
AB-BA-B120°Oβ
A
tan⁡−1(−B/2A−B3/2)\tan^{-1}\left(\dfrac{-B/2}{A-B\sqrt3/2}\right)
B
tan⁡−1(A0.7B)\tan^{-1}\left(\dfrac{A}{0.7B}\right)
C
tan⁡−1(3B2A−B)\tan^{-1}\left(\dfrac{\sqrt3B}{2A-B}\right)
D
tan⁡−1(Bcos⁡θA−Bsin⁡θ)\tan^{-1}\left(\dfrac{B\cos\theta}{A-B\sin\theta}\right)
171
[JEE Main 2021, 26 August Shift 2, Q11] A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :
Not attempted
A
hyperbola
B
parabola in the direction of motion of plane
C
straight line vertically down the plane
D
parabola in a direction opposite to the motion of plane
172
[JEE Main 2021, 26 August Shift 1, Q2] The magnitudes of vectors OA→\overrightarrow{OA}, OB→\overrightarrow{OB} and OC→\overrightarrow{OC} in the given figure are equal. The direction of OA→+OB→−OC→\overrightarrow{OA}+\overrightarrow{OB}-\overrightarrow{OC} with the xx-axis will be :
Not attempted
xyABC30°60°45°O
A
tan⁡−1(1−3−2)(1+3+2)\tan^{-1}\dfrac{(1-\sqrt3-\sqrt2)}{(1+\sqrt3+\sqrt2)}
B
tan⁡−1(3−1+2)(1+3−2)\tan^{-1}\dfrac{(\sqrt3-1+\sqrt2)}{(1+\sqrt3-\sqrt2)}
C
tan⁡−1(3−1+2)(1−3+2)\tan^{-1}\dfrac{(\sqrt3-1+\sqrt2)}{(1-\sqrt3+\sqrt2)}
D
tan⁡−1(1+3−2)(1−3−2)\tan^{-1}\dfrac{(1+\sqrt3-\sqrt2)}{(1-\sqrt3-\sqrt2)}
173
[JEE Main 2021, 26 August Shift 1, Q24] Two spherical balls having equal masses with radius of 5 cm5\ \text{cm} each are thrown upwards along the same vertical direction at an interval of 3 s3\ \text{s} with the same initial velocity of 35 m s−135\ \text{m s}^{-1}, then these balls collide at a height of .......... m. (Take g=10 m s−2g=10\ \text{m s}^{-2})
Not attempted
Your answer: —
Correct answer: 50
174
[JEE Main 2021, 27 July Shift 2, Q21] A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30∘30^\circ with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle θ\theta with the line AB should be ________ ∘^\circ, so that the swimmer reaches point B.
Not attempted
AB30°θ
Your answer: —
Correct answer: 30
175
[JEE Main 2021, 27 July Shift 1, Q10] Assertion A : If A, B, C, D are four points on a semi-circular arc with centre at O such that ∣AB→∣=∣BC→∣=∣CD→∣|\overrightarrow{AB}|=|\overrightarrow{BC}|=|\overrightarrow{CD}|, then AB→+AC→+AD→=4AO→+OB→+OC→\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{AD}=4\overrightarrow{AO}+\overrightarrow{OB}+\overrightarrow{OC}. Reason R : Polygon law of vector addition yields AB→+BC→+CD→=AD→=2AO→\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD}=\overrightarrow{AD}=2\overrightarrow{AO}. In the light of the above statements, choose the most appropriate answer from the options given below :
Not attempted
BCADO
A
A\textbf{A} is not correct but R\textbf{R} is correct.
B
A\textbf{A} is correct but R\textbf{R} is not correct.
C
Both A\textbf{A} and R\textbf{R} are correct and R\textbf{R} is the correct explanation of A\textbf{A}.
D
Both A\textbf{A} and R\textbf{R} are correct but R\textbf{R} is not the correct explanation of A\textbf{A}.
176
[JEE Main 2021, 27 July Shift 1, Q17] A ball is thrown up with a certain velocity so that it reaches a height hh. Find the ratio of the two different times of the ball reaching h3\dfrac h3 in both the directions.
Not attempted
A
2−12+1\dfrac{\sqrt2-1}{\sqrt2+1}
B
3−23+2\dfrac{\sqrt3-\sqrt2}{\sqrt3+\sqrt2}
C
3−13+1\dfrac{\sqrt3-1}{\sqrt3+1}
D
13\dfrac13
177
[JEE Main 2021, 25 July Shift 2, Q3] A balloon was moving upwards with a uniform velocity of 1010 m/s. An object of finite mass is dropped from the balloon when it was at a height of 7575 m from the ground level. The height of the balloon from the ground when object strikes the ground was around : (takes the value of gg as 10 m/s210\ \mathrm{m/s^2})
Not attempted
A
250250 m
B
300300 m
C
200200 m
D
125125 m
178
