The intensity of the light from a bulb incident on a surface is \(0.22 \,W / m ^{2}\). The amplitude of the magnetic field in this light-wave is_______ \(\times 10^{-9} \,T\). (Given : Permittivity of vacuum \(\epsilon_{0}=8.85 \times 10^{-12} \,C ^{2} N ^{-1} m ^{-2}\), speed of light in vacuum \(c =3 \times 10^{8} \,ms ^{-1}\) )

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

Given a thin convex lens (refractive index \(\mu_2\) ), kept in a liquid (refractive index \(\mu_1, \mu_1 \lt \mu_2\) ) having radii of curvatures \(\left|R_1\right|\) and \(\left|R_2\right|\). Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?

Two blocks of masses \(m\) and \(M,(M \gt m)\), are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released then
(\(\mu=\) coefficient of friction between the two blocks)

(A) The time period of small oscillation of the two blocks is \(\mathrm{T}=2 \pi \sqrt{\frac{(\mathrm{~m}+\mathrm{M})}{\mathrm{k}}}\)
(B) The acceleration of the blocks is \(\mathrm{a}=\frac{\mathrm{kx}}{\mathrm{M}+\mathrm{m}}\) (\(\mathrm{x}=\) displacement of the blocks from the mean position)
(C) The magnitude of the frictional force on the upper block is \(\frac{m \mu|x|}{M+m}\)
(D) The maximum amplitude of the upper block, if it does not slip, is \(\frac{\mu(M+m) g}{k}\)
(E) Maximum frictional force can be \(\mu(\mathrm{M}+\mathrm{m}) \mathrm{g}\).
Choose the correct answer from the options given below:

The equivalent capacitance of the combination shown is

The number of air molecules per \(\mathrm{cm}^3\) increased from \(3 \times 10^{19}\) to \(12 \times 10^{19}\). The ratio of collision frequency of air molecules before and after the increase in number respectively is \(.........\)

A spaceship orbits around a planet at a height of \(20\,km\) from its surface. Assuming that only gravitational field of the plant acts on the spaceship. What will be the number of complete revolutions made by the spaceship in \(24\,hours\) around the plane? [Given: Mass of plane \(= 8 \times 10^{22}\,kg,\) Radius of planet \(= 2\times 10^6\,m,\) Gravitational constant \(G = 6.67\times 10^{-11}\,Mn^2/kg^2\) ]

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as: (where \(\lambda\) is the decay constant)

A potentiometer wire \(PQ\) of \(1\,m\) length is connected to a standard cell \(E _{1}\). Another cell \(E _{2}\) of emf \(1.02\, V\) is connected with a resistance \('r'\) and switch \(S\) (as shown in figure). With switch \(S\) open, the null position is obtained at a distance of \(49\, cm\) from \(Q\). The potential gradient in the potentiometer wire is.......\(V/cm\)

A player caught a cricket ball of mass \(150 \mathrm{~g}\) moving at a speed of \(20 \mathrm{~m} / \mathrm{s}\). If the catching process is completed in \(0.1 \mathrm{~s}\), the magnitude of force exerted by the ball on the hand of the player is _______.

A \(600\,pF\) capacitor is charged by \(200\,V\) supply. It is then disconnected from the supply and is connected to another uncharged \(600\,pF\) capacitor. Electrostatic energy lost in the process is \(.........\,\mu J\).

In a meter bridge experiment \(\mathrm{S}\) is a standard resistance. \(\mathrm{R}\) is a resistance wire. It is found that balancing length is \(l=25 \;\mathrm{cm} .\) If \(\mathrm{R}\) is replaced by a wire of half length and half diameter that of \(\mathrm{R}\) of same material, then the balancing distance \(\left.l^{\prime} \text { (in } \mathrm{cm}\right)\) will now be

A particle of mass \(m\) is acted upon by a force \(F\) given by the empirical law \(F = \frac{R}{{{t^2}}}\,v(t)\). If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot