The combination of gates shown below yields

If a source of power $$4kW$$ produces $${10^{20}}$$ photons/second, the radiation belongs to a part of the spectrum called

A nucleus of mass $$M+$$$$\Delta m$$ is at rest and decays into two daughter nuclei of equal mass $${M \over 2}$$ each. Speed of light is $$c.$$

The speed of daughter nuclei is

A nucleus of mass $$M+$$$$\Delta m$$ is at rest and decays into two daughter nuclei of equal mass $${M \over 2}$$ each. Speed of light is $$c.$$

The binding energy per nucleon for the parent nucleus is $${E_1}$$ and that for the daughter nuclei is $${E_2}.$$ Then

Statement - $$1$$ : When ultraviolet light is incident on a photocell, its stopping potential is $${V_0}$$ and the maximum kinetic energy of the photoelectrons is $${K_{\max }}$$. When the ultraviolet light is replaced by $$X$$-rays, both $${V_0}$$ and $${K_{\max }}$$ increase.

Statement - $$2$$ : Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.

In the circuit shown below, the key $$K$$ is closed at $$t=0.$$ The current through the battery is

A rectangular loop has a sliding connector $$PQ$$ of length $$l$$ and resistance $$R$$ $$\Omega $$ and it is moving with a speed $$v$$ as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents $${I_1},{I_2}$$ and $$I$$ are

The speed of light in the medium is

The initial shape of the wavefront of the beam is

As the beam enters the medium, it will

A point $$P$$ moves in counter-clockwise direction on a circular path as shown in the figure. The movement of $$P$$ is such that it sweeps out a length $$s = {t^3} + 5,$$ where $$s$$ is in metres and $$t$$ is in seconds. The radius of the path is $$20$$ $$m.$$ The acceleration of $$'P'$$ when $$t=2$$ $$s$$ is nearly.

A small particle of mass $$m$$ is projected at an angle $$\theta $$ with the $$x$$-axis with an initial velocity $${v_0}$$ in the $$x$$-$$y$$ plane as shown in the figure. At a time $$t < {{{v_0}\sin \theta } \over g},$$ the angular momentum of the particle is ................,



where $$\widehat i,\widehat j$$ and $$\widehat k$$ are unit vectors along $$x,y$$ and $$z$$-axis respectively.

The figure shows the position$$-$$time $$(x-t)$$ graph of one-dimensional motion of body of mass $$0.4$$ $$kg.$$ The magnitude of each impulse is

Two long parallel wires are at a distance $$2d$$ apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field $$B$$ along the line $$XX'$$ is given by

In a series $$LCR$$ circuit $$R = 200\Omega $$ and the voltage and the frequency of the main supply is $$220V$$ and $$50$$ $$Hz$$ respectively. On taking out the capacitance from the circuit the current lags behind the voltage by $${30^ \circ }.$$ On taking out the inductor from the circuit the current leads the voltage by $${30^ \circ }.$$ The power dissipated in the $$LCR$$ circuit is

Two conductors have the same resistance at $${0^ \circ }C$$ but their temperature coefficients of resistance are $${\alpha _1}$$ and $${\alpha _2}.$$ The respective temperature coefficients of their series and parallel combinations are nearly

Let $$C$$ be the capacitance of a capacitor discharging through a resistor $$R.$$ Suppose $${t_1}$$ is the time taken for the energy stored in the capacitor to reduce to half its initial value and $${t_2}$$ is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio $${t_1}/{t_2}$$ will be

A thin semi-circular ring of radius $$r$$ has a positive charges $$q$$ distributed uniformly over it. The net field $$\overrightarrow E $$ at the center $$O$$ is

Let there be a spherically symmetric charge distribution with charge density varying as $$\rho \left( r \right) = {\rho _0}\left( {{5 \over 4} - {r \over R}} \right)$$ upto $$r=R,$$ and $$\rho \left( r \right) = 0$$ for $$r>R,$$ where $$r$$ is the distance from the erigin. The electric field at a distance $$r\left( {r < R} \right)$$ from the origin is given by

The tension in the string is

A ball is made of a material of density $$\rho $$ where $${\rho _{oil}}\, < \rho < {\rho _{water}}$$ with $${\rho _{oil}}$$ and $${\rho _{water}}$$ representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position?

Two fixed frictionless inclined planes making an angle $${30^ \circ }$$ and $${60^ \circ }$$ with the vertical are shown in the figure. Two blocks $$A$$ and $$B$$ are placed on the two planes. What is the relative vertical acceleration of $$A$$ with respect to $$B$$ ?

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $${30^ \circ }$$ with each other. When suspended in a liquid of density $$0.8g$$ $$c{m^{ - 3}},$$ the angle remains the same. If density of the material of the sphere is $$1.6$$ $$g$$ $$c{m^{ - 3}},$$ the dielectric constant of the liquid is

Statement - 1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.

Statement - 2 : Principle of conservation of momentum holds true for all kinds of collisions.

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $$U\left( x \right) = {a \over {{x^{12}}}} - {b \over {{x^6}}},$$ where $$a$$ and $$b$$ are constants and $$x$$ is the distance between the atoms. If the dissociation energy of the molecule is $$D = \left[ {U\left( {x = \infty } \right) - {U_{at\,\,equilibrium}}} \right],\,\,D$$ is

For a particle in uniform circular motion the acceleration $$\overrightarrow a $$ at a point P(R, θ) on the circle of radius R is (here θ is measured from the x–axis)

A particle is moving with velocity $$\overrightarrow v = k\left( {y\widehat i + x\widehat j} \right)$$, where K is a constant. The general equation for its path is

The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 $$ \times $$ 10^–3 are