[JEE Main 2021, 25 July Shift 2, Q5] Two vectors X⃗\vec X and Y⃗\vec Y have equal magnitude. The magnitude of (X⃗−Y⃗)(\vec X-\vec Y) is nn times the magnitude of (X⃗+Y⃗)(\vec X+\vec Y). The angle between X⃗\vec X and Y⃗\vec Y is :
Not attempted
A
cos⁡−1(n2+1n2−1)\cos^{-1}\left(\dfrac{n^2+1}{n^2-1}\right)
B
cos⁡−1(−n2−1n2−1)\cos^{-1}\left(\dfrac{-n^2-1}{n^2-1}\right)
C
cos⁡−1(n2−1−n2−1)\cos^{-1}\left(\dfrac{n^2-1}{-n^2-1}\right)
D
cos⁡−1(n2+1−n2−1)\cos^{-1}\left(\dfrac{n^2+1}{-n^2-1}\right)
179
[JEE Main 2021, 25 July Shift 2, Q8] The relation between time tt and distance xx for a moving body is given as t=mx2+nxt=mx^2+nx, where mm and nn are constants. The retardation of the motion is : (Where vv stands for velocity)
Not attempted
A
2n2v22n^2v^2
B
2mnv32mnv^3
C
2mv32mv^3
D
2nv32nv^3
180
[JEE Main 2021, 25 July Shift 2, Q16] The instantaneous velocity of a particle moving in a straight line is given as v=αt+βt2v=\alpha t+\beta t^2, where α\alpha and β\beta are constants. The distance travelled by the particle between 11 s and 22 s is :
Not attempted
A
α2+β3\dfrac{\alpha}{2}+\dfrac{\beta}{3}
B
32α+73β\dfrac32\alpha+\dfrac73\beta
C
32α+72β\dfrac32\alpha+\dfrac72\beta
D
3α+7β3\alpha+7\beta
181
[JEE Main 2021, 25 July Shift 1, Q2] Match List I with List II. List IList II(a) C⃗−A⃗−B⃗=0(i) vector diagram (i) in the figure(b) A⃗−C⃗−B⃗=0(ii) vector diagram (ii) in the figure(c) B⃗−A⃗−C⃗=0(iii) vector diagram (iii) in the figure(d) A⃗+B⃗=−C⃗(iv) vector diagram (iv) in the figure\displaystyle\begin{array}{ll}\textbf{List I} & \textbf{List II} \\ \text{(a) } \vec{C}-\vec{A}-\vec{B}=0 & \text{(i) vector diagram (i) in the figure} \\ \text{(b) } \vec{A}-\vec{C}-\vec{B}=0 & \text{(ii) vector diagram (ii) in the figure} \\ \text{(c) } \vec{B}-\vec{A}-\vec{C}=0 & \text{(iii) vector diagram (iii) in the figure} \\ \text{(d) } \vec{A}+\vec{B}=-\vec{C} & \text{(iv) vector diagram (iv) in the figure}\end{array} Choose the correct answer from the options given below :
Not attempted
(i)ACB(ii)ABC(iii)CAB(iv)ABC
A
(a)→(iv), (b)→(i), (c)→(iii), (d)→(ii)(a)\to(iv),\ (b)\to(i),\ (c)\to(iii),\ (d)\to(ii)
B
(a)→(iv), (b)→(iii), (c)→(i), (d)→(ii)(a)\to(iv),\ (b)\to(iii),\ (c)\to(i),\ (d)\to(ii)
C
(a)→(i), (b)→(iv), (c)→(ii), (d)→(iii)(a)\to(i),\ (b)\to(iv),\ (c)\to(ii),\ (d)\to(iii)
D
(a)→(iii), (b)→(ii), (c)→(iv), (d)→(i)(a)\to(iii),\ (b)\to(ii),\ (c)\to(iv),\ (d)\to(i)
182
[JEE Main 2021, 25 July Shift 1, Q8] Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at 4th4^{th} second after its fall to the next droplet is 34.334.3 m. At what rate the droplets are coming from the tap ? (Take g=9.8g=9.8 m/s2^2)
Not attempted
A
11 drop / 77 seconds
B
33 drops / 22 seconds
C
11 drop / second
D
22 drops / second
183
[JEE Main 2021, 22 July Shift 2, Q3] What will be the projection of vector A⃗=i^+j^+k^\vec{A}=\hat{i}+\hat{j}+\hat{k} on vector B⃗=i^+j^\vec{B}=\hat{i}+\hat{j} ?
Not attempted
A
2(i^+j^+k^)2(\hat{i}+\hat{j}+\hat{k})
B
2(i^+j^)\sqrt{2}(\hat{i}+\hat{j})
C
(i^+j^)(\hat{i}+\hat{j})
D
2(i^+j^+k^)\sqrt{2}(\hat{i}+\hat{j}+\hat{k})
184
[JEE Main 2021, 22 July Shift 2, Q30] Three particles PP, QQ and RR are moving along the vectors A⃗=i^+j^\vec A=\hat i+\hat j, B⃗=j^+k^\vec B=\hat j+\hat k and C⃗=−i^+j^\vec C=-\hat i+\hat j respectively. They strike on a point and start to move in different directions. Now particle PP is moving normal to the plane which contains vectors A⃗\vec A and B⃗\vec B. Similarly particle QQ is moving normal to the plane which contains vectors A⃗\vec A and C⃗\vec C. The angle between the direction of motion of PP and QQ is cos⁡−1(1x)\cos^{-1}\left(\frac{1}{\sqrt x}\right). Then the value of xx is _________.
Not attempted
Your answer: —
Correct answer: 3
185
[JEE Main 2021, 20 July Shift 2, Q6] Two vectors P⃗\vec{P} and Q⃗\vec{Q} have equal magnitudes. If the magnitude of P⃗+Q⃗\vec{P}+\vec{Q} is nn times the magnitude of P⃗−Q⃗\vec{P}-\vec{Q}, then angle between P⃗\vec{P} and Q⃗\vec{Q} is :
Not attempted
A
sin⁡−1(n2−1n2+1)\sin^{-1}\left(\frac{n^2-1}{n^2+1}\right)
B
cos⁡−1(n2−1n2+1)\cos^{-1}\left(\frac{n^2-1}{n^2+1}\right)
C
sin⁡−1(n−1n+1)\sin^{-1}\left(\frac{n-1}{n+1}\right)
D
cos⁡−1(n−1n+1)\cos^{-1}\left(\frac{n-1}{n+1}\right)
186
[JEE Main 2021, 20 July Shift 2, Q7] A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time t1t_1. If he remains stationary on a moving escalator then the escalator takes him up in time t2t_2. The time taken by him to walk up on the moving escalator will be :
Not attempted
A
t1t2t2+t1\frac{t_1t_2}{t_2+t_1}
B
t2−t1t_2-t_1
C
t1+t22\frac{t_1+t_2}{2}
D
t1t2t2−t1\frac{t_1t_2}{t_2-t_1}
187
[JEE Main 2021, 20 July Shift 1, Q3] If A⃗\vec{A} and B⃗\vec{B} are two vectors satisfying the relation A⃗⋅B⃗=∣A⃗×B⃗∣\vec{A}\cdot\vec{B}=\left|\vec{A}\times\vec{B}\right|. Then the value of ∣A⃗−B⃗∣\left|\vec{A}-\vec{B}\right| will be :
Not attempted
A
A2+B2−2AB\sqrt{A^2+B^2-\sqrt{2}AB}
B
A2+B2\sqrt{A^2+B^2}
C
A2+B2+2AB\sqrt{A^2+B^2+2AB}
D
A2+B2+2AB\sqrt{A^2+B^2+\sqrt{2}AB}
188
[JEE Main 2021, 20 July Shift 1, Q17] A butterfly is flying with a velocity 424\sqrt{2} m/s in North-East direction. Wind is slowly blowing at 11 m/s from North to South. The resultant displacement of the butterfly in 33 seconds is :
Not attempted
A
1515 m
B
2020 m
C
33 m
D
12212\sqrt{2} m
189
[JEE Main 2021, 18 March Shift 2, Q14] The velocity - displacement graph of a particle is shown in the figure. The acceleration - displacement graph of the same particle is represented by :
Not attempted
xvv₀x₀O
A
(a)
xaO
B
(b)
xaO
C
(c)
xaO
D
(d)
xaO
190
[JEE Main 2021, 18 March Shift 2, Q27] The projectile motion of a particle of mass 55 g is shown in the figure. The initial velocity of the particle is 52 ms−15\sqrt2\ \text{ms}^{-1} and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points AA and BB is x×10−2 kgms−1x\times10^{-2}\ \text{kgms}^{-1}. The value of xx, to the nearest integer, is ______.
Not attempted
v₀45°45°AB
Your answer: —
Correct answer: 5
191
[JEE Main 2021, 18 March Shift 1, Q20] The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by :
Not attempted
A
Figure (a)
tPositionx(t)tVelocityυ(t)tAccelerationa(t)
B
Figure (b)
tPositionx(t)tVelocityυ(t)tAccelerationa(t)
C
Figure (c)
tPositionx(t)tVelocityυ(t)tAccelerationa(t)
D
Figure (d)
tPositionx(t)tVelocityυ(t)tAccelerationa(t)
192
[JEE Main 2021, 18 March Shift 1, Q29] A person is swimming with a speed of 1010 m/s at an angle of 120∘120^\circ with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is xx m/s. The value of xx to the nearest integer is ______.
Not attempted
Your answer: —
Correct answer: 5
193
[JEE Main 2021, 17 March Shift 2, Q10] The velocity of a particle is v=v0+gt+Ft2v=v_0+gt+Ft^2. Its position is x=0x=0 at t=0t=0; then its displacement after time (t=1)(t=1) is:
Not attempted
A
v0+g+Fv_0+g+F
B
v0+g2+Fv_0+\dfrac g2+F
C
v0+2g+3Fv_0+2g+3F
D
v0+g2+F3v_0+\dfrac g2+\dfrac F3
194
[JEE Main 2021, 17 March Shift 2, Q19] A rubber ball is released from a height of 55 m above the floor. It bounces back repeatedly, always rising to 81100\dfrac{81}{100} of the height through which it falls. Find the average speed of the ball. (Take g=10g=10 m/s2^2)
Not attempted
A
3.03.0 m/s
B
3.503.50 m/s
C
2.02.0 m/s
D
2.502.50 m/s
195
[JEE Main 2021, 17 March Shift 1, Q4] A car accelerates from rest at a constant rate α\alpha for some time after which it decelerates at a constant rate β\beta to come to rest. If the total time elapsed is tt seconds, the total distance travelled is:
Not attempted
vtt1t2v′
A
αβ2(α+β)t2\dfrac{\alpha\beta}{2(\alpha+\beta)}t^2
B
αβ4(α+β)t2\dfrac{\alpha\beta}{4(\alpha+\beta)}t^2
C
4αβ(α+β)t2\dfrac{4\alpha\beta}{(\alpha+\beta)}t^2
D
2αβ(α+β)t2\dfrac{2\alpha\beta}{(\alpha+\beta)}t^2
196
[JEE Main 2021, 16 March Shift 2, Q28] A swimmer can swim with velocity of 1212 km/h in still water. Water flowing in a river has velocity 66 km/h. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is ______∘^\circ. (Round off to the Nearest Integer) (Find the angle in degrees)
Not attempted
Your answer: —
Correct answer: 120
197
[JEE Main 2021, 16 March Shift 1, Q16] The velocity-displacement graph describing the motion of a bicycle is shown in the figure. The acceleration-displacement graph of the bicycle's motion is best described by :
Not attempted
50100200400x(m)v(ms⁻¹)
A
Graph (a)
1820200400x(m)a(ms⁻²)
B
Graph (b)
1820200400x(m)a(ms⁻²)
C
Graph (c)
1820200400x(m)a(ms⁻²)
D
Graph (d)
1820200400x(m)a(ms⁻²)
198
[JEE Main 2021, 26 February Shift 2, Q2] The trajectory of a projectile in a vertical plane is y=αx−βx2y=\alpha x-\beta x^2 where α\alpha and β\beta are constants and xx and yy are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection θ\theta and the maximum height attained HH are respectively given by
Not attempted
A
tan⁡−1α, 4α2β\tan^{-1}\alpha,\ \frac{4\alpha^2}{\beta}
B
tan⁡−1α, α24β\tan^{-1}\alpha,\ \frac{\alpha^2}{4\beta}
C
tan⁡−1(βα), α2β\tan^{-1}\left(\frac{\beta}{\alpha}\right),\ \frac{\alpha^2}{\beta}
D
tan⁡−1β, α22β\tan^{-1}\beta,\ \frac{\alpha^2}{2\beta}
199
[JEE Main 2021, 26 February Shift 2, Q13] A scooter accelerates from rest for time t1t_1 at constant rate a1a_1 and then retards at constant rate a2a_2 for time t2t_2 and comes to rest. The correct value of t1t2\frac{t_1}{t_2} will be
Not attempted
A
a1+a2a1\frac{a_1+a_2}{a_1}
B
a1a2\frac{a_1}{a_2}
C
a2a1\frac{a_2}{a_1}
D
a1+a2a2\frac{a_1+a_2}{a_2}
200
[JEE Main 2021, 25 February Shift 2, Q6] A stone is dropped from the top of a building. When it crosses a point 5 m below the top, another stone starts to fall from a point 25 m below the top. Both stones reach the bottom of building simultaneously. The height of the building is :
Not attempted
A
50 m50\ \text{m}
B
35 m35\ \text{m}
C
45 m45\ \text{m}
D
25 m25\ \text{m}
201
[JEE Main 2021, 25 February Shift 2, Q24] If P⃗×Q⃗=Q⃗×P⃗\vec P\times\vec Q=\vec Q\times\vec P, the angle between P⃗\vec P and Q⃗\vec Q is θ (0∘<θ<360∘)\theta\ (0^\circ<\theta<360^\circ). The value of ′θ′'\theta' will be ___________ ∘^\circ.
