A current of \(2\, mA\) was passed through an unknown resistor which dissipated a power of \(4.4\, W\). Dissipated power when an ideal power supply of \(11\, V\) is connected across it is

A simple pendulum, made of a string of length \(l\) and a bob of mass \(m\) , is released from a small angle \(\theta_0\). It strikes a block of mass \(M\), kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle \(\theta_1\). Then \(M\) is given by

Given below are two statements: one is labelled as Assertion\((A)\) and the other is labelled as Reason \((R).\) \(Assertion\) \((A)\) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading. \(Reason\) \((R)\) : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling. In the light of the above statements, choose the correct answer from the options given below :

A particle executes \(S.H.M.,\) the graph of velocity as a function of displacement is :-

Two radioactive elements \(A\) and \(B\) initially have same number of atoms. The half life of \(A\) is same as the average life of \(B\). If \(\lambda_A\) and \(\lambda_B\) are decay constants of \(A\) and \(B\) respectively, then choose the correct relation from the given options.

In a radioactive material, fraction of active material remaining after time \(t\) is \(\frac{9}{16}\) The fraction that was remaining after \(\frac{t}{2}\) is 

Two beams, \(A\) and \(B\), of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam \(A\) has maximum intensity ( and beam \(B\) has zero intensity), a rotation of polaroid through \(30 ^o \) makes the two beams appear equally bright. If the initial intensities of the two beams are \(I_A\) and \(I_B\)  respectively, then \(\frac{{{I_A}}}{{{I_B}}}\)=

An engine of a train, moving with uniform acceleration, passes the signal-post with velocity \(u\) and the last compartment with velocity \(v\). The velocity with which middle point of the train passes the signal post is