For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is _______.

A block of mass \(200\, g\) is kept stationary on a smooth inclined plane by applying a minimum horizontal force \(F =\sqrt{ x }N\) as shown in figure. The value of \(x =.....\)

Figure shows the variation in temperature \(\left( {\Delta T} \right)\) with the amount of heat supplied \((Q)\) in an isobaric process corresponding to a monoatomic \((M)\), diatomic \((D)\) and a polyatomic \((P)\) gas. The initial state of all the gases are the same and the scales for the two axes coincide. Ignoring vibrational degrees of freedom, the lines \(a, b\) and \(c\) respectively correspond to

For the circuit shown below, calculate the value of \({I}_{{z}}\) : (In \({mA}\))

Critical angle of incidence for a pair of optical media is \(45^{\circ}\). The refractive indices of first and second media are in the ratio _______.

A man of \(60\,kg\) is running on the road and suddenly jumps into a stationary trolly car of mass \(120\,kg\). Then. the trolly car starts moving with velocity \(2\,ms ^{-1}\). The velocity of the running man was _________\(ms ^{-1}\). when he jumps into the car

In a Young’s double slit experiment, the slits are placed \(0.320\,mm\) apart. Light of wavelength \(\lambda = 500\,nm\) is incident on the slits. The total number of bright fringes that are observed in the angular range \( - {30^o} \le \theta  \le {30^o}\) is

A car moving with a speed of \(54\) km/h takes a turn of radius \(20\) m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take \(g=10\) m/s\(^2\))

The least count of the main scale of a screw gauge is \(1\, mm\). The minimum number of divisions on its circular scale required to measure \(5\,\mu m\) diameter of a wire is

The translational degrees of freedom \((f)\) and rotational degrees of freedom \((f)\) of \(\mathrm{CH}_4\) molecule are _______.