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Two speakers $S_1\text{and}{S}_2$ are derived from the same amplifier and placed at the same distance from $x$-axis as shown in figure. The speakers vibrate in phase at $680\text{Hz}$. A man stands at a point on the $x$-axis at a very large distance from the origin and starts moving parallel to the $y$-axis. The speed of sound is $340\text{m/s}$. Then, at what angle $\theta$ with the $x-$ axis will the intensity of sound drop to a minimum for the first time?

A body started with velocity of $12\text{m/s}$ and moving with an acceleration of $2{\text{m/s}}^2$. The distance travelled by the body in the $8^{\text{th}}$ second is

A flywheel is rotating about a fixed axis passing through its COM. It has a kinetic energy of $420\text{Joules}$ when its angular speed is $20\text{rad/s}$. The moment of inertia of the wheel about the fixed axis is

A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train A, records a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train B, he records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train B to that of train A is

One fourth length of a uniform rod of length 2l and mass m is placed on a horizontal table and the rod is held horizontal. The rod is released from rest. Find the normal reaction on the rod as soon as the rod is released

A force $F=(5\sqrt{3}\hat{i}+5\hat{j})\text{N}$ is acting on a body at point $(1,1)\text{m}$. Calculate torque of this body w.r.t to point $(1,0)\text{m}$

Two bodies of masses $3\text{kg}$ and $5\text{kg}$ are moving with velocities $25\text{m/s}$ and $15\text{m/s}$ towards each other due to mutual force of attraction as shown in the figure. What is the velocity of their center of mass?

The capacitance of a parallel plate air condenser is 2 $\mu$ F. A dielectric of constant 4 is introduced as shown in the figure to fill half the space between the parallel plates. Its capacitance now will be?

A projectile is thrown from the base of an incline of ${30}^{\circ }$ as shown in the figure. It is thrown at an angle of ${60}^{\circ }$ from the horizontal direction at a speed of $10\text{m/s}$. The total time of flight is: $(g=10{\text{m/s}}^2)$

A tuning fork $A$ when sounded with a tuning fork $B$ of frequency $480\text{Hz}$ produces $5$ beats per second. When the prongs of $A$ are loaded with wax, it gives $3$ beats per second. The original frequency of the tuning fork $A$ is:

A stone of mass of 16 kg is attached to a string 144 m long and is whirled in a horizontal circle. The maximum tension the string can withstand is 16 Newton. The maximum velocity of revolution that can be given to the stone without breaking it, will be

Find the minimum horizontal force $\left(F\right)$ needed to start the slipping at any part of the system. (Take $g=10m/s^2$)

Two point charges each of +1$\mu$C are at a distance of 3 m apart. The work done in bringing the two charges closer to a distance 1 m apart is

A body of mass $25\text{kg}$ slides down a smooth incline as shown. Find the work done by force of gravity till the body reaches the bottom of the inclined plane ($g=10{\text{ms}}^{-2}$)

A flexible pipe of length $l$ connects two points A and B in space having altitude difference $h$ as shown in figure. A rope passed through the pipe is fixed at point A. What will be the acceleration of the rope as soon as it got released ? Assume that friction is absent inside the pipe.

A solid sphere of uniform density and radius $R$ applies a gravitational force of attraction equal to $F_1$ on a particle placed at a distance $2R$ from the centre of the sphere. A spherical cavity of radius $\frac{R}{2}$ is now made in the sphere as shown in the figure. The sphere with the cavity now applies a gravitational force $F_2$ on the same particle. The ratio $\frac{F_1}{F_2}$ is

The equivalent resistance between points $A$ and $B$ is

Angular width (b) of central maximum of a diffraction pattern on a single slit does not depend upon

[DCE 2000; 01]

A man applies a constant force of $5\text{N}$ on an object of mass $2\text{kg}$ and displaces it by $5\text{m}$. The object was initially at rest. The final velocity of object is

The fraction of atoms of radioactive element that decays in 6 days is $\frac{7}{8}$. The fraction that decays in 10 days will be

A fan is running at $300\text{rpm}$. It is switched off. It comes to rest by uniformly decreasing its angular speed in $10$ seconds. The total number of revolutions in this period are :-

Assuming that the mass $m$ of the largest stone that can be moved by a flowing river depends upon the velocity $v$ of the water, its density $\rho$ and the acceleration due to gravity is $g$. Here, $m$ is directly proportional to

A uniform rod of mass $M$ and length $L$ is pivoted at one end such that it can rotate in a vertical plane. There is negligible friction at the pivot. The free end of the rod is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle $\theta$ with the vertical is

A bullet of mass $20\text{g}$ and moving with $600\text{m/s}$ collides with a block of mass $4\text{kg}$ hanging with the string. What is velocity of bullet when it comes out of block, if block rises to height $0.2\text{m}$ after collision?

(Take $g=10{\text{m/s}}^2$)

A wheel is rotating at $900\text{rpm}$ about its axis. When power is cut off, it comes to rest in $60\text{s}$. The angular retardation is $\left(rad/s^2\right)$

A boy stretches a stone against the rubber tape of a catapult or 'gulel' (a device used to detach mangoes from the tree by boys in Indian villages) through a distance of $24\text{cm}$ before leaving it. The tape returns to its initial normal position, accelerating the stone over the stretched length. The stone leaves the gulel with a speed of $2.2\text{m/s}$. Assuming that acceleration is constant while the stone was being pushed by the tape, find the magnitude.

If a uniform rod made of material having poisson's ratio $0.5$, suffers longitudinal strain of $2\times {10}^{-3}$, what is the percentage increase in volume?

A source of sound of frequency $50H_Z$ is producing longitudinal waves in air. The amplitude of vibrations of air particles is 5mm and the speed of the wave is $330m{s}^{-1}$. Write the equation of the wave.

Figure shows a small block of mass 'm' which is started with a speed 'v' on the horizontal part of the bigger block of mass 'M' placed on a horizontal floor. The curved part of the surface shown is semicircular. All the surfaces are frictionless. Find the speed of the bigger block when the smaller block reaches the point A of the surface.

The displacement of a body in $6s$ starting from rest with an acceleration of $15{\text{cm/s}}^2$ is

At what temperature will the speed of sound in hydrogen be the same as in oxygen at 100${}^{\circ }$ C? Molar masses of oxygen and hydrogen are in the ratio 16:1.

In the figure shown below, a ball is moving with a velocity of $u_1=7\text{m/s}$ in downward direction towards a surface, while the surface is moving in upward direction with a constant velocity $u_2=3\text{m/s}$. If the coefficient of restitution has value of $e=0.8$ and after collision with the surface, the ball rebounds back with velocity $v\text{m/s}$, find the rebound velocity. (Neglect all external forces)

A particle's motion is given by $s=a(t+b(e^{(-\frac{t}{b})}-1))$, where ($s$ is in metre, $a$ and $b$ are constants and $t$ is in sec). What will be the instantaneous speed of the particle at $t=\infty$

On a highway, the maximum speed of vehicles is $50\text{m/s}$. The material of the road provides a coefficient of static friction ${\mu }_s=0.35$. If the highway has a circular turn with a radius of curvature $90\text{m}$, then what should be the banking angle $\left(\theta \right)$ for this turn to ensure safe driving ?

A ball collides with smooth fixed inclined plane of inclination $\theta$ after falling vertically through a distance $h\text{m}$. If it moves horizontally just after the impact, then the coefficient of restitution is

What is the effective capacitance between points $X$ and $Y?$

The potential energy of a system is represented as shown in the figure. The force acting on the system will be represented by

Find the most probable speed $\left(V_{mp}\right)$ of nitrogen gas molecules at $T=560\text{K}$. (Given: Numerical value of $\sqrt{R}$ is $2.88$, where $R$ is gas constant)

If kinetic energy of a body is given as $k=Cx$ where $C$ is constant and $x$ is distance from origin then, dimensional formula for $C$ is

To keep system of 3 charges in equilibrium as shown in figure, $q_0$ must be

A force of magnitude $12\text{N}$ acts on a particle in the direction of a vector $\overrightarrow{A}=2\hat{i}-4\hat{j}+4\hat{k}$, which results in the change of position of the particle from $(3,3,5)\text{m}$ to $(2,-1,4)\text{m}$. The work done by the force is (in Joule )

An electron and a proton are at a distance of $1\dot{A}$. The dipole moment will be $(C\times m)$

Two cars are moving in the same direction with a speed of $30{\text{km h}}^{-1}$. They are separated from each other by $5\text{km}$. Third car moving in the opposite direction meets the two cars after an interval of 4 minutes. What is the speed of the third car?

A boy of mass $60\text{kg}$. He wants to swim in a river with the help of a wooden log. If relative density of wood is $0.6$, what is the minimum volume of wooden log?

(density of river water is $1000{\text{kg/m}}^3$)

The following figure shows the displacement versus time graph for two particles $A$ and $B$ executing simple harmonic motions. The ratio of their maximum velocities (respectively) is