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In a common emitter amplifier circuit using n-p-n transistor, the phase difference between the input and the output voltages will be

A ball is projected from a point A with some velocity at an angle ${30}^{\circ }$ with horizontal as shown in figure. Consider a target at point B. The ball will hit the target. It is thrown with velocity $v_0$ equal to

A cubical block (side $2\text{m}$) of mass $20\text{kg}$ slides on inclined plane lubricated with the oil of viscosity $\eta ={10}^{-1}\text{Poise}$ with constant velocity of $10\text{m/s}$. Find out the thickness of the layer of liquid. $(g=10{\text{m/s}}^2)$

Two bodies $A$ and $B$ are travelling with constant velocities of $20\text{m/s}$ and $30\text{m/s}$ in the same positive direction. The relative velocity of $A$ with respect $B$ is

A coil wrapped around a toroid has inner radius of $10.0\text{cm}$ and an outer radius $20.0\text{cm}$. If the wire wrapped makes $600\text{turns}$ and carries current of $10.0\text{A}$. Choose the correct alternatives.

$[B_{max}$ and $B_{min}$ are maximum and minimum magnetic fields inside the toroid$]$

Two
towers on top of two hills are 40 km apart. The line joining them
passes 50 m above a hill halfway between the towers. What is the
longest wavelength of radio waves, which can be sent between the
towers without appreciable diffraction effects?

In the circuit shown in figure when switch S₁ is closed and S₂ is open, the ideal voltmeter shows a reading of 18V. When switch S₂ is closed and S₁ is open, the reading of the voltmeter id 24V. When S₁ and S₂ both are closed the voltmeter reading will be

A parallel plate capacitor contains a mica sheet (thickness $={10}^{-3}m$) and a sheet of fibre (thickness $=0.5\times {10}^{-3}m$). The dielectric constant of mica is 8 and that of fibre is 2.5. Assuming that the fibre breaks down when subjected to an electric field of $6.4\times {10}^{6}V/m$, find the maximum safe voltage that can be applied to the capacitor.

A lens has a power of $10\text{D}$ when placed in air. When it is immersed in water$(\mu =\frac{4}{3})$, the change in power is

(Refractive index of lens material is $1.5$)

A parallel beam of light emerges from the opposite surface of the sphere when a point source of light lies at the surface of the sphere. The refractive index of the sphere is

A force $10\text{N}$ acts tangentially at the highest point of a solid sphere of mass $10\text{kg}$ kept on a rough horizontal plane. If the sphere rolls without slipping, find the acceleration of the centre of the sphere (in $\text{m}/{\text{s}}^2$).

Two fixed point charges + 4ee and +e units are separated by a distance 'a'. Where should the third point charge be placed for it to be in equilibrium?

A sphere of diameter 7.0 cm and mass 266.5 g floats in a bath of a liquid. As the temperature is raised, the sphere begins to sink at a temperature of ${35}^{\circ }C$. If the density of the liquid is $1.527g/c{m}^3$ at $0^{\circ }C$, find the coefficient of cubical expansion of the liquid. Neglect the expansion of the sphere.

Equal volume of two immiscible liquids of densities $\rho$ and $2\rho$ are filled in a vessel as shown in the figure. Two small holes are punched at depths $h/2$ and $3h/2$ from the surface of the lighter liquid. If $v_1$ and $v_2$ are the velocities of efflux at these two holes, then $v_1/v_2$ is

An electron in ground state of hydrogen has an angular momentum $L_1$ and an electron in the first excited state of Lithium has an angular momentum $L_2$. Then

A block of mass $m$ is in equilibrium on an inclined plane as shown.





Find out the normal force acting on the block

In a certain region there exist a uniform electric field $\overrightarrow{E}$ and a uniform magnetic field $\overrightarrow{B}$ both directed along z-axis. A particle of charge $Q$ and mass $m$ is projected at time $t=0$ with a velocity $v_0$ along $x$-axis. Find the velocity at any instant of time $t$.

Read the following and write the correct pairs. Initially, the two plates (A and B) are given charges as shown. Find the final charges on the plates after the key k is closed. All plates are conducting, parallel and of infinite length and breadth.



$\begin{array}{cccc}& \text{List-I}& & \text{List-II}\\ \text{(P)}& \text{Final charge on plate A}& \left(1\right)& \frac{Q}{2}\\ \text{(Q)}& \text{Final charge on plate B}& \left(2\right)& \text{Q}\\ \text{(R)}& \text{Final charge on plate C}& \left(3\right)& \text{Q/4}\\ \text{(S)}& \text{Final charge on plate D}& \left(4\right)& \frac{3Q}{2}\end{array}$

Which of the following option has the correct combination considering column –I and column – II

If the absorptive power of a surface is $0.6$ then the energy incident if the energy reflected is $70\text{J}$ is -



Assume transmissivity is zero.

Three rods of identical area of cross-section and

made from the same metal form the sides of an

isosceles triangle ABC , right angled at B. The

points A and B are maintained at temperatures

T and $\sqrt{2}$T respectively. In the steady state the

temperature of the point C is $T_c$. Assuming that

only heat conduction takes place, $\frac{T_C}{T}$ is equal to

A charged particle
oscillates about its mean equilibrium position with a frequency of
10⁹ Hz. What is the frequency of the electromagnetic waves
produced by the oscillator?

An object is displaced from point $A(0,0)m$ to a point $B(3,4)m$ under the influence of a force $\overrightarrow{F}=4\hat{i}-2\hat{j}.$ The workdone by this force is

The pressures of the gas in a constant volume gas thermometer are 80 cm, 90 cm and 100 cm of mercury at the ice point, the steam point and in a heated wax bath respectively. Find the temperature of the wax bath.

A cubical block of steel of each side equal to $l$ is floating on mercury in a vessel. The density of steel is ${\rho }_s$ and that of mercury is ${\rho }_m$. The height of the block above the mercury level is given by

A charged particle of mass m and charge q is released from rest in a uniform electric field E. Neglecting the effect of gravity, the kinetic energy of the charged particle after t second is

A wheel rotating at a speed of $600\text{rpm}$ (revolutions per minute) about its axis is brought to rest by applying a constant torque for $10$ seconds. The angular velocity $5$ seconds after the application of the torque is $n\pi \text{rad/s}$ where $n$ is

Three particles, each of mass 200 g, are kept at the corners of an equilateral triangle of side 10 cm. Find the moment of intertia of the system about an axis

(a) joining two of the particles and

(b) passing through one of the particles and perpendicular to the plane of the particles.

A particle is dropped from the top of a building . When it crosses a point $5\text{m}$ below the top , another particles starts to fall from a point $25\text{m}$ below the top , both particles reach the bottom of the building simultaneously. The height of the building is :

$[g=10{\text{m/s}}^2]$

A block of mass m rigidly attached with a spring k is compressed through a distance A. If the block is released, the period of oscillation of the block for a complete cycle is equal to