A parallel- plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constant k₁, k₂, k₃ and k₄ as shown in the figure below. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by

An electric dipole is placed at an angle of 30º with an electric field intensity 2 ×10⁵ N/C. It experiences a torque equal to 4 N m. The charge on the dipole, if the dipole length is 2cm, is

Three sound waves of equal amplitudes have frequencies (n –1), n, (n + 1). They superimpose to give beats. The number of beats produced per second will be

The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L meter long. The length of the open pipe will be

A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3 s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5 s. The value of m in kg is :

A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas ?