Question 1: Palette 1/60

Allen JEE Main-2023 MCQ

A particle starts with an initial velocity of $10.0 \, ms^{-1}$ along x-direction and accelerates uniformly at the rate of $2.0 \, ms^{-2}$ . The time taken by the particle to reach the velocity of $60.0 \, ms^{-1}$ is ____.

A

6s

B

3s

C

30s

D

25s

Question 2: Palette 2/60

Allen JEE Main-2023 MCQ

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 $45^{\circ}$ , it's range is maximum. Reason R: For maximum range, the value of $\sin2\theta$ should be equal to one. In the light of the above statements, choose the correct answer from the options given below:

A

Both A and R are correct but R is NOT the correct explanation of A

B

Both A and R are correct R is the correct explanation of A

C

A is true but R is false

D

A is false but R is true

Question 3: Palette 3/60

Allen JEE Main-2023 MCQ

Two projectiles A and B are thrown with initial velocities of 40 m/s and 60 m/s at angles $30^{\circ}$ and $60^{\circ}$ with the horizontal respectively. The ratio of their ranges respectively is $(g = 10 \, m/s^{2})$

A

$\sqrt{3}:2$

B

$2:\sqrt{3}$

C

1:1

D

4:9

Question 4: Palette 4/60

Allen JEE-Advanced 2023 MCQ

A particle of mass m is moving in the xy-plane such that its velocity at a point $(x, y)$ is given as $\vec{v} = \alpha(y\hat{x} + 2x\hat{y})$ , where $\alpha$ is a non-zero constant. What is the force $\vec{F}$ acting on the particle?

A

$\vec{F}=2m\alpha^{2}(x\hat{x}+y\hat{y})$

B

$\vec{F}=m\alpha^{2}(y\hat{x}+2x\hat{y})$

C

$\vec{F} = 2m\alpha^2(y\hat{x} + x\hat{y})$

D

$\vec{F} = m\alpha^2 (x\hat{x} + 2y\hat{y})$

Question 5: Palette 5/60

Allen 2022 MCQ

A projectile is projected with velocity of 25 m/s at an angle θ with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of θ will be: [Use g = 10 m/s²] (JEE-Main 2022)

A

$\frac{1}{2}\sin^{-1}\left(\frac{5t^{2}}{4R}\right)$

B

$\frac{1}{2}\sin^{-1}\left(\frac{4R}{5t^{2}}\right)$

C

$\tan^{-1}\left(\frac{4t^{2}}{5R}\right)$

D

$\cot^{-1}\left(\frac{R}{20t^{2}}\right)$

Question 6: Palette 6/60

Allen JEE-Main 2021 MCQ

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 :

A

B

C

D

Question 7: Palette 7/60

Allen JEE-Main 2021 MCQ

The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by :

A

B

C

D

Question 8: Palette 8/60

Allen JEE-Main 2021 MCQ

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at $4^{th}$ second after its fall to the next droplet is 34.3 m. At what rate the droplets are coming from the tap? (Take $g = 9.8 \, m/s^{2}$ )

A

3 drops / 2 seconds

B

2 drops / second

C

1 drop / second

D

1 drop / 7 seconds

Question 9: Palette 9/60

Allen JEE-Main 2021 MCQ

A ball is thrown up with a certain velocity so that it reaches a height 'h'. Find the ratio of the two different times of the ball reaching $\frac{h}{3}$ in both the directions.

A

$\frac{\sqrt{2}-1}{\sqrt{2}+1}$

B

$\frac{1}{3}$

C

$\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$

D

$\frac{\sqrt{3}-1}{\sqrt{3}+1}$

Question 10: Palette 10/60

Allen JEE-Main 2021 MCQ

A butterfly is flying with a velocity $4\sqrt{2}$ m/s in North-East direction. Wind is slowly blowing at 1 m/s from North to South. The resultant displacement of the butterfly in 3 seconds is:

A

3 m

B

20 m

C

$12\sqrt{2}m$

D

15 m

Question 11: Palette 11/60

Allen JEE-Main 2020 MCQ

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v, he sees that rain drops are coming at an angle $60^{\circ}$ from the horizontal. On further increasing the speed of the car to $(1 + \beta)v$ , this angle changes to $45^{\circ}$ . The value of $\beta$ is close to:

