The volume $(V)$ of a monatomic gas varies with its temperature $(T)$, as shown in the graph. The ratio of work done by the gas, to the heat absorbed by it, when it undergoes a change from state A to state B, is

An astronomical refracting telescope will have large angular magnification and high angular resolution, when it has an objective lens of

The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom is

An electron of mass $m$ with an initial velocity $\mathbf{v} = v_0 \hat{i}$ (where $v_0 > 0)$

For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is

When the light of frequency $2\nu_0$ (where $\nu_0$ is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is $v_1.$

In the circuit shown in the figure, the input voltage $V_i$ is $20V, V_{BE} = 0$ and $V_{CE} = 0.$

In a p-n junction diode, change in temperature due to heating

In the combination of the following gates, the output $Y$ can be written in terms of inputs $A$ and $B$ as

An EM wave is propagating in a medium with a velocity $\mathbf{V} = V \hat{i}.$ The instantaneous oscillating electric field of this EM wave is along the $+y$ axis. Then the direction of the oscillating magnetic field of the EM wave will be along

The refractive index of the material of a prism is $\sqrt{2}$ and the angle of the prism is $30^{\circ}.$ One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is

The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is $20$ cm, the length of the open organ pipe is

An object is placed at a distance of $40$ cm from a concave mirror of focal length $15$ cm. If the object is displaced through a distance of $20$ cm towards the mirror, the displacement of the image will be

The magnetic potential energy stored in a certain inductor is $25$ mJ, when the current in the inductor is $60$ mA. This inductor is of inductance

An electron falls from rest through a vertical distance $h$ in a uniform and vertically upward directed electric field $E.$ The direction of the electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance $h.$ The time of fall of the electron, in comparison to the time of fall of the proton is

The electrostatic force between the metal plates of an isolated parallel plate capacitor $C$ having a charge $Q$ and area $A,$ is

A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of $27^{\circ}C$, two successive resonances are produced at $20$ cm and $73$ cm$$ of column length. If the frequency of the tuning fork is $320$

A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is $20$ m/s$^2$ at a distance of $5$ m from the mean position. The time period of oscillation is

A metallic rod of mass per unit length $0.5$ kg/m is lying horizontally on a smooth inclined plane which makes an angle of $30^{\circ}$ with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induction $0.25$ T is acting on it in the vertical direction. The current flowing in the rod to keep it stationary is

A thin diamagnetic rod is placed vertically between the poles of an electromagnet. When the current in the electromagnet is switched on, then the diamagnetic rod is pushed up, out of the horizontal magnetic field. Hence the rod gains gravitational potential energy. The work required to do this comes from

An inductor $20$ mH, a capacitor $100 \mu F$ and a resistor $50 \Omega$ are connected in series across a source of emf, $V = 10 \sin 314 t.$ The power loss in the circuit is

Current sensitivity of a moving coil galvanometer is $5$ div/mA and its voltage sensitivity (angular deflection per unit voltage applied) is $20$ div/V. The resistance of the galvanometer is

At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere? Given: $$Mass of oxygen molecule $(m) = 2.76 \times 10^{-26}$ kg$,$Boltzmann's constant $k_B = 1.38 \times 10^{-23}$

A body initially at rest and sliding along a frictionless track from a height $h$ (as shown in the figure) just completes a vertical circle of diameter $D.$ The height $h$ is equal to

Three objects, A: (a solid sphere), B: (a thin circular disk) and C: (a circular ring), each have the same mass $M$ and radius $R.$ They all spin with the same angular speed $\omega$ about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation

A moving block having mass $m,$ collides with another stationary block having mass $4m.$ The lighter block comes to rest after collision. When the initial velocity of the lighter block is $v,$ then the value of coefficient of restitution $(e)$ will be

Which one of the following statements is incorrect?

A toy car with charge $q$ moves on a frictionless horizontal plane surface under the influence of a uniform electric field $\mathbf{E}.$ Due to the force $q \mathbf{E},$ its velocity increases from $0$ to $6$ m/s in one second duration. At that instant, the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between

A block of mass $m$ is placed on a smooth inclined wedge ABC of inclination $\theta$ as shown in the figure. The wedge is given an acceleration $a$ towards the right. The relation between $a$ and $\theta$ for the block to remain stationary on the wedge is

The moment of the force, $\vec{F} = 4 \hat{i} + 5 \hat{j} - 6 \hat{k}$

A student measured the diameter of a small steel ball using a screw gauge of least count $0.001$ cm. The main scale reading is $5$ mm and zero of circular scale division coincides with $25$ divisions above the reference level. If screw gauge has a zero error of $-0.004$ cm, the correct diameter of the ball is

A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere?

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B, and C are $K_A, K_B,$ and $K_C,$

The efficiency of an ideal heat engine working between the freezing point and boiling point of water is

If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct?

A solid sphere is in rolling motion. In rolling motion, a body possesses translational kinetic energy ($K_t$) as well as rotational kinetic energy ($K_r$) simultaneously. The ratio $K_t : (K_t + K_r)$

A small sphere of radius $r$ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity is proportional to

The power radiated by a black body is $P$ and it radiates maximum energy at wavelength, $\lambda_0.$ If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $\frac{3}{4} \lambda_0,$

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $A$ and the second wire has cross-sectional area $3A.$ If the length of the first wire is increased by $\Delta l$ on applying a force $F,$ how much force is needed to stretch the second wire by the same amount?

A sample of $0.1$ g of water at $100^{\circ}C$ and normal pressure $(1.013 \times 10^5$ N/m$^2)$

A carbon resistor of $(47 \pm 4.7)$k$\Omega$ is to be marked with rings of different colours for its identification. The colour code sequence will be:

A set of ‘n’ equal resistors, of value ‘R’ each, are connected in series to a battery of emf ‘E’ and internal resistance ‘R’. The current drawn is I. Now, the ‘n’ resistors are connected in parallel to the same battery. Then the current drawn from battery becomes 10 I. The value of ‘n’ is:

A battery consists of a variable number ‘n’ of identical cells (having internal resistance ‘r’ each) which are connected in series. The terminals of the battery are short-circuited and the current I is measured. Which of the graphs shows the correct relationship between I and n?

Unpolarised light is incident from air on a plane surface of a material of refractive index $\mu.$ At a particular angle of incidence $i,$ it is found that the reflected and refracted rays are perpendicular to each other. Which of the following options is correct for this situation?

In Young’s double slit experiment, the separation $d$ between the slits is $2$ mm, the wavelength $\lambda$ of the light used is $5896$ Å and distance $D$ between the screen and slits is $100$