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One $\text{mole}$ of an ideal monoatomic gas is initially at $500\text{K}$. If $300\text{J}$ of heat is added at constant volume, the final temperature of the gas is
(Assume $R=8\text{J/mol K}$)

A uniform solid sphere is placed on a smooth horizontal surface. An impulse $I$ is given horizontally to the sphere at a height $h=\frac{4R}{5}$ above the centre line. ${}^{\prime }{m}^{\prime }$ and ${}^{\prime }{R}^{\prime }$ are the mass and radius of the sphere respectively.


Find angular velocity $\left(\omega \right)$ of the sphere and linear velocity $\left(v\right)$ of the centre of mass of the sphere after the impulse.

Initially key was placed on $\left(1\right)$ till the capacitor got fully charged. Key is placed on $\left(2\right)$ at $t=0$. The time when the energy in both capacitor and inductor will be same is

A $5\text{kg}$ block slides down an inclined plane, having angle of inclination ${30}^{\circ }$ from horizontal. Find the acceleration (${\text{m/s}}^2$) of block, if the coefficient of kinetic friction is ${\mu }_k=\frac{1}{2\sqrt{3}}$. Take $g=10{\text{m/s}}^2$ .

Two blocks with masses $m_1=3\text{kg}$ and $m_2=4\text{kg}$ are touching each other on a fricionless surface. If a force of $5\text{N}$ is applied on $m_1$ as shown in figure. The acceleration of each block is

Calculate the focal length of a reading glass of a person if this distance of distinct vision is 75 cm.

Calculate the weight of 0.1 moles of Na_{​​​​​2}​CO₃ ?

An ideal black body at room temperature is thrown into a furnace. It is observed that

A galvanometer has coil resistance $100\Omega$ and gives a full scale deflection for $30\text{mA}$ current . If it is to work as a voltmeter of $30\text{V}$ range, the resistance required to be added will be

An air chamber of volume ‘V’ and pressure ‘P’ has a neck area of cross-section ‘A’ into which a ball of mass ‘m’ just fits and can move up and down without friction. When the ball is pressed down a little and released it executes S.H.M. The time period of oscillations of the ball is (assuming pressure – volume variations to be isothermal). ($p_0$ = atm pressure)

If an electron revolves around a proton, then its time period $T$ is ($R=$ radius of orbit)-

If $\underset{\frac{\pi }{2}}{\overset{a}{\int }}\sin xdx=\frac{1}{2}$, then $a=?$

The coil of a moving coil voltmeter is 40 mm long and 30 mm wide and has 100 turns on it. The control spring exerts a torque of $240\times {10}^{-6}N-m$ when the deflection is 100 divisions on full scale. If the flux density of the magnetic field in the airgap is $1.0Wb/m^2$, the resistance that must be put in series with the coil to give one volt per division is ________$\Omega$. (Assume resistance of the voltmeter coil is negligible)

Two identical discs of the same radius $R$ are rotating about the axes in opposite directions at the same angular speed $\omega$ . The discs are in the same horizontal plane. At the time $t=0$, the point $P$ and $Q$ are facing each other, as shown in the figure. The relative speed between the two points $P$ and $Q$ is $v_r$. In each period of the rotation $\left(T\right)$ of the disc, $v_r$ as a function of the time is best represented by

Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are

[IIT-JEE 1988; RPMT 1995; AIIMS 1997; MP PMT 1997;MP PET 1999; BHU 2002; KCET 2000, 05]

The threshold frequency for certain metal is ${\nu }_0.$ When light of frequency $2{\nu }_0$ is incident on it the maximum velocity of photo electrons is $4\times {10}^6{\text{ms}}^{-1}.$ If the frequency of incident radiation is increased to $4{\nu }_0$, then the maximum velocity of photo electrons will be-

A parallel plate capacitor of capacitance $90\text{pF}$ is connected to a battery of emf $20\text{V}$. If a dielectric material of dielectric constant $K=\frac{5}{3}$ is inserted between the plates, the magnitude of induced charge will be:

A particle is projected from a point O with a velocity u in a direction making an angle $\alpha$ upward with the horizontal. After some time at point P it is moving at right angle with its initial direction of projection. The time of flight from O to P is

Fundamental Period of the function $f\left(\theta \right)=\frac{\sin \theta +\sin 2\theta }{\cos \theta +\cos 2\theta },\theta \in R-\left\{\right(2n+1)\pi ,2m\pi \pm \frac{\pi }{3},n,m\in Z\}$ is

In the given circuit, if no current flows through the galvanometer when the key $K$ is closed, the bridge is balanced. The balancing condition for bridge is

Wavelength of light of frequency $100$ $Hz$ is,

The ratio of intensity between two coherent sound sources is $4:1$. When they interfere in space, the difference of loudness between points of maximum and minimum intensity in decibel ($dB$) is

Two stones are thrown up simultaneously with initial speeds $u_1$ and $u_2(u_2>u_1)$. They hit the ground after $6\text{s}$ and $10\text{s}$ respectively. Which graph correctly represents the time variation of, $\Delta x=(x_2-x_1)$, the relative position of the second stone with respect to the first upto $t=10\text{s}$?

Assume that the stones do not rebound after hitting the ground.

In Wheat stones network P = 2 $\Omega$, Q = 2 $\Omega$ , R = 2$\Omega$ and S = 3 $\Omega$ . The resistance with which S is to shunted in order that the bridge may be balanced is

Find the mass $\left(m\right)$ of the rocket as a function of time, if it moves with a constant acceleration $a$ in the absence of external force. The gas escapes with a constant velocity $u$ relative to the rocket and its initial mass was $m_0$.

A ring of radius $R=50\text{cm}$ having uniformly distributed charge $Q=2\text{C}$ is mounted in the middle of a rod suspended by two identical strings. The tension in strings in equilibrium is $T_o=2\text{N}$. Now a vertical magnetic field is switched on, and the ring is rotated at constant angular velocity $\omega$. Find the maximum $\omega$ with which the ring can be rotated if the strings can withstand a maximum tension of $3\text{N}$. (Take $D=1\text{m}$ and $B=0.05\text{T}$)

The magnitude of the resultant of two equal vectors is equal to the magnitude of either vector. The angle between the resultant and either vector will be

A tuning fork vibrates at $250\text{Hz}$. Find the length of the shortest closed organ pipe that will resonate with the tuning fork.
[Speed of sound in air $=340\text{m/s}$]