A

0.41

B

0.50

C

0.37

D

0.73

Question 12: Palette 12/60

Allen JEE-Main 2020 MCQ

A particle starts from the origin at t = 0 with an initial velocity of $3.0\hat{i}$ m/s and moves in the x-y plane with a constant acceleration ( $6.0\hat{i} + 4.0\hat{j}$ )m/s $^{2}$ . The x-coordinate of the particle at the instant when its y-coordinate is 32 m is D meters. The value of D is

A

50

B

32

C

60

D

40

Question 13: Palette 13/60

Allen JEE-Main 2020 MCQ

Starting from the origin at time t = 0, with initial velocity $5\hat{j}ms^{-1}$ , a particle moves in the x-y plane with a constant acceleration of $(10\hat{i} + 4\hat{j})ms^{-2}$ . At time t, its coordinates are $(20\ m, y_{0}\ m)$ . The values of t and $y_{0}$ , are respectively:

A

4s and 52 m

B

2s and 24 m

C

2s and 18 m

D

5s and 25 m

Question 14: Palette 14/60

Allen JEE-Advanced 2020 MSQ

Starting at time t = 0 from the origin with speed $1 \, ms^{-1}$ , a particle follows a two-dimensional trajectory in the x-y plane so that its coordinates are related by the equation $y = \frac{x^{2}}{2}$ . The x and y components of its acceleration are denoted by $a_{x}$ and $a_{y}$ , respectively. Then

A

$a_{x} = 1 \, ms^{-2}$ implies that when the particle is at the origin, $a_{y} = 1 \, ms^{-2}$

B

$a_{x} = 0$ implies $a_{y} = 1 \, ms^{-2}$ at all times

C

At t = 0, the particle's velocity points in the x-direction

D

$a_{x}=0$ implies that at t=1 s, the angle between the particle's velocity and the x axis is $45^{\circ}$

Question 15: Palette 15/60

Allen JEE-Main 2019 MCQ

A particle is moving with speed $v = b\sqrt{x}$ along positive x-axis. Calculate the speed of the particle at time $t = \tau$ (assume that the particle is at origin at t = 0).

A

$\frac{b^{2}\tau}{4}$

B

$\frac{b^{2}\tau}{2}$

C

$b^{2}\tau$

D

$\frac{b^{2}\tau}{\sqrt{2}}$

Question 16: Palette 16/60

Allen JEE-Main 2019 MCQ

The position co-ordinates of a particle moving in a 3-D coordinate system is given by $x = a \cos \omega t$ $y = a \sin \omega t$ and $z = a \omega t$ The speed of the particle is :

A

$a\omega$

B

$\sqrt{3}a\omega$

C

$\sqrt{2}a\omega$

D

$2a\omega$

Question 17: Palette 17/60

Allen JEE-Main 2019 MCQ

Two guns A and B can fire bullets at speeds 1 km/s and 2 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 :

A

1:2

B

1:4

C

1:8

D

1:16

Question 18: Palette 18/60

Allen JEE-Main 2019 MCQ

A particle moves from the point $(2.0\hat{i} + 4.0\hat{j})m$ , at t = 0, with an initial velocity $(5.0\hat{i} + 4.0\hat{j})ms^{-1}$ . It is acted upon by a constant force which produces a constant acceleration $(4.0\hat{i} + 4.0\hat{j})ms^{-2}$ . What is the distance of the particle from the origin at time 2s?

A

$20\sqrt{2}m$

B

$10\sqrt{2}m$

C

5 m

D

15 m

Question 19: Palette 19/60

Allen JEE-Main 2019 MCQ

A plane is inclined at an angle $\alpha = 30^{\circ}$ with respect to the horizontal. A particle is projected with a speed $u = 2 ms^{-1}$ from the base of the plane, making an angle $\theta = 15^{\circ}$ 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 $g = 10 ms^{-2}$ )

A

$14\mathrm{cm}$

B

$20\mathrm{cm}$

C

$18\mathrm{cm}$

D

$26\mathrm{cm}$

Question 20: Palette 20/60

Allen JEE-Main 2019 MCQ

The trajectory of a projectile near the surface of the earth is given as $y = 2x - 9x^{2}$ . If it were launched at an angle $\theta_{0}$ with speed $v_{0}$ then ( $g = 10 ms^{-2}$ ):

A

$\theta_{0} = \cos^{-1}\left(\frac{1}{\sqrt{5}}\right)$ and $v_{0} = \frac{5}{3}ms^{-1}$

