Two charged spherical conductors of radius $R_1$ and $R_2$ are connected by a wire. Then the ratio of surface charge densities of the spheres $\left(\frac{\sigma_1}{\sigma_2}\right)$ is:

A spring is stretched by $5$ cm by a force of $10$ N. The time period of the oscillations when a mass of $2$ kg is suspended by it is:

A convex lens ‘A’ of focal length $20$ cm and a concave lens ‘B’ of focal length $5$ cm are kept along the same axis with a distance ‘d’ between them. If a parallel beam of light falling on ‘A’ leaves ‘B’ as a parallel beam, then the distance ‘d’ in cm will be:

Column - I gives certain physical terms associated with flow of current through a metallic conductor. Column - II gives some mathematical relations involving electrical quantities. Match Column - I and Column - II with appropriate relations.

The electron concentration in an $n$-type semiconductor is the same as hole concentration in a $p$-type semiconductor. An external electric field is applied across each of them. Compare the currents in them.

A radioactive nucleus $^{A}_{Z}X$ undergoes spontaneous decay in the sequence $^{A}_{Z}X \rightarrow _{Z-1}B \rightarrow _{Z-3}C \rightarrow _{Z-2}D$

Water falls from a height of $60$ m at the rate of $15$ kg/s to operate a turbine. The losses due to frictional force are $10\%$ of the input energy. How much power is generated by the turbine?$\newline (g=10$ m/s$^2)$

The number of photons per second on an average emitted by the source of monochromatic light of wavelength $600$ nm, when it delivers the power of $3.3 \times 10^{-3}$ watt will be:$\newline (h=6.6 \times 10^{-34}$

For a plane electromagnetic wave propagating in the x-direction, which one of the following combinations gives the correct possible directions for the electric field ($E$) and magnetic field ($B$) respectively?

The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section, and same material is $0.25 \Omega.$ What will be the effective resistance if they are connected in series?

In a potentiometer circuit a cell of EMF $1.5$ V gives a balance point at $36$ cm length of wire. If another cell of EMF $2.5$ V replaces the first cell, then at what length of the wire, the balance point occurs?

The velocity of a small ball of mass $M$ and density $d,$ when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is $d_2,$ then the viscous force acting on the ball will be:

Polar molecules are the molecules:

A parallel plate capacitor has a uniform electric field $E$ in the space between the plates. If the distance between the plates is $d$ and the area of each plate is $A,$ the energy stored in the capacitor is:$\newline (\varepsilon_0 =$

The equivalent capacitance of the combination shown in the figure is:

Consider the following statements (A) and (B) and identify the correct answer.$\newline (A)$ A Zener diode is connected in reverse bias, when used as a voltage regulator.$\newline (B)$ The potential barrier of p-n junction lies between $0.1 V$ to $0.3 V.$

A particle is released from height $S$ from the surface of the Earth. At a certain height, its kinetic energy is three times its potential energy. The height from the surface of Earth and the speed of the particle at that instant are respectively:

If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{E}{G}$ has the dimensions of:

Match Column - I and Column - II and choose the correct match from the given choices.

A body is executing simple harmonic motion with frequency $n,$ the frequency of its potential energy is:

A cup of coffee cools from $90^{\circ}C$ to $80^{\circ}C$ in $t$ minutes, when the room temperature is $20^{\circ}C.$

A capacitor of capacitance $C$ is connected across an ac source of voltage $V$, given by$\newline V = V_0 \sin \omega t.$

An infinitely long straight conductor carries a current of 5 A as shown. An electron is moving with a speed of $10^5$ m/s parallel to the conductor. The perpendicular distance between the electron and the conductor is $20$ cm at an instant. Calculate the magnitude of the force experienced by the electron at that instant.

