In a collinear collision, a particle with an initial speed v0 strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is :

A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let P2 be the pressure inside the inner bubble and P0, the pressure outside the outer bubble. Radius of another bubble with pressure difference P2 $$-$$ P0 between its inside and outside would be :

As shown in the figure, forces of 105 N each are applied in opposite directions, on the upper and lower faces of a cube of side 10 cm, shifting the upper face parallel to itself by 0.5 cm. If the side of another cube of the same material is 20 cm, then under similar conditions as above, the displacement will be :

When an air bubble of radius r rises from the bottom to the surface of a lake its radius becomes {{5r} \over 4}. Taking the atmospheric pressure to be equal to 10 m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature) :

A thin uniform tube is bent into a circle of radius $$r$$ in the vertical plane. Equal volumes of two immiscible liquids, whose densities are $${\rho }_1$$ and $${\rho }_2$$ $$\left({\rho }_1>{\rho }_2\right),$$ fill half the circle. The angle $$\theta$$ between the radius vector passing through the common interface and the vertical is :

A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, \left( {{dr \over r}} \right) is:

A body takes 10 minutes to cool from 60oC to 50oC. The tempertature of surroundings is constant at 25oC. Then, the temperature of the body after next 10 minutes will be approximately :

A disc rotates about its axis of symmetry in a horizontal plane at a steady rate of $$3.5$$ revolutions per second. A coin placed at a distnce of 1.25 cm from the axis of rotation remains at rest on the disc. The coefficient of friction between the coin and the disc is : (g = 10 m/s2)

In the given circuit, the current through zener diode is :

Truth table for the following digital circuit will be :

In a common emitter configuration with suitable bias, it is given that $$R_L$$ is the load resistance and $$R_{BE}$$ is small signal dynamic resistance (input side). Then, voltage gain, current gain and power gain are given, respectively, by : $$\beta$$ is curret gain, $${\mathrm{I}}_B,{\mathrm{I}}_C$$ and $${\mathrm{I}}_E$$ are respectively base, collector and emitter currents.

The reading of the ammeter for a silicon diode in the given circuit is :

A particle executes simple harmonic motion and is located at x = a, b and c at times t0, 2t0 and 3t0 respectively. The freqquency of the oscillation is :

An oscillator of mass M is at rest in its equilibrium position in a potential V = {1 \over 2} k(x $$-$$ X)2. A particle of mass m comes from right with speed u and collides completely inelastically with M and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after 13 collisions is : (M = 10, m = 5, u = 1, k = 1)

Two simple harmonic motions, as shown below, are at right angles. They are combined to form Lissajous figures. x(t) = A sin (at + $$\delta$$) y(t) = B sin (bt) Identify the correct match below.

A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1012/sec. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 and Avogadro number = 6.02 × 1023 gm mole–1)

A monochromatic beam of light has a frequency v = {3 \over {2\pi }} \times {10^{12}}Hz and is propagating along the direction {{\widehat i + \widehat j} \over {\sqrt 2 }}. It is polarized along the $$\hat{k}$$ direction. The acceptable form for the magnetic field is :

An EM wave from air enters a medium. The electric fields are $$\overrightarrow{E_1}$$ = {E_{01}}\widehat x\cos \left[ {2\pi v\left( {{z \over c} - t} \right)} \right] in air and $$\overrightarrow{E_2}$$ = $$E_{02}\hat{x}\cos \left[k\left(2z-ct\right)\right]$$ in medium, where the wave number k and frequency $$\nu$$ refer to their values in air. The medium is non-magnetic. If $${\epsilon }_{r_1}$$ and $${\epsilon }_{r_2}$$ refer to relative permittivities of air and medium respectively, which of the following options is correct ?

A plane polarized monochromatic EM wave is traveling in vacuum along z direction such that at t = t1 it is found that the electric field is zero at a spatial point z1. The next zero that occurs in its neighbourhood is at z2. The frequency of the electroagnetic wave is :

A plane electromagnetic wave of wavelength $$\lambda$$ has an intensity I. It is propagatting along the positive Y-direction. The allowed expressions for the electric and magnetic fields are givn by :