Browse and search thousands of solved questions for your preparation.
Free questions with full explanations — locked behind signup to protect quality.
The most acidic compound among the following is:
A missile is fired for maximum range with an initial velocity of $20 \text{ m/s}$. If $g=10 \text{ m/s}^2$, the range of the missile is:
Two points are located at a distance of $10 \text{ m}$ and $15 \text{ m}$ from the source of oscillation. The period of oscillation is $0.05 \text{ s}$ and the velocity of the wave is $300 \text{ m/s}$. What is the phase difference between the oscillations of two points?
A particle moves in the x-y plane according to rule $x = a \sin \omega t$ and $y = a \cos \omega t$. The particle follows:
The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is:
Consider a drop of rainwater having a mass of $1\text{ g}$ falling from a height of $1\text{ km}$. It hits the ground with a speed of $50\text{ m/s}$. Take $g$ as constant with a value $10\text{ m/s}^2$. The work done by the (i) gravitational force and the (ii) resistive force of air is:
The position vector of a particle $\vec{R}$ as a function of time $t$ is given by: $\vec{R} = 4\sin(2\pi t)\hat{i} + 4\cos(2\pi t)\hat{j}$, where $R$ is in meters, $t$ is in seconds and $\hat{i}, \hat{j}$ denote unit vectors along x and y-directions, respectively. Which one of the following statements is **wrong** for the motion of the particle?
A body of mass $4m$ is lying in the $xy$-plane at rest. It suddenly explodes into three pieces. Two pieces each of mass $m$ move perpendicular to each other with equal speeds $v$. The total kinetic energy generated due to the explosion is:
Two particles A and B move with constant velocities $\mathbf{v}_1$ and $\mathbf{v}_2$. At the initial moment, their position vectors are $\mathbf{r}_1$ and $\mathbf{r}_2$ respectively. The condition for particles A and B for their collision is:
The wave described by $y = 0.25\sin(10\pi x - 2\pi t)$, where $x$ and $y$ are in metres and $t$ in seconds, is a wave traveling along the:
In the hydrocarbon $\overset{6}{C}H_3-\overset{5}{C}H=\overset{4}{C}H-\overset{3}{C}H_2-\overset{2}{C}\equiv\overset{1}{C}H$, the state of hybridisation of carbons 1, 3 and 5 are in the following sequence:
A car turns at a constant speed on a circular track of radius $100 \text{ m}$, taking $62.8 \text{ s}$ for every circular lap. The average velocity and average speed for each circular lap, respectively, is:
A string is stretched between fixed points separated by $75.0 \text{ cm}$. It is observed to have resonant frequencies of $420 \text{ Hz}$ and $315 \text{ Hz}$. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is:
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 $19.4 \text{ m/s}$ 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 $330 \text{ m/s}$), is:
The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe $L$ metre long. The length of the open pipe will be
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:
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:
The products A and B in the following reaction sequence are :