The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by \(4\, \%\), will be ......... \(\%\)

A physical quantity C is related to four other quantities \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) and s as follows \(\mathrm{C}=\frac{\mathrm{pq}^2}{\mathrm{r}^3 \sqrt{\mathrm{~s}}}\)
The percentage errors in the measurement of \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) and s are \(1 \%, 2 \% 3 \%\) and \(2 \%\) respectively. The percentage error in the measurement of C will be _____\(\%\).

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

List \(I\)	List \(II\)
\(A\) Troposphere	\(I\) Approximate \(\quad 65-75\, km\) over Earth's surface
\(B\) E-Part of Stratosphere	\(II\) Approximate \(300\,km\) over Earth's surface
\(C\) \(F _2\)-Part of Thermosphere	\(III\)  Approximate \(10\,km\) over Earth's surface
\(D\) \(F _2\)-Part of Thermosphere	\(IV\) Approximate \(100\,km\) over Earth's surface

Choose the correct answer from the options given below:

The half-life of a radioactive nucleus is \(5\) years, The fraction of the original sample that would decay in \(15\) years is

Steel ruptures when a shear of \(3 .5 \times 10^8\,\,N\,m^{-2}\) is applied. The force needed to punch a \(1\,cm\) diameter hole in a steel sheet \(0.3\,cm\) thick is nearly

Equivalent resistance of the following network is _______ \(\Omega\).

In the figure shown below, a resistance of \(150.4 \Omega\) is connected in series to an ammeter A of resistance \(240 \Omega\). A shunt resistance of \(10 \Omega\) is connected in parallel with the ammeter. The reading of the ammeter is _____ mA.

A given object takes \(n\) times the time to slide down \(45^{\circ}\) rough inclined plane as it takes the time to slide down an identical perfectly smooth \(45^{\circ}\) inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is _______.