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Six moles of an ideal gas undergo a cyclic process shown in the figure. If the temperatures are given as $T_A=600\text{K}$, $T_B=800\text{K}$, $T_C=2200\text{K}$ and $T_D=1200\text{K}$, then the work done per cycle is

Can Bernoulli’s equation be used to describe the flow of water through a rapid in a river? Explain.

A metal has a work function of $2.5\times {10}^{-19}$ J. What should be the threshold frequency beyond which if I shine light on the metal, photo electrons will come out?

Figure shows a light rod of length l rigidly attached to a small heavy block at one end and a hook at the other end. The system is released from rest with the rod in a horizontal position. There is a fixed smooth ring at a depth h below the initial position of the hook and the hook gets into the ring as it reaches there. What should be the minimum value of h so that the block moves in a complete circle about the ring?

Blocks A and C start from rest and move to the right with acceleration and $a_A=12tm/s^{2}and{a}_C=3m/s^2.$ Here t is in seconds. The time when block B again comes to rest is$(g=10m/s^2)$

An insect crawls up a hemispherical surface very slowly as shown in the figure. The coefficient of static friction between the insect and the surface is $\frac{1}{3}$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical, then the maximum possible value of $\alpha$ is given by

A particle $A$ of mass $m$ and initial velocity $v$ collides with a particle $B$ of mass $\frac{m}{2}$ which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths ${\lambda }_A$ to ${\lambda }_B$ after the collision is

An observer can see through a pin-hole the top end of a thin rod of height h, placed as shown in figure. The breaker height is 3h and its radius h. when the beaker is filled with a liquid upto a height 2 h, he can see the lower end of the rod. Then refractive index of the liquid is

The isothermal elasticity of a gas is equal to

The threshold wavelength for photoelectric emission from a material is 5200$\dot{A}$. Photoelectrons will be emitted when this material is illuminated with monochromatic radiation from a

The wavelengths of ${\text{K}}_{\alpha }$ and ${\text{L}}_{\alpha }$ $\text{X}-$ rays of a material are $21.3\text{pm}$ and $141\text{pm}$ respectively. Find the wavelength of ${\text{K}}_{\beta }\text{X}-$ ray of the material.

A disc of mass $M$ and radius $R$ is rolling with angular speed $\omega$ on a horizontal plane. The magnitude of angular momentum of the disc about the origin O is $x$ times $M{R}^2\omega$. Then the value of $x$ is

1. You toss a small ball vertically up in the air. How are the velocity and acceleration vectors of the ball oriented with respect to one another during the ball’s flight up and down?

When temperature of an ideal gas is increased from ${27}^{\circ }\text{C}$ to ${227}^{\circ }\text{C}$ keeping its mass and pressure constant, then volume of the gas will be increased by

Krypton (planet of superman) has mass twice that of earth and radius thrice that of earth. What would be the weight of superman on krypton if his weight on earth is $900\text{N}?$

A black body radiates heat energy at the rate of $2\times {10}^5{\text{J-s}}^{-1}{\text{m}}^{-2}$ at a temperature of ${127}^{\circ }\text{C}$. The temperature of black body, at which the rate of heat radiation is $32\times {10}^5{\text{J-s}}^{-1}{\text{m}}^{-2}$ is

For a perfectly reflecting body:

( Given a→ absorptive power, r→ reflective power, t→ transmissive power.)

A frictionless wire AB is fixed on a circular frame of radius R. A very small spherical ball slips on this wire. The time taken by this ball to slip from A to B is

A cylindrical uniform rod of the area of cross-section A is acted upon by two forces (each F) as shown. The shearing stress on the section xy is

Four forces P, 2P, 3P and 4P act along sides of a square taken in order. Find their resultant.

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

In
deriving the single slit diffraction pattern, it was stated that the
intensity is zero at angles of nλ/a.
Justify this by suitably dividing the slit to bring out the
cancellation.

body just begins to slide down. The coefficient of friction is 1/√3. What is the angle of inclination?

The surface area $\left(X\right)$ of a nucleus varies with mass number $\left(A\right)$ as:

A flexible wire bent in the form of a circle is placed in a uniform magnetic field perpendicular to the plane of the coil. The radius of the coil changes as shown in the figure.

The graph of magnitude of induced emf in the coil is represented by

One mole of ideal gas undergoes a linear process as shown in figure below. Its temperature expressed as a function of volume V is.

If $A=\left[\begin{array}{cc}\frac{1}{\sqrt{5}}& \frac{2}{\sqrt{5}}\\ \frac{-2}{\sqrt{5}}& \frac{1}{\sqrt{5}}\end{array}\right],B=\left[\begin{array}{cc}1& 0\\ i& 1\end{array}\right],i=\sqrt{-1}$ and $Q=A^{T}BA,$ then the inverse of the matrix $A{Q}^{2021}{A}^T$ is equal to

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