A circular hole of radius $\left(\frac{a}{2}\right)$ is cut out of a circular disc of radius 'a' as shown in figure. The centroid of the remaining circular portion with respect to point 'O' will be :
If one mole of an ideal gas at $(P_1, V_1)$ is allowed to expand reversibly and isothermally (A to B) its pressure is reduced to one-half of the original pressure. This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value (B → C). Then it is restored to its initial state by a reversible adiabatic compression (C to A). The net work done by the gas is equal to :
In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. If each spring has spring constant k, the frequency of oscillation of given body is :
Match List - I with List - II.
A point charge of +12 µC is at a distance 6 cm vertically above the centre of a square of side 12 cm. The magnitude of the electric flux through the square will be ________ × 10³ Nm²/C.