Not attempted
Your answer: —
Correct answer: 180
202
[JEE Main 2021, 25 February Shift 1, Q9] An engine of a train, moving with uniform acceleration, passes the signal-post with velocity uu and the last compartment with velocity vv. The velocity with which middle point of the train passes the signal post is :
Not attempted
A
v2−u22\sqrt{\frac{v^2-u^2}{2}}
B
v2+u22\sqrt{\frac{v^2+u^2}{2}}
C
v−u2\frac{v-u}{2}
D
u+v2\frac{u+v}{2}
203
[JEE Main 2021, 25 February Shift 1, Q12] In an octagon ABCDEFGH of equal sides, what is the sum of AB→+AC→+AD→+AE→+AF→+AG→+AH→\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{AD}+\overrightarrow{AE}+\overrightarrow{AF}+\overrightarrow{AG}+\overrightarrow{AH}, if AO→=2i^+3j^−4k^\overrightarrow{AO}=2\hat{i}+3\hat{j}-4\hat{k} ?
Not attempted
ABCDEFGHO
A
16i^+24j^+32k^16\hat{i}+24\hat{j}+32\hat{k}
B
−16i^−24j^+32k^-16\hat{i}-24\hat{j}+32\hat{k}
C
16i^−24j^+32k^16\hat{i}-24\hat{j}+32\hat{k}
D
16i^+24j^−32k^16\hat{i}+24\hat{j}-32\hat{k}
204
[JEE Main 2021, 24 February Shift 1, Q57] If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph?
Not attempted
A
(A)
B
(B)
C
(C)
D
(D)
205
When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed vv, he sees that rain drops are coming at an angle 60∘60^\circ from the horizontal. On further increasing the speed of the car to (1+β)v(1+\beta)v, this angle changes to 45∘45^\circ. The value of β\beta is close to:
Not attempted
A
0.500.50
B
0.410.41
C
0.370.37
D
0.730.73
206
A clock has a continuously moving second's hand of 0.10.1 m length. The average acceleration of the tip of the hand (in units of ms−2ms^{-2}) is of the order of:
Not attempted
A
10−110^{-1}
B
10−310^{-3}
C
10−410^{-4}
D
10−210^{-2}
207
The velocity (vv, in m/s) versus time (tt, in s) graph of a body moving in a straight line is shown in the figure: the velocity stays constant at 4 m/s4\ \text{m/s} from t=0t=0 to t=1 st=1\ \text{s}, then decreases linearly, becoming zero at point SS (at t=4.333 st=4.333\ \text{s}) and reaching −2 m/s-2\ \text{m/s} at t=6 st=6\ \text{s}. The total distance covered by the body in 6 s6\ \text{s} is:
Not attempted
t(s) v(m/s) 4 S (4.333s) -2 0 v 1 6
A
373 m\dfrac{37}{3}\ \text{m}
B
494 m\dfrac{49}{4}\ \text{m}
C
11 m11\ \text{m}
D
12 m12\ \text{m}
208
A balloon is moving up in air vertically above a point A on the ground. When it is at a height h1h_1, a girl standing at a distance dd (point B) from A sees it at an angle 45∘45^\circ with respect to the vertical. When the balloon climbs up a further height h2h_2, it is seen at an angle 60∘60^\circ with respect to the vertical if the girl moves further by a distance 2.464 d2.464\,d (point C). Then the height h2h_2 is (given tan⁡30∘=0.5774\tan 30^\circ = 0.5774):
Not attempted
A B C h2 h1 d 2.464 d 45° 60°
A
1.464 d
B
0.732 d
C
0.464 d
D
d
209
A helicopter rises from rest on the ground vertically upwards with a constant acceleration gg. A food packet is dropped from the helicopter when it is at a height hh. The time taken by the packet to reach the ground is close to [gg is the acceleration due to gravity]:
Not attempted
A
t=1.8hgt = 1.8\sqrt{\dfrac{h}{g}}
B
t=2h3gt = \sqrt{\dfrac{2h}{3g}}
C
t=3.4hgt = 3.4\sqrt{\dfrac{h}{g}}
D
t=23hgt = \dfrac{2}{3}\sqrt{\dfrac{h}{g}}
210
The speed-time graph for a particle is a straight line from v=0v=0 at t=0t=0 to v=8 m/sv=8\text{ m/s} at t=5 st=5\text{ s} (as shown). Find the distance travelled (in m) by the particle during the interval t=0t=0 to t=5 st=5\text{ s}.
