If the wavelength of the first member of Lyman series of hydrogen is \(\lambda\). The wavelength of the second member will be _______.

In the following circuit, the correct relation between output \(( Y )\) and inputs \(A\) and \(B\) will be

Let \(\eta_{1}\) is the efficiency of an engine at \(T _{1}=447^{\circ}\,C\) and \(T _{2}=147^{\circ}\,C\) while \(\eta_{2}\) is the efficiency at \(T _{1}=947^{\circ}\,C\) and \(T _{2}=47^{\circ}\,C\). The ratio \(\frac{\eta_{1}}{\eta_{2}}\) will be.

Two coherent monochromatic light beams of intensities \(I\) and \(4I\) are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is \(x\)I. The value of \(x\) is _______.

A pendulum bob has a speed of \(3\, {m} / {s}\) at its lowest position. The pendulum is \(50 \,{cm}\) long. The speed of bob, when the length makes an angle of \(60^{\circ}\) to the vertical will be \( .......\,{m} / {s}\) \(\left(g=10 \,{m} / {s}^{2}\right)\)

An massless equilateral triangle \(EFG\) of side \('a'\) (As shown in figure) has three particles of mass \(m\) situated at its vertices. The moment of intertia of the system about the line \(EX\) perpendicular to \(EG\) in the plane of \(EFG\) is \(\frac{ N }{20}\, ma ^{2}\) where \(N\) is an integer. The value of \(N\) is

Proton \((P)\) and electron \((e)\) will have same deBroglie wavelength when the ratio of their momentum is (assume, \(m _{ p }=1849\,m _{ e }\))

The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is \(\left(\frac{x}{100}\right) \% .\) If the relative errors in measuring the mass and the diameter are \(6.0 \%\) and \(1.5 \%\) respectively, the value of \(x\) is

The energy \(E\) and momentum \(p\) of a moving body of mass \(m\) are related by some equation. Given that c represents the speed of light, identify the correct equation.

The escape velocity of a body on a planet  \('A'\)  is \(12 \,kms ^{-1}\). The escape velocity of the body on another planet  \('B'\) , whose density is four times and radius is half of the planet  \('A'\), is ................... \(kms ^{-1}\)

A circuit is arranged as shown in figure. The output voltage \({V}_{0}\) is equal to \(\ldots \ldots . {V}\).

A radioactive nuclei with decay constant \(0.5/s\) is being produced at a constant rate of \(100\, nuclei/s\). If at \(t\, = 0\) there were no nuclei, the time when there are \(50\, nuclei\) is