For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where \(\gamma\) is the ratio of specific heats):

Figure shows the circuit that contains three resistances (9 Ω each) and two inductors (4 mH each). The reading of ammeter at the moment switch K is turned ON, is__________ A.

A radioactive substance decays to \(\left(\frac{1}{16}\right)^{t h}\) of its initial activity in \(80\, days.\) The half life of the radioactive substance expressed in days is ... .

A parallel plate capacitor has a capacitance \(\mathrm{C}=200 \mathrm{pF}\). It is connected to \(230 \mathrm{~V}\) ac supply with an angular frequency \(300 \mathrm{rad} / \mathrm{s}\). The \(\mathrm{rms}\) value of conduction current in the circuit and displacement current in the capacitor respectively are _______.

When a beam of white light is allowed to pass through convex lens parallel to principal axis, the different colours of light converge at different point on the principle axis after refraction. This is called:

In a Young's double slit experiment, the distance between the two identical slits is \(6.1\) times larger than the slit width. Then the number of intensity maxima observed with in the central maximum of the single slit diffraction pattern is

Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to......

All resistances in figure are \(1\,\Omega\) each. The value of current ' \(I\) ' is \(\frac{a}{5}\,A\). The value of \(a\) is

Two identical blocks \(A\) and \(B\) each of mass \(m\) resting on the smooth horizontal floor are connected by a light spring of natural length \(L\) and spring constant \(K\). A third block \(C\) of mass \(m\) moving with a speed \(v\) along the line joining \(A\) and \(B\) collides with \(A\).The maximum compression in the spring is

A wire of resistance \(160\,\Omega\) is melted and drawn in wire of one-fourth of its length. The new resistance of the wire will be \(......\Omega\)

One mole of an ideal monoatomic gas is taken along the path \(ABCA\)  as shown in the \(PV\) diagram. The maximum temperature attained by the gas along the path \(BC\)  is given by