Not attempted
t (s)v (m/s)580
Your answer: —
Correct answer: 20
211
A tennis ball is released from a height hh and after freely falling on a wooden floor it rebounds and reaches height h2\dfrac{h}{2}. The velocity versus height of the ball during its motion may be represented graphically by: (graphs are drawn schematically and are not to scale)
Not attempted
A
Graph (A)
v hh/2 h
B
Graph (B)
v hh/2 h
C
Graph (C)
v hh/2 h
D
Graph (D)
v hh/2 h
212
Starting from the origin at time t=0t=0, with initial velocity 5j^ ms−15\hat{j}\ \text{ms}^{-1}, a particle moves in the xx-yy plane with a constant acceleration of (10i^+4j^) ms−2(10\hat{i}+4\hat{j})\ \text{ms}^{-2}. At time tt, its coordinates are (20 m,y0 m)(20\ \text{m}, y_0\ \text{m}). The values of tt and y0y_0 are, respectively:
Not attempted
A
2 s and 24 m2\ \text{s and } 24\ \text{m}
B
4 s and 52 m4\ \text{s and } 52\ \text{m}
C
2 s and 18 m2\ \text{s and } 18\ \text{m}
D
5 s and 25 m5\ \text{s and } 25\ \text{m}
213
A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement (s)(s)-time (t)(t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale):
Not attempted
A
Graph (A): straight line
ts
B
Graph (B): horizontal line
ts
C
Graph (C): concave-up curve
ts
D
Graph (D): concave-down curve
ts
214
Train AA and train BB are running on parallel tracks in opposite directions with speeds of 36 km/hour36\ \text{km/hour} and 72 km/hour72\ \text{km/hour} respectively. A person is walking in train AA in the direction opposite to its motion with a speed of 1.8 km/hour1.8\ \text{km/hour}. Speed (in ms−1\text{ms}^{-1}) of this person as observed from train BB will be close to (take the distance between the tracks as negligible):
Not attempted
A
30.5 ms−130.5\ \text{ms}^{-1}
B
28.5 ms−128.5\ \text{ms}^{-1}
C
31.5 ms−131.5\ \text{ms}^{-1}
D
29.5 ms−129.5\ \text{ms}^{-1}
215
A particle starts moving with velocity u⃗=3i^\vec u=3\hat i (m/s) from the origin, with constant acceleration a⃗=6i^+4j^\vec a=6\hat i+4\hat j (m/s2^2). When the particle's yy-coordinate is 32 m32\ \text{m}, find its xx-coordinate at that instant.
Not attempted
A
4848
B
6060
C
1212
D
2424
216
The position of a particle moving along a straight line varies with time as x2=at2+2bt+cx^2=at^2+2bt+c, where a,b,ca,b,c are constants. If the acceleration of the particle varies with position as x−nx^{-n}, find nn.
Not attempted
Your answer: —
Correct answer: 3
217
A particle moves such that its position vector is r⃗(t)=cos⁡(ωt) i^+sin⁡(ωt) j^\vec{r}(t) = \cos(\omega t)\,\hat{i} + \sin(\omega t)\,\hat{j}, where ω\omega is a constant and tt is time. Which of the following statements is true for the velocity v⃗(t)\vec{v}(t) and the acceleration a⃗(t)\vec{a}(t) of the particle?
Not attempted
A
v⃗\vec{v} is perpendicular to r⃗\vec{r}, and a⃗\vec{a} is directed away from the origin
B
v⃗\vec{v} and a⃗\vec{a} are both perpendicular to r⃗\vec{r}
C
v⃗\vec{v} and a⃗\vec{a} are both parallel to r⃗\vec{r}
D
v⃗\vec{v} is perpendicular to r⃗\vec{r}, and a⃗\vec{a} is directed towards the origin
218
A ball is dropped from rest from the top of a 100 m100\text{ m} high tower on a planet. In the last 0.5 s0.5\text{ s} before it hits the ground, it covers a distance of 19 m19\text{ m}. The acceleration due to gravity (in m/s2\text{m/s}^2) near the surface of this planet is
Not attempted
Your answer: —
Correct answer: 8
219
A particle AA is moving along the x-axis with its coordinate as a function of time tt given by x(t)=10+8t−3t2x(t)=10+8t-3t^2. Another particle BB is moving along the y-axis with its coordinate as a function of time given by y(t)=5−8t3y(t)=5-8t^3. At t=1 st=1\ s, the speed of BB as measured in the reference frame of AA is v m/s\sqrt{v}\ m/s. Then vv is _____.
Not attempted
Your answer: —
Correct answer: 580
220
[JEE Main 2019, 12 April Shift 2, Q21] Two particles are projected from the same point with the same speed uu such that they have the same range RR, but different maximum heights, h1h_1 and h2h_2. Which of the following is correct?
Not attempted
A
R2=2h1h2R^2=2h_1h_2
B
R2=16h1h2R^2=16h_1h_2
C
R2=4h1h2R^2=4h_1h_2
D
R2=h1h2R^2=h_1h_2
221
[JEE Main 2019, 12 April Shift 2, Q22] A particle is moving with speed υ=bx\upsilon=b\sqrt x along positive xx-axis. Calculate the speed of the particle at time t=τt=\tau (assume that the particle is at origin at t=0t=0).
