What is the relative decrease in focal length of a lens for an increase in optical power by 0.1 D from 2.5D ? ['D' stands for dioptre]

If \(M_0\) is the mass of isotope \({ }_5^{12} B, M_p\) and \(M_n\) are the masses of proton and neutron, then nuclear binding energy of isotope is _______.

A galaxy is moving away from the earth at a speed of \(286\, kms ^{-1}\). The shift in the wavelength of a red line at \(630\, nm\) is \(x \times 10^{-10}\, m\). The value of \(x ,\) to the nearest integer, is........ [Take the value of speed of light \(c,\) as \(3 \times 10^{8}\) \(\left. ms ^{-1}\right]\)

Two cells are connected between points \(A\) and \(B\) as shown. Cell \(1\) has emf of \(12\,V\) and internal resistance of \(3\,\Omega\). Cell \(2\) has emf of \(6\,V\) and internal resistance of \(6\,\Omega\). An external resistor \(R\) of \(4\,\Omega\) is connected across \(A\) and \(B\). The current flowing through \(R\) will be \(.............A\).

A bulb and a capacitor are connected in series across an AC supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb:

Two different metal bodies \(A\) and \(B\) of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is :

A circular disc of radius \(b\) has a hole of radius \(a\) at its centre (see figure). If the mass per unit area of the disc varies as \(\left( {\frac{{{\sigma _0}}}{r}} \right)\), then the radius of gyration of the disc about its axis passing through the centre is

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density \(\sigma_{\mathrm{o}}\). Choose the correct option from the following.

In young's double slit experiment, the fringe width is \(12\,mm\). If the entire arrangement is placed in water of refractive index \(\frac{4}{3}\), then the fringe width becomes \((in\,mm)\)

A child stands on the edge of the cliff \(10\,m\) above the ground and throws a stone horizontally with an initial speed of \(5\,ms ^{-1}\). Neglecting the air resistance, the speed with which the stone hits the ground will be \(..........ms ^{-1}\) (given, \(g =10\,ms ^{-2}\))

A green light is incident from the water to the air - water interface at the critical angle \((\theta)\). Select the correct statement .

A faulty thermometer reads \(5^{\circ} C\) in melting ice and \(95^{\circ} C\) in steam. The correct temperature on absolute scale will be. \(.........K\) when the faulty thermometer reads \(41^{\circ} C\).

A rod with circular cross-section area \(2\,cm ^2\) and length \(40\,cm\) is wound uniformly with \(400\) turns of an insulated wire. If a current of \(0.4\,A\) flows in the wire windings, the total magnetic flux produced inside windings is \(4\,\pi \times 10^{-6}\,Wb\). The relative permeability of the rod is (Given : Permeability of  vacuum \(\left.\mu_0=4 \pi \times 10^{-7} \;NA ^{-2}\right)\)