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A vertical cylinder with a massless piston filled with one mole of an ideal gas. The piston can move freely without friction. The piston is slowly raised so that the gas expands isothermally at temperature $300K.$ The amount of work done in increasing the volume two times is $(R=\frac{25}{3}\text{J/mol-K},\ln 2=0.7)$

In the common base mode of a transistor, the collector current is 5.488 mA for an emitter current of 5.60 mA. The value of the base current amplification factor $\left(\beta \right)$ will be

Two masses $m$ and $m/2$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $K$ at the centre of mass of the rod - mass system as shown in the figure.
Because of torsional constant $K$, the restoring torque is $\tau =K\theta$ for angular displacement $\theta .$
If the rod is rotated by ${\theta }_{\circ }$ and released so that rod oscillates. The tension in the rod, when it passes through its mean position will be

A spherical ball contract in volume of0.01% when subjected to non uniform pressure of 100 atmosphere. What is the bulk modulus of it's material in CGS Unit?

What is the radius of curvature of the parabola traced out by the projectile in the previous problem at a point where the particle velocity makes an angle $\frac{\theta }{2}$ with the horizontal ?

A uniform stick of length $l$ is hinged so as to rotate about a horizontal axis perpendicular to the stick, at a distance ${}^{\prime }{x}^{\prime }$ from the centre. The value of $x$, for which the time period is minimum will be

A Parallel beam of white light is incident on a thin film of air of uniform thickness. Wavelengths $7200\dot{A}$ and $5400\dot{A}$ are observed to be missing from the spectrum of reflected light viewed normally. The other wavelength in the visible region missing in the reflected spectrum is

The amplifier A shown in the figure has open loop gain of 100, input impedance $Z_i$ of $1k\Omega$ and output impedance $Z_0$ of $100\Omega$. If a negative feedback factor $\beta =0.99$ is used, the new values of $Z_i$ and $Z_0$ respectively are

A wheel of moment of inertia 0.500 ${\text{kg-m}}^2$ and radius 20.0 cm is rotating about its axis at an angular speed of 20.0 rad/s. It picks up a stationary particle of mass 200 g at its edge. Find the new angular speed of the wheel

The specific heat of hydrogen gas at constant pressure is $C_P=3.4\times {10}^{3}cal/k{g}^{\circ }C$ and at constant volume is $C_r=2.4\times {10}^{3}cal/k{g}^{\circ }C$ If one kilogram hydrogen gas is heated from ${10}^{\circ }$ to ${20}^{\circ }$ at constant pressure, the external work done on the gas to maintain it at constant pressure is

A proton is released at rest $10\text{cm}$ from a charged sheet (perpendicular to it) having uniform electric field around it of intensity $123\text{N/C}$ towards (perpendicular to) the sheet. It will strike the sheet after the time (approximately)

(Charge on proton is $1.6\times {10}^{-19}\text{C}$ and mass of proton is $1.6\times {10}^{-27}\text{kg}$)

A sample of paramagnetic salt contains $2.0\times {10}^{34}$ atomic dipoles each of dipole moment $1.5\times {10}^{-23}{\text{JT}}^{-1}$. The sample is placed under a homogeneous magnetic field of $0.64\text{T}$, and cooled to a temperature of $4.2\text{K}$. The degree of magnetic saturation achieved is equal to $15\%$. What is the total dipole moment of the sample for a magnetic field of $0.98\text{T}$ and a temperature of $2.8\text{K}$ ?

(Assume Curie's law)

In the given circuit, charge $Q_2$ on the $2\mu F$ capacitor changes as $C$ is varied from $1\mu F$ to $3\mu F$. $Q_2$ as a function of $C$ is given properly by

(figures are drawn schematically and not to scale)

A spring balance A shows a reading of 2 kg, when an aluminium block is suspended from it. Another balance B shows a reading of 5 kg, when a beaker full of liquid is placed in its pan. The two balances are arranged such that the Al – block is completely immersed inside the liquid as shown in the figure. Then

What is the quantity of
electricity in coulombs needed to reduce 1 mol of

?
Consider the reaction:

A ray of light incident parallel to the base PQ of an isosceles right-angled triangular prism PQR suffers two successive total internal reflections at the faces PQ and QR before emerging reversed in direction as shown

If the refractive index of the material of the prism is $\mu$, then

A solid sphere of mass 1kg rolls on a table with linear speed 2m/s. Find its total K.E

In which of the following cases is the contact force between $A$ and $B$ is maximum. If mass of each block is $1\text{kg}$ and assume all surfaces to be smooth :-

Three point charges $q_1=q,q_2=q$ and $q_3=Q$ are placed at points having position vectors $\overrightarrow{r_1},\overrightarrow{r_2}$ and $(\overrightarrow{r_1}+\overrightarrow{r_2})$ respectively. It is known that, $|\overrightarrow{r_1}|=|\overrightarrow{r_2}|=\overrightarrow{r}.$ The net electrostatic force on $q_3$ is $\sqrt{3}$ times the force applied by either of $q_1$ or $q_2$ on $q_3$. Find $\overrightarrow{r_1}\cdot \overrightarrow{r_2}$

Figure shows two vessels with adiabatic walls, one containing 0.1 g of helium $(\gamma =1.67,M=4gmo{l}^{-1})$ and the other containg some amount of hydrogen $(\gamma =1.4,M=2gmo{l}^{-1})$. Initially, the temperatures of the two gases are equal. The gases are electrically heated for some time during which equal amou nts of heat are given to the two gases. It is found that the temperatures rise through the same amo unt in the two vessels. Calculate the mass of hydrogen.

A particle is moving along the positive $x$-axis and at $t=0$, the particle is at $x=0$. The acceleration of the particle is a function of time. The acceleration at any time $t$ is given by $a=2(1–[t\left]\right)$ where $\left[t\right]$ is the greatest integer function. Assuming that the particle is at rest initially, the displacement of the particle in $4s$ is