Not attempted
A
b2τ4\dfrac{b^2\tau}{4}
B
b2τ2\dfrac{b^2\tau}{2}
C
b2τb^2\tau
D
b2τ2\dfrac{b^2\tau}{\sqrt2}
222
[JEE Main 2019, 12 April Shift 1, Q1] The trajectory of a projectile near the surface of the earth is given as y=2x−9x2y=2x-9x^2. If it were launched at an angle θ0\theta_0 with speed v0v_0, then (g=10 ms−2g=10\ \text{ms}^{-2}):
Not attempted
A
θ0=sin⁡−1(25)\theta_0=\sin^{-1}\left(\dfrac{2}{\sqrt5}\right) and v0=35 ms−1v_0=\dfrac35\ \text{ms}^{-1}
B
θ0=sin⁡−1(15)\theta_0=\sin^{-1}\left(\dfrac{1}{\sqrt5}\right) and v0=53 ms−1v_0=\dfrac53\ \text{ms}^{-1}
C
θ0=cos⁡−1(25)\theta_0=\cos^{-1}\left(\dfrac{2}{\sqrt5}\right) and v0=35 ms−1v_0=\dfrac35\ \text{ms}^{-1}
D
θ0=cos⁡−1(15)\theta_0=\cos^{-1}\left(\dfrac{1}{\sqrt5}\right) and v0=53 ms−1v_0=\dfrac53\ \text{ms}^{-1}
223
[JEE Main 2019, 12 April Shift 1, Q6] A shell is fired from a fixed artillery gun with an initial speed uu such that it hits the target on the ground at a distance RR from it. If t1t_1 and t2t_2 are the values of the time taken by it to hit the target in the two possible ways, the product t1t2t_1t_2 is:
Not attempted
A
2Rg\dfrac{2R}{g}
B
Rg\dfrac{R}{g}
C
R2g\dfrac{R}{2g}
D
R4g\dfrac{R}{4g}
224
[JEE Main 2019, 10 April Shift 2, Q1] A plane is inclined at an angle α=30∘\alpha=30^\circ with respect to the horizontal. A particle is projected with a speed u=2 ms−1u=2\ \text{ms}^{-1}, from the base of the plane, making an angle θ=15∘\theta=15^\circ with respect to the plane as shown in the figure. The distance from the base, at which the particle hits the plane is close to: (Take g=10 ms−2g=10\ \text{ms}^{-2})
Not attempted
uα = 30°θ = 15°
A
26 cm26\ \text{cm}
B
14 cm14\ \text{cm}
C
20 cm20\ \text{cm}
D
18 cm18\ \text{cm}
225
[JEE Main 2019, 10 April Shift 1, Q25] A ball is thrown upward with an initial velocity V0V_0 from the surface of the earth. The motion of the ball is affected by a drag force equal to mγv2m\gamma v^2 (where mm is the mass of the ball, vv is its instantaneous velocity and γ\gamma is a constant). Time taken by the ball to rise to its zenith is:
Not attempted
A
1γgtan⁡−1(γg V0)\dfrac{1}{\sqrt{\gamma g}}\tan^{-1}\left(\sqrt{\dfrac{\gamma}{g}}\,V_0\right)
B
12γgtan⁡−1(2γg V0)\dfrac{1}{\sqrt{2\gamma g}}\tan^{-1}\left(\sqrt{\dfrac{2\gamma}{g}}\,V_0\right)
C
1γgsin⁡−1(γg V0)\dfrac{1}{\sqrt{\gamma g}}\sin^{-1}\left(\sqrt{\dfrac{\gamma}{g}}\,V_0\right)
D
1γgln⁡(1+γg V0)\dfrac{1}{\sqrt{\gamma g}}\ln\left(1+\sqrt{\dfrac{\gamma}{g}}\,V_0\right)
226
[JEE Main 2019, 9 April Shift 2, Q16] The position of a particle as a function of time tt is given by x(t)=at+bt2−ct3x(t)=at+bt^2-ct^3 where aa, bb and cc are constants. When the particle attains zero acceleration, then its velocity will be:
Not attempted
A
a+b24ca+\dfrac{b^2}{4c}
B
a+b2ca+\dfrac{b^2}{c}
C
a+b22ca+\dfrac{b^2}{2c}
D
a+b23ca+\dfrac{b^2}{3c}
227
[JEE Main 2019, 9 April Shift 2, Q26] The position vector of a particle changes with time according to the relation r⃗(t)=15t2i^+(4−20t2)j^\vec r(t)=15t^2\hat i+(4-20t^2)\hat j. What is the magnitude of the acceleration at t=1t=1?
Not attempted
A
4040
B
100100
C
5050
D
2525
228
[JEE Main 2019, 9 April Shift 1, Q20] A ball is thrown vertically up (taken as +z+z-axis) from the ground. The correct momentum-height (pp-hh) diagram is:
Not attempted
A
Graph (1)
phO
B
Graph (2)
phO
C
Graph (3)
phO
D
Graph (4)
phO
229
[JEE Main 2019, 9 April Shift 1, Q27] The stream of a river is flowing with a speed of 2 km/h2\ \text{km/h}. A swimmer can swim at a speed of 4 km/h4\ \text{km/h}. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight?
Not attempted
A
60∘60^\circ
B
150∘150^\circ
C
90∘90^\circ
D
120∘120^\circ
230
[JEE Main 2019, 8 April Shift 1, Q14] Ship AA is sailing towards north-east with velocity v⃗=30i^+50j^ km/hr\vec v=30\hat i+50\hat j\ \text{km/hr} where i^\hat i points east and j^\hat j north. Ship BB is at a distance of 80 km80\ \text{km} east and 150 km150\ \text{km} north of Ship AA and is sailing towards west at 10 km/hr10\ \text{km/hr}. AA will be at minimum distance from BB in:
Not attempted
A
3.2 hrs3.2\ \text{hrs}
B
2.6 hrs2.6\ \text{hrs}
C
4.2 hrs4.2\ \text{hrs}
D
2.2 hrs2.2\ \text{hrs}
231
[JEE Main 2019, 12 January Shift 2, Q17] Two particles AA, BB are moving on two concentric circles of radii R1R_1 and R2R_2 with equal angular speed ω\omega. At t=0t=0, their positions and direction of motion are shown in the figure. The relative velocity v⃗A−v⃗B\vec v_A-\vec v_B at t=π2ωt=\dfrac{\pi}{2\omega} is given by:
Not attempted
XYABR1R2
A
−ω(R1+R2)i^-\omega(R_1+R_2)\hat i
B
ω(R1+R2)i^\omega(R_1+R_2)\hat i
C
ω(R1−R2)i^\omega(R_1-R_2)\hat i
D
ω(R2−R1)i^\omega(R_2-R_1)\hat i
232
A particle starts from rest at the origin and moves along the positive xx-axis with constant (uniform) acceleration a0a_0. In terms of standard aa-tt, vv-tt and xx-tt graphs, which qualitative statement about the three graphs is correct: (A) the aa-tt graph is a horizontal line at a0a_0; (B) the vv-tt graph is a straight line through the origin with slope a0a_0; (C) the vv-tt graph is horizontal; (D) the xx-tt graph is a parabola through the origin that gets steeper with time?
