The refractive index of a prism with apex angle \(A\) is \(\cot A / 2\). The angle of minimum deviation is _______.

The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of \(176 rad / s\). The frequency of this simple harmonic oscillator is _________ Hz. \(\left[\right.\) take \(\left.\pi=\frac{22}{7}\right]\)

An object viewed from a near point distance of \(25\, {cm}\), using a microscopic lens with magnification \('6',\) gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length \(0.6\, {m}\), if the focal length of the eyepiece is euqal to \(.... \,{cm} .\)

A uniformly charged disc of radius \(R\) having surface charge density \(\sigma\) is placed in the \({xy}\) plane with its center at the origin. Find the electric field intensity along the \(z\)-axis at a distance \(Z\) from origin :-

In a hydrogen like atom electron make transition from an energy level with quantum number \(n\) to another with quantum number \((n- 1)\). If \(n > >  1\), the frequency ofradiation emitted is proportional to

A ball of mass \(0.5 \mathrm{~kg}\) is attached to a string of length \(50 \mathrm{~cm}\). The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is \(400 \mathrm{~N}\). The maximum possible value of angular velocity of the ball in rad/s is _______.

The temperature of an open room of volume \(30\ m^3\) increases from \(17^o C\) to \(27vC\) due to sunshine. The atmospheric pressure in the room remains \(1 \times 10^5\ Pa\). Ifni and nr are the number of molecules in the room before and after heating, then \(n_f-n_i\) will be :

The refractive index of a transparent liquid filled in an equilateral hollow prism is \(\sqrt{2}\). The angle of minimum deviation for the liquid will be

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A:\) The binding energy per nucleon is practically independent of the atomic number for nuclei of mass number in the range \(30\) to \(170\). Reason \(R\) : Nuclear force is short ranged. In the light of the above statements, choose the correct answer from the options given below on

A wire of resistance \(R_{1}\) is drawn out so that its length is increased by twice of its original length.The ratio of new resistance to original resistance is.

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 light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of crosssectional area \('a'\) is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is \((a\,<\,<\,A)\)