\(2\, moles\) of helium gas is mixed with \(3\, moles\) of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume ....... \(J/mol\, K\) ? \((R = 8.3\, J/mol\, K)\)

Read the following statements: \((A)\) Volume of the nucleus is directly proportional to the mass number. \((B)\) Volume of the nucleus is independent of mass number. \((C)\) Density of the nucleus is directly proportional to the mass number. \((D)\) Density of the nucleus is directly proportional to the cube root of the mass number. \((E)\) Density of the nucleus is independent of the mass number. Choose the correct option from the following options.

The current of \(5 \mathrm{~A}\) flows in a square loop of sides \(1\) \(\mathrm{m}\) is placed in air. The magnetic field at the centre of the loop is \(\mathrm{X} \sqrt{2} \times 10^{-7} \mathrm{~T}\). The value of \(\mathrm{X}\) is _______.

A diatomic gas \((\gamma=1.4)\) does \(200 \mathrm{~J}\) of work when it is expanded isobarically. The heat given to the gas in the process is _______.

The range of the projectile projected at an angle of \(15^{\circ}\) with horizontal is \(50\,m\). If the projectile is projected with same velocity at an angle of \(45^{\circ}\) with horizontal, then its range will be \(........\,m\)

The density of a material in \(SI\, units\) is \(128\, kg\, m^{-3}\). In certain units in which the unit of length is \(25\, cm\) and the unit of mass \(50\, g\), the numerical value of density of the material is

Given below are two statements:
Statement \(I\): Electromagnetic waves carry energy as they travel through space and this energy is equally shared by the electric and magnetic fields.
Statement \(II\): When electromagnetic waves strike a surface, a pressure is exerted on the surface.
In the light of the above statements, choose the most appropriate answer from the options given below:

An electron is travelling with a velocity \(v\) in free space and when it enters a medium, its velocity is reduced by \(20\%\). The de Broglie wavelength of electron in the medium is \(\alpha\lambda_0\), where \(\lambda_0\) is its de Broglie wavelength in free space. The value of \(\alpha\) is _______.

A \(16\, \Omega\) wire is bend to form a square loop. A \(9 \,{V}\) supply having internal resistance of \(1 \,\Omega\) is connected across one of its sides. The potential drop across the diagonals of the square loop is \(.......\,\times 10^{-1} \,{V}\)

Two capacitors, each having capacitance \(40\,\mu F\) are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant \(K\) such that the equivalence capacitance of the system became \(24\,\mu F\). The value of \(K\) will be.

A parallel plate capacitor was made with two rectangular plates, each with a length of \(l=3 \mathrm{~cm}\) and breath of \(\mathrm{b}=1 \mathrm{~cm}\). The distance between the plates is \(3 \mu \mathrm{~m}\). Out of the following, which are the ways to increase the capacitance by a factor of 10 ?
A. \(l=30 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m}\)
B. \(l=3 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=30 \mu \mathrm{~m}\)
C. \(l=6 \mathrm{~cm}, \mathrm{~b}=5 \mathrm{~cm}, \mathrm{~d}=3 \mu \mathrm{~m}\)
D. \(l=1 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=10 \mu \mathrm{~m}\)
E. \(l=5 \mathrm{~cm}, \mathrm{~b}=2 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m}\)
Choose the correct answer from the options given below:

In a potentiometer arrangement, a cell gives a balancing point at \(75\, cm\) length of wire. This cell is now replaced by another cell of unknown emf. If the ratio of the emf's of two cells respectively is \(3: 2\), the difference in the balancing length of the potentiometer wire in above two cases will be.........\(cm .\)