A sphere and a cube, both of copper have equal volumes and are black. They are allowed to cool at same temperature and in same atmosphere. The ratio of their rate of loss of heat will be

An alternating voltage is applied to a series LCR circuit. If the current leads the voltage by ${45}^{\circ }$, then $(\tan {45}^{\circ }=1)$

A horizontal wire of mass '$m$', length '$l$' and resistance '$R$' is sliding on the vertical rails on which uniform magnetic field '$B$' is directed perpendicular. The terminal speed of the wire as it falls under the force of gravity is ( $\mathrm{g}=$ acceleration due to gravity)

Frequency of the series limit of Balmer series of hydrogen atom in terms of Rydberg's constant (R) and velocity of light (c) is

A string is stretched between two rigid supports separated by $75\mathrm{cm}$. There are no resonant frequencies between $420\mathrm{Hz}$ and $315\mathrm{Hz}$. The lowest resonant frequency for the string is

A straight wire carrying a current (I) is turned into a circular loop. If the magnitude of the magnetic moment associated with it is '$M$', then the length of the wire will be

The diffraction fringes obtained by a single slit are of

A particle moves around a circular path of radius '$r$' with uniform speed '$V$'. After moving half the circle, the average acceleration of the particle is

On dry road, the maximum speed of a vehicle along a circular path is '$V$'. When the road becomes wet, maximum speed becomes $\frac{\mathrm{V}}{2}$. If coefficient of friction of dry road is '$\mu$' then that of wet road is

A wire of length $3\mathrm{m}$ connected in the left gap of a meter-bridge balances $8\mathrm{\Omega }$ resistance in the right gap at a point, which divides the bridge wire in the ratio $3:2$. The length of the wire corresponding to resistance of $1\mathrm{\Omega }$ is

By adding soluble impurity in a liquid, angle of contact

For a common emitter configuration, if '$\alpha$' and '$\beta$' have their usual meanings, the incorrect relation between '$\alpha$' and '$\beta$' is

A simple pendulum of length '$l$' and a bob of mass '$\mathrm{m}$' is executing S.H.M. of small amplitude '$A$'. The maximum tension in the string will be ($\mathrm{g}=$ acceleration due to gravity)

Which of the following combination of 7 identical capacitors each of $2\mu \mathrm{F}$ gives a capacitance of $\frac{10}{11}\mu \mathrm{F}$ ?

The potential energy of a molecule on the surface of a liquid compared to the molecules inside the liquid is

A progressive wave is given by, $\mathrm{Y}=12\sin (5\mathrm{t}-4\mathrm{x})$. On this wave, how far away are the two points having a phase difference of ${90}^{\circ }$ ?

The de-Broglie wavelength $(\lambda )$ of a particle is related to its kinetic energy (E) as

For a purely inductive or a purely capacitive circuit, the power factor is

The electric field intensity on the surface of a solid charged sphere of radius '$r$' and volume charge density '$\rho$' is (${\epsilon }_0=$ permittivity of free space)

A body is said to be opaque to the radiation if (a, r and t are coefficient of absorption, reflection and transmission respectively)

In a thermodynamic system, $\mathrm{\Delta }U$ represents the increases in its internal energy and dW is the work done by the system then correct statement out of the following is

A combination of two thin lenses in contact have power $+10\mathrm{D}$. The power reduces to $+6\mathrm{D}$ when the lenses are $0.25\mathrm{m}$ apart. The power of individual lens is

The reciprocal of the total effective resistance of LCR a.c. circuit is called

If the radius of the first Bohr orbit is '$r$' then the de-Broglie wavelength of the electron in the $4^{\text{th }}$ orbit will be

A string of length '$L$' fixed at one end carries a body of mass '$\mathrm{m}$' at the other end. The mass is revolved in a circle in the horizontal plane about a vertical axis passing through the fixed end of the string. The string makes angle '$\theta$' with the vertical. The angular frequency of the body is '$\omega$'. The tension in the string is

The temperature of a gas is $-{68}^{\circ }\mathrm{C}$. To what temperature should it be heated, so that the r.m.s. velocity of the molecules be doubled?

The displacement of a particle executing S.H.M. is $x=\mathrm{a}\sin (\omega t-\varphi )$. Velocity of the particle at time $\mathrm{t}=\frac{\varphi }{\omega }$ is $(\cos 0^{\circ }=1)$

A uniformly charged semicircular arc of radius '$r$' has linear charge density '$\lambda$'. The electric field at its centre is ( ${\epsilon }_0=$ permittivity of free space)

A sphere, a cube and a thin circular plate all made of same material and having the same mass are heated to same temperature of ${200}^{\circ }\mathrm{C}$. When these are left in a room.

