Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be

A simple pendulum of length \(1\, m\) is oscillating with an angular frequency \(10\, rad/s\). The support of the pendulum starts oscillating up and down with a small angular frequency of \(1\, rad/s\) and an amplitude of \(10^{-2}\, m\). The relative change in the angular frequency of the pendulum is best given by

In the reported figure, two bodies \(A\) and \(B\) of masses \(200\, {g}\) and \(800\, {g}\) are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be \(.....\,{rad} / {s}\) when \({k}=20 \,{N} / {m} .\)

A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle \(60^o\) with ground level. But he finds the aeroplane right vertically above his position. If \(\upsilon \) is the speed of sound, speed of the plane is

A \(d.c.\) main supply of \(e.m.f.\, 220\, V\) is connected across a storage battery of \(e.m.f.\, 200\, V\) through a resistance of \(1\,\Omega \). The battery terminals are connected to an external resistance \('R'\) . The minimum value of \('R'\), so that a current passes through the battery to charge it is ............... \(\Omega\)

Let \(\left| {{{\vec A}_1}} \right| = 3,\,\left| {\vec A_2} \right| = 5\), and \(\left| {{{\vec A}_1} + {{\vec A}_2}} \right| = 5\). The value of \(\left( {2{{\vec A}_1} + 3{{\vec A}_2}} \right)\cdot \left( {3{{\vec A}_1} - 2{{\vec A}_2}} \right)\) is

A capacitor is discharging through a resistor \(R\). Consider in time \(t _{1}\), the energy stored in the capacitor reduces to half of its initial value and in time \(t_{2}\), the charge stored reduces to one eighth of its initial value. The ratio \(t_{1} / t_{2}\) will be ................

A sample of radioactive material \(A\), that has an activity of \(10\, mCi\, (1\, Ci = 3.7 \times 10^{10}\, decays/s)\), has twice the number of nuclei as another sample of different radioactive material \(B\) which has an activity of \(20\, mCi\). The correct choices for half-lives of \(A\) and \(B\) would then be respectively

Match List \(I\) with List \(II.\)

List \(I\)	List \(II\)
\((a)\) Rectifier	\((i)\) Used either for stepping up or stepping down the \(a.c.\) voltage
\((b)\) Stabilizer	\((ii)\) Used to convert \(a.c.\) voltage into \(d.c.\) voltage
\((c)\) Transformer	\((iii)\) Used to remove any ripple in the rectified output voltage
\((d)\) Filter	\((iv)\) Used for constant output voltage even when the input voltage or load current change

Choose the correct answer from the options given below:

A particle initially at rest starts moving from reference point. \(\mathrm{x}=0\) along \(\mathrm{x}\)-axis, with velocity \(v\) that varies as \(v=4 \sqrt{\mathrm{x} m} / \mathrm{s}\). The acceleration of the particle is _______ \( \mathrm{ms}^{-2}\).

A wire of resistance \(R_{1}\) is drawn out so that its length is increased by twice of its original length.The ratio of new resistance to original resistance is.