In young's double slit experiment, the fringe width is \(12\,mm\). If the entire arrangement is placed in water of refractive index \(\frac{4}{3}\), then the fringe width becomes \((in\,mm)\)

A projectile is launched at an angle ' \(\alpha\) ' with the horizontal with a velocity \(20 \; ms ^{-1}\). After \(10 s\), its inclination with horizontal is ' \(\beta\) '. The value of \(\tan \beta\) will be : \(\left( g =10 \; ms ^{-2}\right)\)

Identify the operation performed by the circuit given below

A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first \(2\text{ s}\) it rotates through an angle \(\theta_1\) and in the next \(2\text{ s}\) it rotates through an angle \(\theta_2\). The ratio \(\dfrac{\theta_2}{\theta_1}\) is _______.

A rod of length \(60 \mathrm{~cm}\) rotates with a uniform angular velocity \(20 \mathrm{rad} \mathrm{s}^{-1}\) about its perpendicular bisector, in a uniform magnetic field \(0.5 \mathrm{~T}\). The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is________\(V\).

Let \(\vec A\, = \,(\hat i\, + \,\hat j)\,\)  and \(\vec B\, = \,(2\hat i\, - \,\hat j)\,.\)  The magnitude of a coplanar vector \(\vec C\) such that  \(\vec A\cdot \vec C\, = \,\vec B\cdot \vec C\, = \vec A\cdot \vec B\) is given by

The equation of wave is given by \(Y=10^{-2} \sin 2 \pi\left(160 t-0.5 x+\frac{\pi}{4}\right)\) Where \(x\) and \(Y\) are in \(m\) and \(t\) in \(s\). The speed of the wave is \(.....\,km h ^{-1}\)

An object viewed from a near point distance of \(25\, {cm}\), using a microscopic lens with magnification \('6',\) gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length \(0.6\, {m}\), if the focal length of the eyepiece is euqal to \(.... \,{cm} .\)