Arrange the four graphs in descending order of total work done; where \(W _{1}, W _{2}, W _{3}\) and \(W _{4}\) are the work done corresponding to figure \(a , b , c\) and d respectively.

In the following circuit, the correct relation between output \(( Y )\) and inputs \(A\) and \(B\) will be

Two equal positive point charges are separated by a distance \(2 a\). The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge \(q_0\) becomes maximum is \(\frac{a}{\sqrt{x}}\). The value of \(x\) is \(................\)

If a copper wire is stretched to increase its length by \(20 \% \). The percentage increase in resistance of the wire is \(..........\%\)

A solid sphere of radius \(R\) carries a charge \((Q+q)\) distributed uniformly over its volume. A very small point like piece of it of mass \(m\) gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge \(q.\) If it acquires a speed \(v\) when it has fallen through a vertical height \(y\) (see figure), then : (assume the remaining portion to be spherical).

Four particles, each of mass \(M\) and equidistant from each other, move along a circle of radius \(R\) under the action of their mutual gravitational attraction. The speed of each particle is

Two iron solid discs of negligible thickness have radius \(R_1\) and \(R_2\) and moment of intertia \(I_1\) and \(I_2\), respectively. For \(R_2=2 R_1\), the ratio of \(I_1\) and \(I_2\) would be \(1 / x\), where \(\mathrm{x}=\) ________ -

A uniformly charged ring of radius \(3a\) and total charge \(q\) is placed in \(xy-\) plane centered at origin. A point charge \(q\) is moving towards the ring along the \(z-\) axis and has speed \(v\) at \(z = 4a\). The minimum value of \(v\) such that it crosses the origin is

The resultant of these forces \(\overrightarrow{O P}, \overrightarrow{O Q}, \overrightarrow{O R}, \overrightarrow{O S}\) and \(\overrightarrow{{OT}}\) is approximately \(\ldots \ldots {N}\). [Take \(\sqrt{3}=1.7, \sqrt{2}=1.4\) Given \(\hat{{i}}\) and \(\hat{{j}}\) unit vectors along \({x}, {y}\) axis \(]\)

The maximum intensity in a Young's double slit experiment is \(I_0\). Distance between the slits (\(d\)) is \(5\lambda\), where \(\lambda\) is the wavelength of light used. The intensity of the fringe, exactly opposite to one of the slits on the screen, placed at \(D = 10d\) is _______.

An electric dipole of dipole moment \(6 \times 10^{-6} \mathrm{Cm}\) is placed in uniform electric field of magnitude \(10^6 \mathrm{~V} / \mathrm{m}\). Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be ____ J.

7.9 MeV \( \alpha \)-particle scatters from a target material of atomic number 79. From the given data the estimated diameter of nuclei of the target material is (approximately) __________m.
\(\left[\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 Nm ^2 / C ^2\right.\) and electron charge \(\left.=1.6 \times 10^{-19} C \right]\)