For emission of light, a light emitting diode (LED) is

A solenoid of length $0.4\mathrm{m}$ and having 500 turns of wire carries a current $3\mathrm{A}$. A thin coil having 10 turns of wire and radius $0.1\mathrm{m}$ carries current $0.4\mathrm{A}$. the torque required to hold the coil in the middle of the solenoid with its axis perpendicular to the axis of the solenoid is $({\mu }_0=4\pi \times {10}^{-7}$ SI units, ${\pi }^2=10)(\sin {90}^{\circ }=1)$

In semiconductors at room temperature,

Considering earth to be a sphere of radius '$R$' having uniform density '$\rho$', then value of acceleration due to gravity '$g$' in terms of $R,\rho$ and $\mathrm{G}$ is

The equation of the wave is $\mathrm{Y}=10\sin (\frac{2\pi \mathrm{t}}{30}+\alpha )$ If the displacement is $5\mathrm{cm}$ at $\mathrm{t}=0$ then the total phase at $\mathrm{t}=7.5\mathrm{s}$ will be $(\sin {30}^{\circ }=0.5)$

The bob of simple pendulum of length '$L$' is released from a position of small angular displacement $\theta$. Its linear displacement at time '$\mathrm{t}$' is ( $\mathrm{g}=$ acceleration due to gravity)

The value of acceleration due to gravity at a depth '$d$' from the surface of earth and at an altitude '$h$' from the surface of earth are in the ratio

A magnetic field of $2\times {10}^{-2}\mathrm{T}$ acts at right angles to a coil of area $100{\mathrm{cm}}^2$ with 50 turns. The average e.m.f. induced in the coil is $0.1\mathrm{V}$, when it is removed from the field in time '$t$'. The value of '$t$' is

In Young's double slit experiment, $8^{\text{th }}$ maximum with wavelength '${\lambda }_1$' is at a distance '$d_1$' from the central maximum and $6^{\text{th }}$ maximum with wavelength '${\lambda }_2$' is at a distance '${\mathrm{d}}_2$'. Then $\frac{{\mathrm{d}}_2}{{\mathrm{d}}_1}$ is

The alternating e.m.f. induced in the secondary coil of a transformer is mainly due to

The efficiency of a heat engine is '$\eta$' and the coefficient of performance of a refrigerator is '$\beta$'. Then

A conducting sphere of radius $0.1\mathrm{m}$ has uniform charge density $1.8\mu \mathrm{C}/{\mathrm{m}}^2$ on its surface. The electric field in free space at radial distance $0.2\mathrm{m}$ from a point on the surface is ( ${\epsilon }_0=$ permittivity of free space)

If ${\mathrm{I}}_0$ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be the intensity when the slit width is doubled?

Two circular coils made from same wire but radius of $1^{\text{st }}$ coil is twice that of $2^{\text{nd }}$ coil. If magnetic field at their centres is same then ratio of potential difference applied across them is ($1^{\text{st }}$ to $2^{\text{nd }}$ coil)

Five current carrying conductors meet at point $\mathrm{P}$. What is the magnitude and direction of the current in conductor $\mathrm{PQ}$?

Water rises in a capillary tube of radius '$r$' upto a height '$h$'. The mass of water in a capillary is '$m$'. The mass of water that will rise in a capillary tube of radius $\frac{{}^{\prime }{r}^{\prime }}{3}$ will be

A person with machine gun can fire 50 g bullets with a velocity of $240\mathrm{m}/\mathrm{s}$. A $60\mathrm{kg}$ tiger moves towards him with a velocity of $12\mathrm{m}/\mathrm{s}$. In order to stop the tiger in track, the number of bullets the person fires towards the tiger is

If '$l$' is the length of the open pipe, '$r$' is the internal radius of the pipe and '$V$ ' is the velocity of sound in air then fundamental frequency of open pipe is

The angle of deviation produced by a thin prism when placed in air is '${\delta }_1$' and that when immersed in water is '${\delta }_2$'. The refractive index of glass and water are $\frac{3}{2}$ and $\frac{4}{3}$ respectively. The ratio ${\delta }_1:{\delta }_2$ is

A thin uniform rod of mass '$m$' and length '$P$' is suspended from one end which can oscillate in a vertical plane about the point of intersection. It is pulled to one side and then released. It passes through the equilibrium position with angular speed '$\omega$'. The kinetic energy while passing through mean position is

Magnetic field at the centre of the hydrogen atom due to motion of electron in ${\mathrm{n}}^{\text{th }}$ orbit is proportional to