B

$\theta_{0} = \sin^{-1}\left(\frac{1}{\sqrt{5}}\right)$ and $v_{0} = \frac{5}{3}ms^{-1}$

C

$\theta_{0} = \sin^{-1}\left(\frac{2}{\sqrt{5}}\right)$ and $v_{0} = \frac{5}{3}ms^{-1}$

D

$\theta_{0} = \cos^{-1}\left(\frac{2}{\sqrt{5}}\right)$ and $v_{0} = \frac{5}{3}ms^{-1}$

Question 21: Palette 21/60

Allen 2019 MCQ

A passenger train of length 60m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr. The ratio of 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 directions is: (JEE-Main 2019)

A

$\frac{5}{2}$

B

$\frac{25}{11}$

C

$\frac{3}{2}$

D

$\frac{11}{5}$

Question 22: Palette 22/60

Allen JEE-Main 2019 MCQ

The position vector of a particle changes with time according to the relation $\vec{r}(t) = 15t^2\hat{i} + (4 - 20t^2)\hat{j}$ . What is the magnitude of the acceleration at $t = 1$ ?

A

40

B

100

C

25

D

50

Question 23: Palette 23/60

Allen JEE-Advanced 2017 MCQ

Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density $\rho$ remains uniform throughout the volume. The rate of fractional change in density $\left(\frac{1}{\rho}\frac{d\rho}{dt}\right)$ is constant. The velocity v of any point on the surface of the expanding sphere is proportional to :

A

$R^{3}$

B

$\frac{1}{R}$

C

R

D

$R^{2/3}$

Question 24: Palette 24/60

Allen JEE-Main 2015 MCQ

Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 10 m/s and 40 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 $g = 10 \, m/s^{2}$ ) (The figure are schematic and not drawn to scale)

A

B

C

D

Question 25: Palette 25/60

Allen JEE-Main 2013 MCQ

A projectile is given an initial velocity of $(\hat{t} + 2\hat{j})$ m/s, where $\hat{t}$ is along the ground and $\hat{j}$ is along the vertical. If $g = 10 \, m/s^{2}$ , the equation of its trajectory is :

A

$y = x - 5x^{2}$

B

$y = 2x - 5x^{2}$

C

$4y = 2x - 5x^{2}$

D

$4y = 2x - 25x^{2}$

Question 26: Palette 26/60

Allen MCQ

Find ratio of average speed and magnitude of average velocity of tip of minute hand in 20 minutes:

A

$\frac{2\pi}{3\sqrt{3}}$

B

$\frac{2\pi}{3}$

C

$\frac{3\sqrt{3}}{2\pi}$

D

None

Question 27: Palette 27/60

Allen MCQ

The motion of a particle is defined by the position vector $\vec{r} = A(\cos t + t\sin t)\hat{\imath} +A(\sin t - t\cos t)\hat{j}$ Where t is expressed in seconds. Determine the value of t for which positions vectors and acceleration vector are perpendicular.

A

0

B

1

C

3

D

5

Question 28: Palette 28/60

Allen MCQ

Now the particle is moving only along the z-axis, and its position is given by, $(t^{2}-2t-3)\hat{k}$ . At what time does the particle stand still?

A

1

B

3

C

5

D

7

Question 29: Palette 29/60

Allen MCQ

A particle is moving towards East with velocity $8 \, ms^{-1}$ and acceleration $4 \, ms^{-2}$ directed towards West. Find the distance travelled in 6 seconds.

A

40 m

B

24 m

C

32 m

D

16 m

Question 30: Palette 30/60

Allen MCQ

A car moving at 160 km/h when crosses the marker-0, driver applies brake and reduces its speed uniformly to 40 km/h at marker-2. The markers are spaced at equal distances along the road as shown below. At which part of the track would the car have been traveling at instantaneous speed of 100 km/h?

A

At marker-1

B

Between marker-0 and marker-1

C

Between marker-1 and marker-2

D

More information required to decide.

Question 31: Palette 31/60

Allen MCQ

Two balls are projected simultaneously from the top of a tall building, one vertically upward and other vertical downwards with the same speed of 60 m/s. Then time interval between the balls striking the ground is :-

A

6 sec.

B

10 sec.

C

12 sec.

D

9 sec.

