The exit surface of a prism with refractive index \(n\) is coated with a material having refractive index \(\frac{ n }{2}\). When this prism is set for minimum angle of deviation it exactly meets the condition of critical angle. The prism angle is _________

A particle executes simple harmonic motion with an amplitude of \(4 \mathrm{~cm}\). At the mean position, velocity of the particle is \(10 \mathrm{~cm} / \mathrm{s}\). The distance of the particle from the mean position when its speed becomes \(5 \mathrm{~cm} / \mathrm{s}\) is \(\sqrt{\alpha} \mathrm{cm}\), where \(\alpha=\)____________.

The output characteristics of a transistor is shown in the figure. When \(V_{C E}\) is \(10\, V\) and \(I_{ C }=4.0\, mA ,\) then value of \(\beta_{ ac }\) is

Heat is given to an ideal gas in an isothermal process. \(A.\) Internal energy of the gas will decrease. \(B.\) Internal energy of the gas will increase. \(C.\) Internal energy of the gas will not change. \(D.\) The gas will do positive work. \(E.\) The gas will do negative work. Choose the correct answer from the options given below :

Identify the characteristics of an adiabatic process in a monoatomic gas.
(A) Internal energy is constant.
(B) Work done in the process is equal to the charge in internal energy.
(C) The product of temperature and volume is a constant.
(D) The product of pressure and volume is a constant.
(E) The work done to change the temperature from \(\mathrm{T}_1\) to \(\mathrm{T}_2\) is proportional to \(\left(\mathrm{T}_2-\mathrm{T}_1\right)\)
Choose the correct answer from the options given below :

A tennis ball is dropped on to the floor from a height of \(9.8\,m\). It rebounds to a height \(5.0\,m\). Ball comes in contact with the floor for \(0.2\,s\). The average acceleration during contact is \(..........ms ^{-2}\). [Given \(g =10\,ms ^{-2}\) ]

As per the given figure, two blocks each of mass \(250\,g\) are connected to a spring of spring constant \(2\,Nm ^{-1}\). If both are given velocity \(V\) in opposite directions, then maximum elongation of the spring is:

A copper wire is stretched to make it \(0.5\%\) longer. The percentage change in its electric resistance if its volume remains unchanged is ................ \(\%\)

The frequency \((v)\) of an oscillating liquid drop may depend upon radius \((r)\) of the drop, density \((\rho)\) of liquid and the surface tension \((s)\) of the liquid as : \(v=r^{ a } \rho^{ b } s ^{ c }\). The values of \(a , b\) and \(c\) respectively are

Match List \(I\) with List \(II\) of Electromagnetic waves with corresponding wavelength range :

List \(I\)	List \(II\)
\((A)\) Microwave	\((I)\) \(400\,nm\) to \(1\,nm\)
\((B)\) Ultraviolet	\((II)\) \(1\,nm\) to \(10^{-3}\,nm\)
\((C)\) \(X-\)Ray	\((III)\) \(1\,mn\) to \(700\,nm\)
\((D)\) Infra-red	\((IV)\) \(0.1\,m\) to \(1\,mm\)

Choose the correct answer from the options given below:

An electron revolves around an infinite cylindrical wire having uniform linear change density \(2 \times 10^{-8}\,Cm ^{-1}\) in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is \(.........\times 10^6\,ms ^{-1}\). Given mass of electron \(=9 \times 10^{-31}\,kg\)

A \(16\  \Omega\) wire is bend to form a square loop. A \(9 \mathrm{~V}\) battery with internal resistance \(1\  \Omega\) is connected across one of its sides. If a \(4\  \mu \mathrm{F}\) capacitor is connected across one of its diagonals, the energy stored by the capacitor will be \(\frac{x}{2} \ \mu \mathrm{J}\). where \(x=\) ________.

There are two infinitely long straight current carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductor is \(1: 1\). The magnetic field at point \(P\) is ...... .