In photoelectric experiment energy of \(2.48 \mathrm{eV}\) irradiates a photo sensitive material. The stopping potential was measured to be \(0.5 \mathrm{~V}\). Work function of the photo sensitive material is _______.

Two particles move at right angle to each other. Their de Broglie wavelengths are \({\lambda _1}\) and \({\lambda _2}\) respectively. The particles suffere perfectly inelastic collision. The de Broglie wavelength \(\lambda \) , of the final particle, is given by

A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with \(3 m / s ^2\). At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is \(5 m / s\). The initial height of the aeroplane is ___________m.
\(\left( g =10 m / s ^2\right)\)

Given are statements for certain thermodynamic variables,
(A) Internal energy, volume (V) and mass (M) are extensive variables.
(B) Pressure (P), temperature (T) and density ( \(\rho\) ) are intensive variables.
(C) Volume (V), temperature (T) and density ( \(\rho\) ) are intensive variables.
(D) Mass (M), temperature (T) and internal energy are extensive variables.

Choose the correct answer from the options given below :

In a Young's double slit experiment, two slits are illuminated with a light of wavelength \(800 nm\). The line joining \(A _1 P\) is perpendicular to \(A _1 A _2\) as shown in the figure. If the first minimum is detected at \(P\), the value of slits separation ' \(a\) ' will be \(.........\,mm\) The distance of screen from slits \(D =5\,cm\)

A pendulume clock loses \(12\;s\) a day if the temperature is \(40^oC\) and gains \(4\;s\) a day if the temperature is \(20^oC\). The temperature at which the clock will show correct time, and the coeffecient of linear expansion \((\alpha)\) of the metal of the pendulum shaft are respectively

Two concentric circular loops of radii \(r _{1}=30\,cm\) and \(r_{2}=50\,cm\) are placed in \(X - Y\) plane as shown in the figure. \(A\) current \(I=7\,A\) is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately.

A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is \(\frac{x}{5}\). The value of \(x\) is _______.

A uniform wire of length \(l\) of weight \(w\) is suspended from the roof with a weight of \(W\) at the other end. The stress in the wire at \(\dfrac{l}{3}\) distance from the top is \(\left(\dfrac{W}{A} + \dfrac{2}{\gamma}\dfrac{w}{A}\right)\), where, \(A\) is the cross sectional area of the wire. The value of \(\gamma\) is _______.

Surface tension of a soap bubble is \(2.0 \times 10^{-2}\; Nm ^{-1}\). Work done to increase the radius of soap bubble from \(3.5\; cm\) to \(7\; cm\) will be \(.........\times 10^{-4}\,J\) [Take \(\pi=\frac{22}{7}\) ]

A small ball of mass \(m\) and density \(\rho\) is dropped in a viscous liquid of density \(\rho_0\). After sometime, the ball falls with constant velocity. The viscous force on the ball is _______.

A stream of a positively charged particles having \(\frac{ q }{ m }=2 \times 10^{11} \frac{ C }{ kg }\) and velocity \(\overrightarrow{ v }_0=3 \times 10^7 \hat{ i ~ m} / s\) is deflected by an electric field \(1.8 \hat{ j } kV / m\). The electric field exists in a region of \(10 cm\) along \(x\) direction. Due to the electric field, the deflection of the charge particles in the \(y\) direction is \(...........mm\)

Two batteries with e.m.f \(12\ V\) and \(13\ V\) are connected in parallel across a load resistor of \(10\,\Omega\) . The internal resistances of the two batteries are \(1\,\Omega\) and \(2\,\Omega\) respectively. The voltage across the load lies between