Question 32: Palette 32/60

Allen MCQ

A particle moves on x-axis as per equation $x = (t^{3} - 9t^{2} + 15t + 2)m$ . Distance travelled by the particle between t = 0 and t = 5 s is

A

25 m

B

39 m

C

23 m

D

52 m

Question 33: Palette 33/60

Allen MCQ

The $\mathrm{XI^{th}}$ class students of ALLEN designed a rocket. The rocket was launched from cycle stand of ALLEN straight up into the air. At $t = 0$ , the rocket is at $y = 0$ with $V_{y}(t = 0) = 0$ . The velocity of the rocket is given by: $V_{y} = (24t - 3t^{2})m / s$ for $0 \leq t \leq t_{b}$ where $t_{b}$ is the time at which fuel burns out. Vertically upward direction is taken as positive. $(g = 10m / s^2)$ The time taken by rocket to reach its maximum height is

A

4 sec.

B

8 sec.

C

8.8 sec.

D

9.6 sec.

Question 34: Palette 34/60

Allen MCQ

Acceleration-velocity graph of a moving particle is shown in figure. The particle is

A

speeding up at P

B

speeding up at Q

C

speeding up at S

D

speeding down at R

Question 35: Palette 35/60

Allen MCQ

A body of mass 5 kg starts from the origin with an initial velocity $\vec{u} = (30\hat{i} + 40\hat{j})ms^{-1}$ . If a constant force $(-6\hat{i} - 5\hat{j})N$ acts on the body, the time in which the y component of the velocity becomes zero, is:

A

5s

B

20 s

C

40 s

D

80 s

Question 36: Palette 36/60

Allen MCQ

A boy throws a ball from shoulder height at an initial velocity of 30 m/s. Spending 4.8 s in air, the ball is caught by another boy as the same shoulder-height level. What is the angle of projection?

A

$37^{\circ}$

B

$30^{\circ}$

C

$53^{\circ}$

D

$60^{\circ}$

Question 37: Palette 37/60

Allen MCQ

A particle is projected from the ground with velocity u at angle $\theta$ with horizontal. The horizontal range, maximum height and time of flight are R, H and T respectively. They are given by $R = \frac{u^{2} \sin 2\theta}{g} H = \frac{u^{2} \sin^{2} \theta}{2g}$ and $T = \frac{2u \sin \theta}{g}$ Now keeping u fixed, $\theta$ is varied from $30^{\circ}$ to $60^{\circ}$ , then

A

R will first increase then decrease, H will increase and T will decrease

B

R will first increase then decrease while H and T both will increase

C

R will decrease while H and T both will increase

D

R will increase while H and T both will also increase

Question 38: Palette 38/60

Allen MCQ

Suppose a player hits several baseballs. Which baseball will be in the air for the longest time?

A

The one with the farthest range.

B

The one which reaches maximum height.

C

The one with the greatest initial velocity.

D

The one leaving the bat at $45^{\circ}$ with respect to the ground.

Question 39: Palette 39/60

Allen MCQ

A ball is hit by a batsman at an angle of $37^{\circ}$ as shown in figure. The man standing at P should run at what minimum velocity so that he catches the ball before it strikes the ground. Assume that height of man is negligible in comparison to maximum height of projectile.

A

3 m/s

B

5 m/s

C

9 m/s

D

12 m/s

Question 40: Palette 40/60

Allen MCQ

A particle P is projected from a point on the surface of smooth inclined plane (see figure). Simultaneously another particle Q is released on the smooth inclined plane from the same position. P and Q collide after t = 4 s. The speed of projection of P is :-

A

5 m/s

B

10 m/s

C

15 m/s

D

20 m/s

Question 41: Palette 41/60

Allen MCQ

A trolley is moving horizontally with a constant velocity of v with respect to earth. A man starts running from one end of the trolley with a velocity 1.5 v with respect to trolley. After reaching the opposite end, the man returns back and continues running with a velocity of 1.5 v w.r.t. the trolley in the backward direction. If the length of the trolley is L then the displacement of the man with respect to earth during the process will be :-

A

$2.5L$

B

$1.5L$

C

$\frac{5L}{3}$

D

$\frac{4L}{3}$

Question 42: Palette 42/60

Allen MCQ

An elevator car (lift) is moving upward with uniform acceleration of $2 \, m/s^{2}$ . At the instant, when its velocity is $2 \, m/s$ upwards a ball is thrown upward from its floor. The ball strikes back the floor $2 \, s$ after its projection. Find the velocity of projection of the ball relative to the lift.

