Question 1: Palette 1/15

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 $y = {{{x^2}} \over 2}$. 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 = 1s, the angle between the particle's velocity and the x axis is 45$^\circ$

Question 2: Palette 2/15

JEE Advanced 2017 MCQ

Three vectors $\overrightarrow P ,\overrightarrow Q $ and $\overrightarrow R $ are shown in the figure. Let $S$ be any point on the vector $\overrightarrow R .$ The distance between the points $P$ and $S$ is $b\left| {\overrightarrow R } \right|.$ The general relation among vectors $\overrightarrow P ,\overrightarrow Q $ and $\overrightarrow S $ is :

A

$\overrightarrow S = \left( {1 - b} \right)\overrightarrow P + b\overrightarrow Q $

B

$\overrightarrow S = \left( {b - 1} \right)\overrightarrow P + b\overrightarrow Q $

C

$\overrightarrow S = \left( {1 - {b^2}} \right)\overrightarrow P + b\overrightarrow Q $

D

$\overrightarrow S = \left( {1 - b} \right)\overrightarrow P + {b^2}\overrightarrow Q $

Question 3: Palette 3/15

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 $\left( {{1 \over \rho } {{d\rho } \over {dt}}} \right)$ is constant. The velocity $v$ of any point on the surface of the expanding sphere is proportional to

A

$R$

B

${R^3}$

C

${1 \over R}$

D

${R^{2/3}}$

Question 4: Palette 4/15

JEE Advanced 2008 MCQ

STATEMENT-1: For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.

STATEMENT-2: If the observer and the object are moving at velocities ${\overrightarrow v _1}$ and ${\overrightarrow v _2}$ respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is ${\overrightarrow v _2}$ - ${\overrightarrow v _1}$.

A

STATEMENT - 1 is True, STATEMENT - 2 is True; STATEMENT - 2 is a correct explanation for STATEMENT ,- 1

B

STATEMENT - 1 is True, STATEMENT - 2 is True; STATEMENT - 2 is NOT a correct explanation for STATEMENT - 1

C

STATEMENT - 1 is True, STATEMENT - 2 is False

D

STATEMENT - 1 is False, STATEMENT - 2 is True

Question 5: Palette 5/15

JEE Advanced 2007 MCQ

While the piston is at a distance 2L from the top, the hole at the top is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top is :

A

$\left( {{{2{P_0}\pi {R^2}} \over {\pi {R^2}{P_0} + Mg}}} \right)(2L)$

B

$\left( {{{{P_0}\pi {R^2} - Mg} \over {\pi {R^2}{P_0}}}} \right)(2L)$

C

$\left( {{{{P_0}\pi {R^2} + Mg} \over {\pi {R^2}{P_0}}}} \right)(2L)$

D

$\left( {{{{P_0}\pi {R^2}} \over {\pi {R^2}{P_0} - Mg}}} \right)(2L)$

Question 6: Palette 6/15

JEE Advanced 2004 MCQ

A body starts from rest at time t = 0, the acceleration time graph is shown in the figure. The maximum velocity attained by the body will be

A

110 m/s

B

55 m/s

C

650 m/s

D

550 m/s

Question 7: Palette 7/15

JEE Advanced 2004 MCQ

A particle starts sliding down a frictionless inclined plane. If S_n is the distance traveled by it from time t = n - 1 sec to t = n sec, the ratio S_n / S_n+1 is

A

${{2n - 1} \over {2n + 1}}$

B

${{2n + 1} \over {2n}}$

C

${{2n} \over {2n + 1}}$

D

${{2n + 1} \over {2n - 1}}$

Question 8: Palette 8/15

JEE Advanced 1999 MSQ

The coordinates of a particle moving in a plane are given by x(t) = a cos(pt) and y(t) = b sin(pt) where a, b (< a) and p are positive constants of approprite dimensions. Then

A

the path of the particle is an ellipse

B

the velocity and acceleration of the particle are normal to each other at t = ${\pi \over {2p}}$

C

the acceleration of the particle is always directed towards a focus

D

the distance traveled by the particle in time interval t = 0 to t = ${\pi \over {2p}}$ is a

Question 9: Palette 9/15

JEE Advanced 1993 MSQ

A particle of mass m moves on the x-axis as follows: it starts from rest at t = 0 from the point x = 0, and come to rest at t = 1 at the point x = 1. NO other information is available about its motion at intermediate times ( 0 < t < 1 ). If $\alpha $ denotes the instantaneous acceleration of the particle, then:

A

$\alpha $ cannot remain positive for all t in the interval $0 \le t \le 1$

B

$\left| \alpha \right|$ cannot exceed 2 at any point in its path.

C

$\left| \alpha \right|$ must be $ \ge $ 4 at some point or points in its path.

D

$\alpha $ must be change sign during the motion, but no other assertion can be made with the information given.

Question 10: Palette 10/15

JEE Advanced 1988 MCQ

A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is

A

1

B

3

C

4

D

$\sqrt {41} $

Question 11: Palette 11/15

JEE Advanced 1985 MCQ

Two identical trains are moving on rails along the equator on the earth in opposite directions with the same speed. They will exert the same pressure on the rails.

A

TRUE

B

FALSE

Question 12: Palette 12/15

JEE Advanced 1984 MCQ

A projectile fired from the ground follows a parabolic path. The speed of the projectile is minimum at the top of its path.

A

TRUE

B

FALSE

Question 13: Palette 13/15

JEE Advanced 1983 MCQ

A river is flowing from west to east at a speed of 5 meters per minute. A man on the south bank of the river, capable of swimming at 10 meters per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction

A

due north

B

$30^\circ $ east of north

C

$30^\circ $ west of north

D

$60^\circ $ east of north

Question 14: Palette 14/15

JEE Advanced 1983 MCQ

Two balls of different masses are thrown vertically upwards with the same speed. They pass through the point of projection in their downward motion with the same speed. (Neglect air resistance)

A

TRUE

B

FALSE

Question 15: Palette 15/15

JEE Advanced 1982 MCQ

A particle is moving eastwards with a velocity of 5 m/s. In 10s the velocity changes to 5 m/s northwards. The average acceleration in this time is

A

zero

B

${1 \over {\sqrt 2 }}m/{s^2}$ towards north-west

C

${1 \over {\sqrt 2 }}m/{s^2}$ towards north-east

D

${1 \over 2}m/{s^2}$ towards north