The output of the given circuit diagram is _______.

Cross-section view of a prism is the equilateral triangle \({ABC}\) in the figure. The minimum deviation is observed using this prism when the angle of incidence is equal to the prism angle. The time taken by light to travel from midpoint of \({BC}\) to \({A}\) is \(.....\times 10^{-10}\, {s}\). \((\) Given, speed of light in vacuum \(=3 \times 10^{8} \,{m} / {s}\) and \(\left.\cos 30^{\circ}=\frac{\sqrt{3}}{2}\right)\)

How many alpha and beta particles are emitted when Uranium \({ }_{92} U ^{238}\) decays to lead \({ }_{82} Pb ^{206}\) ?

Rods x and y of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points A and F are maintained at \( 100^{\circ}C \) and \( 40^{\circ}C \) respectively. Given the thermal conductivity of rod x is three times of that of rod y, the temperature at junction points B and E are (close to):

An ideal gas undergoes a process maintaining relation between pressure \((P)\) and volume \((V)\) as \(P = P_o\left(1 + \left(\dfrac{V_o}{V}\right)^2\right)^{-1}\), where \(P_o\) and \(V_o\) are constants. If two samples \(A\) and \(B\) (two moles each) with initial volumes \(V_o\) and \(3V_o\) respectively undergo above mentioned process and attain same pressure, then the difference at the temperatures of these samples, \(T_B - T_A\) is _____. (\(R = \) gas constant)

A block of mass \(m = 10\,kg\) rests on a horizontal table. The coefficient of friction between the block and the table is \(0.05.\) When hit by a bullet of mass \(50\,g\) moving with speed \(v,\) that gets embedded in it, the block moves and comes to stop after moving a distance of \(2\,m\) on the table. If a freely falling object were to acquire speed \(\frac {v}{10}\) after being dropped from height \(H,\) then neglecting energy losses and taking \(g = 10\,ms^{-2},\) the value of \(H\) is close to ................. \(\mathrm{km}\)

An oscillator of mass \(M\)  is at rest in its equilibrium position in a potential \(V\, = \,\frac{1}{2}\,k{(x - X)^2}.\) 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: \((M = 10,\, m = 5,\, u = 1,\, k = 1 ).\) 

For the given figures, choose the correct options:

The volume of an ideal gas \((\gamma=1.5)\) is changed adiabatically from \(5\) litres to \(4\) litres. The ratio of initial pressure to final pressure is _______.

A vernier callipers has \(20\) divisions on the vernier scale, which coincides with \(19^{\text {th }}\) division on the main scale. The least count of the instrument is \(0.1 \mathrm{~mm}\). One main scale division is equal to _______ \(\mathrm{mm}\).

In an experiment, a set of reading are obtained \(-1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm\). The expected least count of the instrument used in recording these readings is ___________ mm.