A

$10 \, m/s \uparrow$

B

$10 \, m/s \downarrow$

C

$12 \, m/s \uparrow$

D

$12 \, m/s \downarrow$

Question 43: Palette 43/60

Allen MCQ

A flag is mounted on a car moving due North with velocity of 20 km/hr. Strong winds are blowing due East with velocity of 20 km/hr. The flag will point in direction :-

A

East

B

North-East

C

South-East

D

South-West

Question 44: Palette 44/60

Allen MCQ

Wind is blowing in the north direction at speed of 2 m/s which causes the rain to fall at some angle with the vertical. With what velocity should a cyclist drive so that the rain appears vertical to him:

A

2 m/s south

B

2 m/s north

C

4 m/s west

D

4 m/s south

Question 45: Palette 45/60

Allen MCQ

A man is crossing a river flowing with velocity of 5 m/s. He reaches a point directly across the river at a distance of 60 m in 5 sec. His velocity in still water should be :-

A

$12m / s$

B

$13m / s$

C

$5m / s$

D

$10m / s$

Question 46: Palette 46/60

Allen MCQ

A particle is ejected from the tube at $A$ with a velocity $v$ at an angle $\theta$ with the vertical $y$ -axis. A strong horizontal wind gives the particle a constant horizontal acceleration $a$ in the $x$ -direction. If the particle strikes the ground at a point directly under its released position and the downward $y$ -acceleration is taken as $g$ then

A

$h = \frac{2v^{2}\sin\theta\cos\theta}{a}$

B

$h = \frac{2v^{2}\sin\theta\cos\theta}{g}$

C

$h = \frac{2v^2}{g}\sin \theta (\cos \theta +\frac{a}{g}\sin \theta)$

D

$h = \frac{2v^2}{a}\sin \theta (\cos \theta +\frac{g}{a}\sin \theta)$

Question 47: Palette 47/60

Allen MCQ

A stone is projected from point P on the inclined plane with velocity $v_{0} = 10 \, m/s$ directed perpendicular to the plane. The time taken by the stone to strike the horizontal ground S is (Given $PO = \ell = 10 \, meter$ )

A

1.5 sec

B

1.4 sec

C

2 sec

D

2.3 sec

Question 48: Palette 48/60

Allen MCQ

On a particular day rain drops are falling vertically at a speed of 5 m/s. A man holding a plastic board is running to escape from rain as shown. The lower end of board is at a height half that of man and the board makes $45^{\circ}$ with horizontal. The maximum speed of man so that his feet does not get wet, is

A

5 m/s

B

$5\sqrt{2}$ m/s

C

$5/\sqrt{2}$ m/s

D

zero

Question 49: Palette 49/60

Allen MCQ

A 2 m wide truck is moving with a uniform speed of 8 m/s along a straight horizontal road. A pedestrian starts crossing the road at an instant when the truck is 4 m away from him. The minimum constant velocity with which he should run to avoid an accident is :-

A

$1.6\sqrt{5}$ m/s

B

$1.2\sqrt{5}$ m/s

C

$1.2\sqrt{7}$ m/s

D

$1.6\sqrt{7}$ m/s

Question 50: Palette 50/60

Allen MSQ

The position of a particle with time is given by $(x,y) = (8t^{2},3)$ for $t\leq t_1 = (8tt_1,3)$ for $t > t_{1}$ Choose the CORRECT alternative.

A

Particle moves along a straight line parallel to x axis.

B

C

D

Question 51: Palette 51/60

Allen MSQ

The position-time $(x-t)$ graphs for two children A and B returning from their school O to their homes P and Q respectively along straight line path (taken as x axis) are shown in figure below. Choose the CORRECT statement (s):

A

A lives closer to the school than B

B

A starts from the school earlier than B

C

A and B have equal average velocities from 0 to $t_{0}$ .

D

B overtakes A on the way

Question 52: Palette 52/60

Allen MSQ

A ball is thrown from ground such that it just crosses two poles of equal height kept 80 m apart. The maximum height attained by the ball is 80 m. When the ball passes the first pole, its velocity makes $45^{\circ}$ with horizontal. The correct alternatives is/are :- $(g = 10 \, m/s^{2})$

A

Time interval between the two poles is 4 s.

B

Height of the pole is 60 m.

C

Range of the ball is 160 m.

D

Angle of projection is $\tan^{-1}

Question 53: Palette 53/60

Allen MSQ

A projectile is thrown with speed u into air from a point on the horizontal ground at an angle $\theta$ with horizontal. If the air exerts a constant horizontal resistive force on the projectile then select correct alternative(s).

A

At the farthest point, the velocity is horizontal.

B

The time for ascent equals the time for descent.

C

The path of the projectile may be parabolic.

D

The path of the projectile may be a straight line.

Question 54: Palette 54/60

Allen MSQ

A block is thrown horizontally with a velocity of 2 m/s (relative to ground) on a belt, which is moving with velocity 4 m/s in opposite direction of the initial velocity of block. If the block stops slipping on the belt after 4 s it was dropped then choose the correct statement(s) :-

A

Displacement with respect to ground is zero after 2.66 s and magnitude of displacement with respect to ground is 12 m after 4 s.

B

Magnitude of displacement with respect to ground in 4 s is 4 m.

C

Magnitude of displacement with respect to belt in 4 s is 12 m.

D

Displacement with respect to ground is zero in 8/3 s.

Question 55: Palette 55/60

Allen MSQ

A cubical box dimension L = 5/4 meter starts moving with an acceleration $\vec{a} = 0.5 m/s^{2} \hat{i}$ from the state of rest. At the same time, a stone is thrown from the origin with velocity $\vec{V} = v_{1}\hat{i} + v_{2}\hat{j} - v_{3}\hat{k}$ with respect to earth. Acceleration due to gravity $\vec{g} = 10m/s^{2}(-\hat{j})$ . The stone just touches the roof of box and finally falls at the diagonally opposite point then :

A

$v_{1} = \frac{3}{2}$

B

$v_{2} = 5$

C

$v_{3}=\frac{5}{4}$

D

$v_{3} = \frac{5}{2}$

Question 56: Palette 56/60

Allen MCQ

PARAGRAPH FOR QUESTION NO. 11 TO 13 In the figure shown there is a long horizontal bridge over a river 75 m high from water surface. A strong man throws a stone in the parallel plane of the bridge. A observer in a car travelling on the bridge finds the stone going pass by the car while ascending and also while descending between two points on the road 30 m away. The car is travelling at a speed of 15 m/s. The stone is thrown from the bank of river just at the same level of water. What is the angle the velocity makes with the bridge when it goes past the car while ascending?

A

$30^{\circ}$

B

$45^{\circ}$

C

$\tan^{-1}\left(\frac{2}{3}\right)$

D

$\tan^{-1}\left(\frac{3}{2}\right)$

Question 57: Palette 57/60

Allen MCQ

PARAGRAPH FOR QUESTION NO. 11 TO 13 In the figure shown there is a long horizontal bridge over a river 75 m high from water surface. A strong man throws a stone in the parallel plane of the bridge. A observer in a car travelling on the bridge finds the stone going pass by the car while ascending and also while descending between two points on the road 30 m away. The car is travelling at a speed of 15 m/s. The stone is thrown from the bank of river just at the same level of water. Horizontal distance AB travelled by stone is :-

A

0 m

B

75 m

C

120 m

D

240 m

Question 58: Palette 58/60

Allen MCQ

PARAGRAPH FOR QUESTION NO. 11 TO 13 In the figure shown there is a long horizontal bridge over a river 75 m high from water surface. A strong man throws a stone in the parallel plane of the bridge. A observer in a car travelling on the bridge finds the stone going pass by the car while ascending and also while descending between two points on the road 30 m away. The car is travelling at a speed of 15 m/s. The stone is thrown from the bank of river just at the same level of water. What is the distance between car and stone at the instant when particle reaches at point B?

A

0 m

B

75 m

C

120 m

D

240 m

Question 59: Palette 59/60

Allen MCQ

PARAGRAPH FOR QUESTION 14 AND 15 From the ground level, a ball is to be shot with a certain speed. Graph shows the range (R) of the particle versus the angle of projection from horizontal ( $\theta$ ). Values of $\theta_{1}$ and $\theta_{2}$ are

A

$53^{\circ}$ and $37^{\circ}$

B

$26.5^{\circ}$ and $63.5^{\circ}$

C

$18.5^{\circ}$ and $71.5^{\circ}$

D

$15^{\circ}$ and $75^{\circ}$

Question 60: Palette 60/60

Allen MCQ

PARAGRAPH FOR QUESTION 14 AND 15 From the ground level, a ball is to be shot with a certain speed. Graph shows the range (R) of the particle versus the angle of projection from horizontal ( $\theta$ ). The corresponding time of flight vs $\theta$ graph is :-

A

B

C

D