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A stone projected at an angle of ${60}^{\circ }$ from the ground level strikes at an angle of ${30}^{\circ }$ on the roof of a building of height ‘h’. Then the speed of projection of the stone is

In the circuit shown, $L=1\mu H,C=1\mu F$ and $R=1k\Omega$. They are connected in series with an a.c. source $V=V_0\sin \omega t$ as shown. Which of the following options is/are correct?

A light of wavelength $650\text{nm}$ falls on a surface at an angle ${60}^{\circ }$ and bounces back at the same angle from the normal. If the reflectivity of the surface is $50\%$ and intensity of light is $100{\text{W/m}}^2$, find the pressure experienced by the surface due to the reflected radiation.

Two blocks of masses $4kg$ and $10kg$ are connected by a flexible inextensible string as shown in given figure. The pulley is assumed to be light and frictionless. The coefficient of friction between the $4kg$ block and the suface is $0.2$ (${\mu }_s={\mu }_k=0.2$). The angle of inclination of the plane is ${30}^{\circ }$. Assuming the sytem to be released from rest, the acceleration of $10kg$ block is $(g=10m{s}^{-2})$

Find the integral of the given function w.r.t - x

$y=\frac{si{n}^2\sqrt{x}}{2\sqrt{x}}$

A wire carries a steady current of $50\text{A}$ as shown in the figure. Find the magnetic field caused by segment $AB$ of length $1\text{cm}$ of the wire at a point $P$ where $OP=1\text{m}$.

A block of mass m is placed on the plank of mass M as shown in the figure. Coefficient of friction between the
surfaces of m and M is μ and there is no friction between ground and M. A horizontal force F = kt is applied on
the block, were k is a constant and t is the time. Which of the following graphs shows the acceleration of the plank?

In a closed container of constant volume, the pressure of water exhibits an interesting dependence on temperature -

The point D (273.16 K,0.006 atm) is called the triple point, Tp, of water, where all there phases coexist. What is the observed phase change when the temperature is increased from -10⁰C to +10⁰C, while maintaining a constant pressure of 0.006 atm?

Positive charge Q is distributed uniformly over a ircular ring of radius R. A particle having having a mass ma and a negative charge q, is placed on its axis at a distanc ex from the centre. Find the force on the particle. Assuming x<< R, Find the time period of oscillation of the particle if it is released from there.

The dimensional formula of permittivity of free space is

An unpolarized light of intensity $I_0$ passes through three successive Polaroids $P_1,P_2$ and $P_3$. The polarization axes of $P_1$ make an angle ${60}^{\circ }$ with $P_2$ and $P_2$ makes an angle ${30}^{\circ }$ with $P_3$. The intensity of the transmitted light from $P_3$ is

The current through a wire depends on time as $I=(2+3t)\text{A}$. Calculate the charge crossed through a cross-section of the wire in $10\text{s}$.

An ideal liquid is flowing in two pipes one is inclined and second is horizontal. Both the pipes are connected by two vertical tubes of length $h_1$ and $h{­}_2$ as shown in fig. The flow is streamline in both the pipes. If velocity of liquid at A, B and C are 2 m/s, 4 m/s and 4 m/s respectively, the velocity at D will be

A particle moves with constant angular velocity in a circle. During the motion its

The transfer function of a second order band-pass filter, having a centre frequency of 1000 rad/s, selectivity of 100 and a gain 0 dB at the centre frequency is

A particle executes SHM, with an amplitude of $10\text{cm}$. When the particle is at $6\text{cm}$ from the mean position, the magnitude of its velocity is equal to twice of its acceleration. Find the time period of SHM(in seconds)

The area of cross-section of the wider tube shown in figure is $800{\text{cm}}^2$. If a mass of $12\text{kg}$ is placed on the massless piston, the difference in heights $h$ in the level of water in the two tubes is

In an experiment to measure the internal resistance of a cell by a potentiometer, it is found that the balance point is at a length of $2\text{m}$, when the cell is shunted by a $5\Omega$ resistance and at a length of $3\text{m}$, when the cell is shunted by a $10\Omega$ resistance. The internal resistance of the cell is

The instantaneous value of current is given by $I=100\sin \left(100t\right)\text{mA}.$



$\left(ii\right)$ Find the rms value of current.



​​​​​​​$[$1 Mark$]$

Obtain an expression
for the frequency of radiation emitted when a hydrogen atom
de-excites from level n to level (n−1). For large
n, show that this frequency equals the classical frequency of
revolution of the electron in the orbit.

Two magnets, each of magnetic moment $M$ are placed so as to form a cross at right angles to each other. The magnetic moment of the system will be

A series LCR circuit with $100\Omega$ resistance is connected to an AC source of $200\text{V}$ and angular frequency $300\text{rad/s}$. When only the capacitance is removed, the current lags behind the voltage by ${60}^{\circ }$. When only the inductance is removed, the current leads the voltage by ${60}^{\circ }$. The average power dissipated in the LCR circuit is -

The ratio of magnetic dipole moment to that of the angular momentum of an electron of mass $m\text{kg}$ and charge $e\text{C}.$ In Bohr's orbit of the hydrogen atom is-