If \(917 \mathring A\) be the lowest wavelength of Lyman series then the lowest wavelength of Balmer series will be .......\(\mathring A\).

Statement \(I :\) The ferromagnetic property depends on temperature. At high temperature, ferromagnet becomes paramagnet. Statement \(II :\) At high temperature, the domain wall area of a ferromagnetic substance increases. In the light of the above statements, choose the most appropriate answer from the options given below :

charge \(Q\) is uniformly distributed over a long rod \(AB\) of length \(L\) as shown in the figure. The electric potential at the point \(O\) lying at distance \(L\) from the end \(A\) is

A bullet of mass \(0.1\,kg\) moving horizontally with speed \(400\,ms ^{-1}\) hits a wooden block of mass \(3.9\,kg\) kept on a horizontal rough surface. The bullet gets embedded into the block and moves \(20\,m\) before coming to rest. The coefficient of friction between the block and the surface is \(........\) \(\left(\text { Given } g=10 \,ms ^2\right. \text { ) }\)

Given below are two statements : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R.\) Assertion \(A :\) Moment of inertia of a circular disc of mass \('M'\) and radius \('R'\) about \(X, Y\) axes (passing through its plane) and \(Z-\)axis which is perpendicular to its plane were found to be \(I_{x}, I_{y}\) and \({I}_{z}\) respectively. The respective radii of gyration about all the three axes will be the same. Reason \(R\) : A rigid body making rotational motion has fixed mass and shape. In the light of the above statements, choose the most appropriate answer from the options given below :

A rectangles solid box of length \(0.3\, m\) is held horizontally, with one of its sides on the edge of a platform of height \(5\,m\). When released, it slips off the table in a very short time \(= 0.01\, s\), remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to:

An ideal gas has molecules with \(5\,\) degrees of freedom. The ratio of specific heats at constant pressure \((C_p)\) and at constant volume \((C_v)\) is

Match the thermodynamic processes taking place in a system with the correct conditions. In the table: \(\Delta Q\) is the heat supplied, \(\Delta W\) is the work done and \(\Delta U\) is change in internal energy of the system

Process	Condition
\((I)\) Adiabatic	\((A)\; \Delta W =0\)
\((II)\) Isothermal	\((B)\; \Delta Q=0\)
\((III)\) Isochoric	\((C)\; \Delta U \neq 0, \Delta W \neq 0 \Delta Q \neq 0\)
\((IV)\) Isobaric	\((D)\; \Delta U =0\)

In a photoelectric experiment ultraviolet light of wavelength \(280\, {nm}\) is used with lithium cathode having work function \(\phi=2.5\, {eV}\). If the wavelength of incident light is switched to \(400\, {nm}\), find out the change in the stopping potential (in \({V}\)). \(\left({h}=6.63 \times 10^{-34}\, {J} \cdots\right.\), \(\left.{c}=3 \times 10^{8} \,{ms}^{-1}\right)\) 

The mean age of \(25\) teachers in a school is \(40\) years. A teacher retires at the age of \(60\) years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is \(39\) years, then the age (in years) of the newly appointed teacher is..........

For the given circuit the current through battery of \(6\,V\) just after closing the switch ' \(S\) ' will be\(.......A\).

A fighter jet is flying horizontally at a certain altitude with a speed of \(200 \; ms ^{-1}\). When it passes directly overhead an anti-aircraft gun, bullet is fired from the gun, at an angle \(\theta\) with the horizontal, to hit the jet. If the bullet speed is \(400 \; m / s\), the value of \(\theta\) will be \(\dots \; {}^o\)

If \(B\) is a \(3 \times 3\) matrix such that \(B^2 = 0\), then det. \([( I+ B)^{50} -50B]\) is equal to