Two slits are \(1 \mathrm{~mm}\) apart and the screen is located \(1 \mathrm{~m}\) away from the slits. A light wavelength \(500 \mathrm{~nm}\) is used. The width of each slit to obtain \(10\) maxima of the double slit pattern within the central maximum of the single slit pattern is _______ \(\times 10^{-4} \mathrm{~m}\)

Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the \(\sqrt{3}\) times of amplitude of individual motions. The phase difference between the two motions is \(.....(degree)\)

A bullet of mass \(200\,g\) having initial kinetic energy \(90\,J\) is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to \(40\,J\) within 1s, the minimum length of the pool, the bullet has a to travel so that it completely comes to rest is \(.....m\)

A radioactive nucleus can decay by two different processes. Half-life for the first process is \(3.0\, hours\) while it is \(4.5\, hours\) for the second process. The effective half- life of the nucleus will be \(.........\,hours.\)

\(X\) different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are exited to states with principal quantum number \({n}=6\) ? The value of \({X}\) is ..... .

A \(16\, \Omega\) wire is bend to form a square loop. A \(9 \,{V}\) supply having internal resistance of \(1 \,\Omega\) is connected across one of its sides. The potential drop across the diagonals of the square loop is \(.......\,\times 10^{-1} \,{V}\)

A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius \(R _{ e }\). By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that is become \(\sqrt{\frac{3}{2}}\) times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is \(R\), value of \(R\) is\(....R_e\)

A point source of light is placed at the centre of curvature of a hemispherical surface. The source emits a power of \(24\,W\) The radius of curvature of hemisphere is \(10\,cm\) and the inner surface is completely reflecting. The force on the hemisphere due to the light falling on it is \(..........\times 10^{-8}\,N\).

The value of net resistance of the network as shown in the given figure is _______.

Four identical particles of mass \(m\) are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is \(\left(\frac{2 \sqrt{2}+1}{32}\right) \frac{\mathrm{Gm}^2}{\mathrm{~L}^2}\), the length of the sides of the square is _______.

Two projectiles are projected at \(30^{\circ}\) and \(60^{\circ}\) with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:

\({T}_{0}\) is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to \(\frac{1}{16}\) times of its initial value, the modified time

A wind-10.Powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed \(v\), the electrical 10.Power output will be most likely proportional to