The pair of physical quantities not having same dimensions is :

A physical quantity \(Q\) is related to four observables \(a, b, c, d\) as follows :
\(\mathrm{Q}=\frac{\mathrm{ab}{ }^4}{\mathrm{~cd}}\)

where, \(\mathrm{a}=(60 \pm 3) \mathrm{Pa} ; \mathrm{b}=(20 \pm 0.1) \mathrm{m} ; \mathrm{c}=(40 \pm 0.2) \mathrm{Nsm}^{-2}\) and \(\mathrm{d}=(50 \pm 0.1) \mathrm{m}\), then the percentage error in Q is \(\frac{x}{1000}\), where \(x=\) ________ .

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:

The weight of a body at the surface of earth is \(18\,N\). The weight of the body at an altitude of \(3200\,km\) above the earth's surface is \(........\,N\) (given, radius of earth \(R _{ e }=6400\,km\) )

Which of the following equations represents a travelling wave ?

For a free body diagram shown in the figure, the four forces are applied in the ' \(x\) ' and ' \(y\) ' directions. What additional force must be applied and at what angle with positive \(x\)-axis so that the net acceleration of body is zero?

A small soap bubble of radius \(4\,cm\)  is trapped inside another bubble of radius \(6\,cm\) without any contact. Let \(P_2\)  be the pressure inside the inner bubble and \(P_0\)  the pressure outside the outer bubble. Radius of another bubble with pressure difference \(P_2 - P_0\)  between its inside and outside would be....... \(cm\)

Two charged conducting spheres of radii \(a\) and \(b\) are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is _______.

move in opposite direction with speed ratio \(1: 2\). The following figure represents two biconvex lenses \(L_1\) and \(L_2\) having focal length \(10 \mathrm{~cm}\) and \(15 \mathrm{~cm}\) respectively. The distance between \(\mathrm{L}_1 \& \mathrm{~L}_2\) is _______.

The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered by the object between \(t=0\) to \(t=4 \mathrm{~s}\) ?