The half-life of a radioactive nuclide is $100$ hours. The fraction of original activity that will remain after $150$ hours would be:

An inductor of inductance $L,$ a capacitor of capacitance $C$ and a resistor of resistance $R$ are connected in series to an ac source of potential difference $V$ volts as shown in figure.$\newline$Potential difference across $L, C$

A thick current carrying cable of radius $R$ carries current $I$ uniformly distributed across its cross-section. The variation of magnetic field $B(r)$ due to the cable with the distance $r$ from the axis of the cable is represented by:

An electromagnetic wave of wavelength $\lambda$ is incident on a photosensitive surface of negligible work function. If $m$ is the mass of the photoelectron emitted from the surface, the de-Broglie wavelength $\lambda_d$ of the electron is given by:

The escape velocity from the Earth's surface is $v.$ The escape velocity from the surface of another planet having a radius four times that of Earth and same mass density is:

If force $[F],$ acceleration $[A]$ and time $[T]$ are chosen as the fundamental physical quantities, find the dimensions of energy.

Two conducting circular loops of radii $R_1$ and $R_2$ are placed in the same plane with their centres coinciding. If $R_1 >> R_2,$

A point object is placed at a distance of $60$ cm from a convex lens of focal length $30$ cm. If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of $40$ cm from it, the final image would be formed at a distance of:

Three resistors having resistances $r_1, r_2,$ and $r_3$

For the given circuit, the input digital signals are applied at the terminals $A, B,$ and $C.$ What would be the output at the terminal $Y?$

A dipole is placed in an electric field as shown. In which direction will it move?

A series LCR circuit containing $5.0 H$ inductor, $80 \mu F$ capacitor, and $40 \Omega$ resistor is connected to a $230$ V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be:

A car starts from rest and accelerates at $5$ m/s$^2.$ At $t = 4$ s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t = 6$

A particle of mass $m$ is projected with a velocity $v = k V_e (k < 1)$ from the surface of the Earth.$\newline (V_e =$

A particle moving in a circle of radius $R$ with a uniform speed takes a time $T$ to complete one revolution.$\newline$If this particle were projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it equals $4R.$ The angle of projection, $\theta,$

In the product $\vec{F} = q (\vec{v} \times \vec{B}) = q \vec{v} \times \left( \mathbf{B} \hat{i} + \mathbf{B} \hat{j} + \mathbf{B_0} \hat{k} \right),$

A ball of mass $0.15$ kg is dropped from a height $10$ m, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is $\newline (g = 10$ m/s$^2)$

A uniform conducting wire of length $12a$ and resistance $R$ is wound up as a current-carrying coil in the shape of,$\newline (i)$ an equilateral triangle of side $a. \newline (ii)$ a square of side $a. \newline$

Twenty-seven drops of same size are charged at $220$ V each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

A uniform rod of length $200$ cm and mass $500$ g is balanced on a wedge placed at $40$ cm mark. A mass of $2$ kg is suspended from the rod at $20$ cm and another unknown mass $m$

From a circular ring of mass $M$ and radius $R,$ an arc corresponding to a $90^\circ$ sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the center of the ring and perpendicular to the plane of the ring is $K$ times $MR^2.$

A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope since:

A step-down transformer connected to an AC mains supply of $220$ V is made to operate at $11$ V, $44$ W lamp. Ignoring power losses in the transformer, what is the current in the primary circuit?

A screw gauge gives the following readings when used to measure the diameter of a wire.$\newline$Main scale reading: 0 mm$\newline$Circular scale reading: 52 divisions$\newline$Given that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is:

A nucleus with mass number 240 breaks into two fragments each of mass number 120. The binding energy per nucleon of unfragmented nuclei is 7.6 MeV while that of fragments is 8.5 MeV. The total gain in the binding energy in the process is:

A small block slides down on a smooth inclined plane, starting from rest at time $t=0.$ Let $S_n$ be the distance travelled by the block in the interval $t=n−1$

Find the value of the angle of emergence from the prism. Refractive index of the glass is $\sqrt{3}.$