JEE Advanced 2020 Paper 2 Offline

MCQ (More than One Correct Answer)

-2

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_x = 1 ms^-2 implies that when the particle is at the origin, a_y = 1 ms^-2

a_x = 0 implies a_y = 1 ms^-2 at all times

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

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

IIT-JEE 1999 Screening

MCQ (More than One Correct Answer)

-0.75

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

the path of the particle is an ellipse

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

the acceleration of the particle is always directed towards a focus

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

IIT-JEE 1993

MCQ (More than One Correct Answer)

-0.5

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:

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

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

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

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

IIT-JEE 1982

MCQ (More than One Correct Answer)

-0.75

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

zero

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

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

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