The equivalent capacitance between points \(A\) and \(B\) in below shown figure will be..........\(\mu F\).

The effective current \(I\) in the given circuit at very high frequencies will be \(.......A\)

The position of the centre of mass of a uniform semi-circular wire of radius \('R'\) placed in \(x-y\) plane with its centre at the origin and the line joining its ends as \(x\)-axis is given by \(\left(0, \frac{x R}{\pi}\right)\). Then, the value of \(|x|\) is ...... .

When the temperature of a metal wire is increased from \(0^{\circ} \,C\) to \(10^{\circ}\, C\), its length increases by \(0.02 \% .\) The percentage change in its mass density will be closest to:

Given below are two statements Statement \(I\) : When the frequency of an \(a.c.\) source in a series \(LCR\) circuit increases, the current in the circuit first increases, attains a maximum value and then decreases. Statement \(II:\) In a series \(LCR\) circuit, the value of power factor at resonance is one. In the light of given statements, choose the most appropriate answer from the options given below

Consider a circular coil of wire carrying constant current \(I\), forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by \(\phi_{i} .\) The magnetic flux through the area of the circular coil area is given by \(\phi_{0} .\) Which of the following option is correct?

Two point charges \(8 \, \mu C\) and \(-2 \, \mu C\) are located at \(x = 2\) cm and \(x = 4\) cm, respectively on the \(x\)-axis. The ratio of electric flux due to these charges through two spheres of radii \(3\) cm and \(5\) cm with their centers at the origin is _______.

When one moves from a point \(16\) km below the earth's surface to a point \(16\) km above the earth's surface. The change in \(g\) is approximately \(\alpha\) %. The value of \(\alpha\) is _____.
(Take radius of the earth \(= 6400\) km.)

In the given figure, a body of mass \(M\) is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant \(k,\) the frequency of oscillation of given body is :