A wire of resistance \(R\) is bent to form a square \(ABCD\) as shown in the figure. The effective resistance between \(E\) and \(C\) is ( \(E\) is mid-point of arm \(CD\) )

For the series LCR circuit connected with 220 V , 50 Hz a.c source as shown in the figure, the power factor is \(\frac{\alpha}{10}\). The value of \(\alpha\) is _________

A spring of unstretched length \(l\) has a mass \(m\) with one end fixed to a rigid support .Assuming spring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity \(v\) is

A gas is compressed adiabatically, which one of the following statement is NOT true.

If the potential barrier across a \(p - n\) junction is \(0.6\,V\). Then the electric field intensity, in the depletion region having the width of \(6 \times 10^{-6} m\), will be \(......\times 10^{5} N / C\).

A particle is moving in one dimension (along the x-axis) under the action of a variable force. Its position \( x \) (in meters) varies with time \( t \) (in seconds) according to the equation \( x = -3t^3 + 18t^2 + 16t + 16 \). The velocity of the particle when its acceleration becomes zero is _________ \( \text{m/s} \).

The pitch and the number of divisions, on the circular scale, for a given screw gauge are \(0.5\,mm\) and \(100\) respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies \(3\) divisions below the mean line. The readings of the main scale and the circular scale for a thin sheet, are \(5.5\,mm\) and \(48\) respectively, the thickness of this sheet is

A radioactive nucleus decays by two different processes. The half life for the first process is \(10\, s\) and that for the second is \(100 s\). the effective half life of the nucleus is close to\(.....sec\)

A plane progressive wave is given by \(y=2 \cos 2 \pi(330 t-x) m\). The frequency of the wave is _______.

A particular hydrogen - like ion emits the radiation of frequency \(3 \times 10^{15} \mathrm{~Hz}\) when it makes transition from \(n=2\) to \(n=1\). The frequency of radiation emitted in transition from \(n=3\) to \(n=1\) is \(\frac{x}{9} \times 10^{15} \mathrm{~Hz}\), when \(x=\) = _____.