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A source of sound S emitting waves of frequency $100 \text{ Hz}$ and an observer O are located at some distance from each other. The source is moving with a speed of $19.4 \text{ ms}^{-1}$ at an angle of $60^\circ$ with the source-observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air $330 \text{ ms}^{-1}$), is:
A string of length $l$ is fixed at both ends and is vibrating in second harmonic. The amplitude at antinode is $2\text{ mm}$. The amplitude of a particle at a distance $l/8$ from the fixed end is:
The engine of a motorcycle can produce a maximum acceleration of $5 \text{ m/s}^2$. Its brakes can produce a maximum retardation of $10 \text{ m/s}^2$. What is the minimum time in which it can cover a distance of $1.5 \text{ km}$?
A man throws balls with the same speed vertically upwards one after the other at an interval of $2 \text{ seconds}$. What should be the speed of the throw so that more than two balls are in the sky at any time? (Given $g=9.8 \text{ m/s}^2$)
An aeroplane is flying horizontally with a velocity $u = 600\text{ km/h}$ at a height of $1960\text{ m}$. When it is vertically at a point $A$ on the ground, a bomb is released from it. The bomb strikes the ground at point $B$. The distance $AB$ is:
An object is thrown along a direction inclined at an angle of $45^\circ$ with the horizontal direction. The horizontal range of the particle is equal to:
A ball is projected with kinetic energy $E$ at an angle of $45^\circ$ to the horizontal. At the highest point during its flight, its kinetic energy will be:
A particle shows a distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point:
A small telescope has an objective of focal length $140\text{ cm}$ and an eyepiece of focal length $5.0\text{ cm}$. The magnifying power of the telescope for viewing a distant object is:
Two bodies are projected with the same velocity. If one is projected at an angle of $30^{\circ}$ and the other at an angle of $60^{\circ}$ to the horizontal, the ratio of the maximum heights reached is:
A car starts from rest and accelerates at $5 \text{ m/s}^2$. At $t=4 \text{ s}$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t=6 \text{ s}$? (Take $g=10 \text{ m/s}^2$)
A particle moving in a circle of radius $R$ with a uniform speed takes a time $T$ to complete one revolution. If this particle were projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it equals $4R$. The angle of projection, $\theta$ is then given by:
A bullet is fired from a gun at the speed of $280 \text{ m s}^{-1}$ in the direction $30^{\circ}$ above the horizontal. The maximum height attained by the bullet is: ($g=9.8 \text{ m s}^{-2}, \sin 30^{\circ}=0.5$)
The graph that shows the correct variation of $\frac{1}{v}$ with $\frac{1}{u}$ for a concave mirror, where $u$ is the object distance and $v$ is the image distance, is:
A particle moves a distance x in time t according to equation x = (t + 5)⁻¹. The acceleration of the particle is proportional to:
Two cars P and Q start from a point at the same time in a straight line and their positions are represented by $x_P(t) = at + bt^2$ and $x_Q(t) = ft - t^2$. At what time do the cars have the same velocity?
The distance travelled by a particle starting from rest and moving with an acceleration 4/3 ms⁻², in the third second is
A particle covers half of its total distance with speed v₁ and the rest half distance with speed v₂. Its average speed during the complete journey is
A lift is going up. The total mass of the lift and the passenger is 1500 kg. The variation in the speed of the lift is as given in the graph. The height to which the lift takes the passenger is
If the velocity of a particle is $v = At + Bt^2$, where $A$ and $B$ are constants, then the distance travelled by it between 1 s and 2 s is: