In a Young's double slit experiment, \(16\) fringes are observed in a certain segment of the screen when light of wavelength \(700 \,nm\) is used. If the wavelength of light is changed to \(400 \,nm\), the number of fringes observed in the same segment of the screen would be........

Displacement of a wave is expressed as \(x(t)=5 \cos \left(628 t+\frac{\pi}{2}\right) m\). The wavelength of the wave when its velocity is \(300 \mathrm{~m} / \mathrm{s}\) is :

A soap bubble of surface tension \(0.04 N / m\) is blown to a diameter of 7 cm . If \((15000- x ) \mu J\) of work is done in blowing it further to make its diameter 14 cm , then the value of x is _________ .\((\pi=22 / 7)\)

A bullet of mass \(20\,g\) has an initial speed of \(1\,ms^{-1}\) just before it starts penetrating a mud wall of thickness \(20\,cm.\) If the wall offers a mean resistances of \(2.5 \times 10^{-2}\,N,\) the speed of the bullet after emerging from the other side of the wall is close to .............. \(\mathrm{ms}^{-1}\)

Three conductors of same length having thermal conductivity \(\mathrm{k}_1, \mathrm{k}_2\) and \(\mathrm{k}_3\) are connected as shown in figure.

Area of cross sections of \(1^{\text {st }}\) and \(2^{\text {nd }}\) conductor are same and for \(3^{\text {rd }}\) conductor it is double of the \(1^{\text {st }}\) conductor. The temperatures are given in the figure. In steady state condition, the value of \(\theta\) is _______ \({ }^{\circ} \mathrm{C}\).
(Given : \(\mathrm{k}_1=60 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}, \mathrm{k}_2=120 \mathrm{Js}^{-1}\mathrm{~m}^{-1}\) \( \mathrm{~K}^{-1}, \mathrm{k}_3=135 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}\) )

A body cools from \(80^{\circ}\,C\) to \(60^{\circ}\,C\) in \(5\) minutes. The temperature of the surrounding is \(20^{\circ} C\). The time it takes to cool from \(60^{\circ}\,C\) to \(40^{\circ}\,C\) is........... \(s\)

The maximum vertical height to which a man can throw a ball is \(136\,m\). The maximum horizontal distance upto which he can throw the same ball is \(.....\,m\)

The width of fringe is \(2\,mm\) on the screen in a double slits experiment for the light of wavelength of \(400\,nm\). The width of the fringe for the light of wavelength \(600\,nm\) will be \(..............\,mm\)

A wire \(X\) of length \(50\; cm\) carrying a current of \(2\,A\) is placed parallel to a long wire \(Y\) of length \(5\,m\). The wire \(Y\) carries a current of \(3\,A\). The distance between two wires is \(5\,cm\) and currents flow in the same direction. The force acting on the wire \(Y\) is.

Conductor wire ABCDE with each \(\operatorname{arm} 10 \mathrm{~cm}\) in length is placed in magnetic field of \(\frac{1}{\sqrt{2}}\) Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of \(10 \mathrm{~cm} / \mathrm{s}\), induced emf between points A and E is _____ mV.

There are two infinitely long straight current carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductor is \(1: 1\). The magnetic field at point \(P\) is ...... .

A force is applied to a steel wire ' \(A\) ', rigidly clamped at one end. As a result elongation in the wire is \(0.2\,mm\). If same force is applied to another steel wire ' \(B\) ' of double the length and a diameter \(2.4\) times that of the wire ' \(A\) ', the elongation in the wire ' \(B\) ' will be \(............\times 10^{-2}\,mm\) (wires having uniform circular cross sections)

Consider a sample of oxygen behaving like an ideal gas. At \(300 \,K ,\) the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be : (Molecular weight of oxygen is \(32 \,g / mol\) \(\left. R =8.3 \,J K ^{-1} mol ^{-1}\right)\)