For an ideal gas the instantaneous change in pressure \('{p} '\) with volume \('v'\) is given by the equation \(\frac{{dp}}{{dv}}=-{ap} .\) If \({p}={p}_{0}\) at \({v}=0\) is the given boundary condition, then the maximum temperature one mole of gas can attain is : (Here \({R}\) is the gas constant)

Two masses \(m\) and \(\frac{m}{2}\) are connected at the two ends of a massless rigid rod of length \(l\). The rod is suspended by a thin wire of torsional constant \(k\) at the centre of mass of the rodmass system (see figure). Because of torsional constant \(k\), the restoring torque is \(\tau  = k\,\theta \) for angular displacement \(\theta \). If the rod is rotated by \(\theta _0\) and released, the tension in it when it passes through its mean position will be

A polarizer - analyser set is adjusted such that the intensity of light coming out of the analyser is just \(10 \%\) of the original intensity. Assuming that the polarizer - analyser set does not absorb any light, the angle by which the analyser need to be rotated further to reduce the output intensity to be zero, is.....\(^o\)

The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass \(4\;kg\). (The coordinates of the same are shown in figure) are

In a compound microscope, the magnified virtual image is formed at a distance of \(25\, cm\) from the eye-piece. The focal length of its objective lens is \(1\, cm .\) If the magnification is \(100\) and the tube length of the microscope is \(20\, cm ,\) then the focal length of the eye-piece lens (in \(cm\) ) is

An electron revolving in \(\mathrm{n}^{\text {th }}\) Bohr orbit has magnetic moment \(\mu_n\). If \(\mu_n\) \(\alpha\) \(n^x\), the value of \(x\) is _______.

When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted election is \(v _{1}\). When the frequency of incident radiation is increased to five times the threshold value, the maximum velocity of emitted electron becomes \(v _{2}\). If \(v _{2}= x\) \(v _{1}\), the value of \(x\) will be...........

A ray of light passing through an equilateral prism is having velocity \(2.12 \times 10^8\) m/s in the prism material, then the minimum angle of deviation is _________ degrees.

A capacitance of \(2\ μF\) is required in an electrical circuit across a potential difference of \(1.0\ kV\). A large number of \(1\ μF\) capacitors are available which can withstand a potential difference of not more than \(300\ V\). The minimum number of capacitors required to achieve this is

The momentum of an electron revolving in \(n ^{\text {th }}\) orbit is given by: (Symbols have their usual meanings)

List - I	List - II
(A) Heat capacity of body	\(\text{(I) } \mathrm{J} \mathrm{kg}^{-1}\)
(B) Specific heat capacity of body	\(\text{(II) } \mathrm{JK}^{-1}\)
(C) Latent heat	\(\text{(III) } \mathrm{J} \mathrm{kg}^{-1} \mathrm{~K}^{-1}\)
(D) Thermal conductivity	\(\text{(IV) } \mathrm{Jm}^{-1} \mathrm{~K}^{-1} \mathrm{~s}^{-1}\)

Choose the correct answer from the options given below: