The value of numerical aperature of the objective lens of a microscope is \(1.25\). If light of wavelength \(5000\,\mathop A\limits^o \) is used, the minimum separation between two points, to be seen as distinct, will be....\(\mu m\)

A \(2\, \mu F\) capacitor \(C _{1}\) is first charged to a potential difference of \(10\, V\) using a battery.Then the battery is removed and the capacitor is connected to an uncharged capacitor \(C _{2}\) of \(8\, \mu F\). The charge in \(C _{2}\) on equilibrium condition is \(\ldots\,\mu C\). (Round off to the Nearest Integer)

A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is \(200 \mathrm{~N} / \mathrm{m}\). The block is pushed such that the length of the spring becomes 1 m and then released. At distance \(\mathrm{x} \mathrm{m}(\mathrm{x} \lt 2)\) from the wall. the speed of the block will be :

If \(B\) is magnetic field and \(\mu_0\) is permeability of free space, then the dimensions of \(\left(B / \mu_0\right)\) is

Two conductors have the same resistances at \(0^{\circ} \mathrm{C}\) but their temperature coefficients of resistance are \(\alpha_1\) and \(\alpha_2\). The respective temperature coefficients for their series and parallel combinations are _______.

A heat engine is involved with exchange of heat of \(1915\, J,\) \(-40\, J ,+125\, J\) and \(-Q\,J\), during one cycle achieving an efficiency of \(50.0 \%\). The value of \(Q\) is.......\(J\)

A coil of area A and N turns is rotating with angular velocity \(\omega\) in a uniform magnetic field \(\vec{B}\) about an axis perpendicular to \(\vec{B}\). Magnetic flux \(\varphi\) and induced \(\operatorname{emf} \varepsilon\) across it, at an instant when \(\vec{B}\) is parallel to the plane of coil, are :

If the potential barrier across a \(p - n\) junction is \(0.6\,V\). Then the electric field intensity, in the depletion region having the width of \(6 \times 10^{-6} m\), will be \(......\times 10^{5} N / C\).

Assume that protons and neutrons have equal masses. Mass of a nucleon is \(1.6 \times 10^{-27}\,kg\) and radius of nucleus is \(1.5 \times 10^{-15} A ^{1 / 3}\,m\). The approximate ratio of the nuclear density and water density is \(n \times 10^{13}\). The value of \(n\) is \(.................\)

A spring stretches by \(2\) mm when it is loaded with a mass of \(200\) g. From equilibrium position the mass is further pulled down by \(2\) mm and released. The frequency associated with the system and maximum energy in the spring are __________ Hz and __________ J, respectively. (Take g \(= 10\) m/s\(^2\))

Two identical bodies \(A\) and \(B\) of equal masses have initial velocities \(\vec{v_1} = 4\hat{i}\) m/s and \(\vec{v_2} = 4\hat{j}\) m/s respectively. The body \(A\) has acceleration \(\vec{a_1} = 6\hat{i} + 6\hat{j}\) m/s\(^2\) while the acceleration of the other body \(B\) is zero. The centre of mass of the two bodies moves in __________ path.

A fringe width of \(\,6 mm\) was produced for two slits separated by \(1\, mm\) apart. The screen is placed \(10\, m\) away. The wavelength of light used is \('x'\, nm.\) The value of \('x'\) to the nearest integer is

If the distance between object and its two times magnified virtual image produced by a curved mirror is \(15 \mathrm{~cm}\), the focal length of the mirror must be _______.