A capacitance of 2 $$\mu $$F is required in an electrical circuit across a potential difference of 1.0 kV. A large number of 1 $$\mu $$F 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:

In a coil of resistance 100 $$\Omega $$, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is:

A magnetic needle of magnetic moment 6.7 $$\times$$ 10^-2 A m² and moment of inertia 7.5 $$\times$$ 10^-6 kg m² is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is:

C_P and C_v are specific heats at constant pressure and constant volume respectively. It is observed that
C_P – C_v = a for hydrogen gas
C_P – C_v = b for nitrogen gas
The correct relation between a and b is