Not attempted
A
(B), (C)
B
(A) only
C
(A), (B), (C)
D
(A), (B), (D)
233
Two vectors A⃗1,A⃗2\vec A_1,\vec A_2 satisfy ∣A⃗1∣=3|\vec A_1|=3, ∣A⃗2∣=5|\vec A_2|=5 and ∣A⃗1+A⃗2∣=5|\vec A_1+\vec A_2|=5. Find the value of (2A⃗1+3A⃗2)⋅(3A⃗1−2A⃗2)(2\vec A_1+3\vec A_2)\cdot(3\vec A_1-2\vec A_2).
Not attempted
A
−118.5-118.5
B
−112.5-112.5
C
−99.5-99.5
D
−106.5-106.5
234
Two particles A,BA, B are moving on two concentric circles of radii R1R_1 and R2R_2 with equal angular speed ω\omega. At t=0t=0, their positions and directions of motion are as shown in the figure (AA on the inner circle of radius R1R_1 just above the positive xx-axis moving counter-clockwise; BB on the outer circle of radius R2R_2 just below the positive xx-axis moving clockwise). The relative velocity v⃗A−v⃗B\vec v_A - \vec v_B at t=π2ωt=\dfrac{\pi}{2\omega} is given by:
Not attempted
Created by potrace 1.16, written by Peter Selinger 2001-2019
A
−ω(R1+R2)i^-\omega(R_1+R_2)\hat i
B
ω(R1+R2)i^\omega(R_1+R_2)\hat i
C
ω(R1−R2)i^\omega(R_1-R_2)\hat i
D
ω(R2−R1)i^\omega(R_2-R_1)\hat i
235
[JEE Main 2019, 12 January Shift 1, Q12] A passenger train of length 60 m60\ \text{m} travels at a speed of 80 km/hr80\ \text{km/hr}. Another freight train of length 120 m120\ \text{m} travels at a speed of 30 km/hr30\ \text{km/hr}. The ratio of the times taken by the passenger train to completely cross the freight train when: (i) they are moving in the same direction, and (ii) in the opposite direction is:
Not attempted
A
52\dfrac{5}{2}
B
2511\dfrac{25}{11}
C
32\dfrac{3}{2}
D
115\dfrac{11}{5}
236
[JEE Main 2019, 11 January Shift 2, Q14] A particle moves from the point (2.0i^+4.0j^) m\left(2.0\hat i+4.0\hat j\right)\ \text{m}, at t=0t=0, with an initial velocity (5.0i^+4.0j^) m s−1\left(5.0\hat i+4.0\hat j\right)\ \text{m s}^{-1}. It is acted upon by a constant force which produces a constant acceleration (4.0i^+4.0j^) m s−2\left(4.0\hat i+4.0\hat j\right)\ \text{m s}^{-2}. What is the distance of the particle from the origin at time 2 s2\ \text{s}?
Not attempted
A
202 m20\sqrt2\ \text{m}
B
102 m10\sqrt2\ \text{m}
C
5 m5\ \text{m}
D
15 m15\ \text{m}
237
[JEE Main 2019, 11 January Shift 1, Q1] A body is projected at t=0t=0 with a velocity 10 m s−110\ \text{m s}^{-1} at an angle of 60∘60^\circ with the horizontal. The radius of curvature of its trajectory at t=1 st=1\ \text{s} is RR. Neglecting air resistance and taking g=10 m s−2g=10\ \text{m s}^{-2}, the value of RR is:
Not attempted
A
2.5 m2.5\ \text{m}
B
10.3 m10.3\ \text{m}
C
2.8 m2.8\ \text{m}
D
5.1 m5.1\ \text{m}
238
[JEE Main 2019, 11 January Shift 1, Q2] A particle is moving along a circular path with a constant speed of 10 m s−110\ \text{m s}^{-1}. What is the magnitude of the change in velocity of the particle, when it moves through an angle of 60∘60^\circ around the centre of the circle?
Not attempted
A
zero
B
10 m/s10\ \text{m/s}
C
103 m/s10\sqrt3\ \text{m/s}
D
102 m/s10\sqrt2\ \text{m/s}
239
[JEE Main 2019, 10 January Shift 2, Q9] Two vectors A⃗\vec A and B⃗\vec B have equal magnitudes. The magnitude of (A⃗+B⃗)(\vec A+\vec B) is nn times the magnitude of (A⃗−B⃗)(\vec A-\vec B). The angle between A⃗\vec A and B⃗\vec B is:
Not attempted
A
cos⁡−1[n2−1n2+1]\cos^{-1}\left[\dfrac{n^2-1}{n^2+1}\right]
B
cos⁡−1[n−1n+1]\cos^{-1}\left[\dfrac{n-1}{n+1}\right]
C
sin⁡−1[n2−1n2+1]\sin^{-1}\left[\dfrac{n^2-1}{n^2+1}\right]
D
sin⁡−1[n−1n+1]\sin^{-1}\left[\dfrac{n-1}{n+1}\right]
240
[JEE Main 2019, 10 January Shift 2, Q25] A particle starts from the origin at time t=0t=0 and moves along the positive xx-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time t=5 st=5\ \text{s}?
Not attempted
123456789100123t (s)v (m/s)
A
10 m10\ \text{m}
B
6 m6\ \text{m}
C
3 m3\ \text{m}
D
9 m9\ \text{m}
241
[JEE Main 2019, 10 January Shift 2, Q27] Two forces PP and QQ, of magnitude 2F2F and 3F3F, respectively, are at an angle θ\theta with each other. If the force QQ is doubled, then their resultant also gets doubled. Then, the angle θ\theta is:
Not attempted
A
120∘120^\circ
B
60∘60^\circ
C
90∘90^\circ
D
30∘30^\circ
242
[JEE Main 2019, 10 January Shift 1, Q21] Two guns AA and BB can fire bullets at speeds 11 km/s and 22 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is:
Not attempted
A
1:21:2
B
1:41:4
C
1:81:8
D
1:161:16
243
[JEE Main 2019, 10 January Shift 1, Q29] In the cube of side aa shown in the figure, the vector from the central point of the face ABODABOD to the central point of the face BEFOBEFO will be:
Not attempted
zyxOFBEADaaaGH
A
12a(i^−k^)\dfrac12a(\hat i-\hat k)
B
12a(j^−i^)\dfrac12a(\hat j-\hat i)
C
12a(k^−i^)\dfrac12a(\hat k-\hat i)
D
12a(j^−k^)\dfrac12a(\hat j-\hat k)
244
[JEE Main 2019, 9 January Shift 2, Q23] The position co-ordinates of a particle moving in a 3-D coordinate system is given by x=acos⁡ωtx=a\cos\omega t, y=asin⁡ωty=a\sin\omega t and z=aωtz=a\omega t. The speed of the particle is:
Not attempted
A
aωa\omega
B
3 aω\sqrt3\,a\omega
C
2 aω\sqrt2\,a\omega
D
2aω2a\omega
245
[JEE Main 2019, 9 January Shift 2, Q26] In a car race on straight road, car AA takes a time tt less than car BB at the finish and passes finishing point with a speed vv more than that of car BB. Both the cars start from rest and travel with constant acceleration a1a_1 and a2a_2 respectively. Then vv is equal to
Not attempted
A
a1+a22t\dfrac{a_1+a_2}{2}t
B
2a1a2 t\sqrt{2a_1a_2}\,t
C
2a1a2a1+a2t\dfrac{2a_1a_2}{a_1+a_2}t
D
a1a2 t\sqrt{a_1a_2}\,t
246
[JEE Main 2019, 9 January Shift 1, Q5] A particle is moving with a velocity v⃗=K(yi^+xj^)\vec v=K(y\hat i+x\hat j), where KK is a constant. The general equation for its path is:
Not attempted
A
y=x2+constanty=x^2+\text{constant}
B
y2=x+constanty^2=x+\text{constant}
C
y2=x2+constanty^2=x^2+\text{constant}
D
xy=constantxy=\text{constant}
247
[JEE Main 2018, 8 April, Q53] All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.
Not attempted
A
Graph (A): velocity versus time
timevelocity
B
Graph (B): velocity versus position
positionvelocity
C
Graph (C): distance versus time
timedistance
D
Graph (D): position versus time
timeposition
248
[JEE Main 2017, 2 April, Q48] A body is thrown vertically upwards. Which one of the following graphs correctly represents the velocity versus time?
Not attempted
A
Graph A
tv
B
Graph B
tv
C
Graph C
tv
D
Graph D
tv
249
[JEE Main 2015, 4 April, Q86] Two stones are thrown up simultaneously from the edge of a cliff 240 m240\,\text{m} high with initial speed of 10 m/s10\,\text{m/s} and 40 m/s40\,\text{m/s} respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first? (Assume stones do not rebound after hitting the ground and neglect air resistance, take g=10 m/s2g=10\,\text{m/s}^2) (The figures are schematic and not drawn to scale)
Not attempted
A
Graph (A)
B
Graph (B)
C
Graph (C)
D
Graph (D)
250
[JEE Main 2014, 6 April, Q18] From a tower of height HH, a particle is thrown vertically upwards with a speed uu. The time taken by the particle, to hit the ground, is nn times that taken by it to reach the highest point of its path. The relation between HH, uu and nn is:
Not attempted
A
2gH=nu2(n−2)2gH=nu^2(n-2)
B
gH=(n−2)u2gH=(n-2)u^2
C
2gH=n2u22gH=n^2u^2
D
gH=(n−2)2u2gH=(n-2)^2u^2
251
A projectile is given an initial velocity of (i^+2j^) m/s(\hat i + 2\hat j)\ \mathrm{m/s}, where i^\hat i is along the ground and j^\hat j is along the vertical. If g=10 m/s2g = 10\ \mathrm{m/s^2}, the equation of its trajectory is:
Not attempted
A
y=2x−5x2y = 2x - 5x^2
B
4y=2x−5x24y = 2x - 5x^2
C
4y=2x−25x24y = 2x - 25x^2
D
y=x−5x2y = x - 5x^2
Write x(t)x(t) and y(t)y(t) separately and eliminate tt.
Deconstruction\textbf{Deconstruction}: Trajectory for ux=1u_x = 1, uy=2u_y = 2, g=10g = 10. Strategy\textbf{Strategy}: Independent horizontal and vertical motion. Execution\textbf{Execution}: - x=tx = t, y=2t−5t2y = 2t - 5t^2. - Substituting t=xt = x: y=2x−5x2y = 2x - 5x^2. Verification\textbf{Verification}: Standard form y=xtan⁡θ−gx22u2cos⁡2θy = x\tan\theta - \dfrac{gx^2}{2u^2\cos^2\theta} with tan⁡θ=2\tan\theta = 2, u2cos⁡2θ=1u^2\cos^2\theta = 1: y=2x−5x2y = 2x - 5x^2. Final Answer\textbf{Final Answer}: Option (1).