The water is filled upto height of \(12\, {m}\) in a tank having vertical sidewalls. A hole is made in one of the walls at a depth \('{h}'\) below the water level. The value of \('h'\) for which the emerging stream of water strikes the ground at the maximum range is \(.....\,{m}\).

In the given circuit diagram, the currents, \({I_1} =  - \,0.3\,A,\,{I_4} = 0.8\,A\) and \({I_5} = 0.4\,A,\) are flowing as shown. The currents \(I_2,\,I_3\) and \(I_6,\) respectively are

A circular loop of radius \(20\text{ cm}\) and resistance \(2\ \Omega\) is placed in a time varying magnetic field \(\vec{B} = (2t^2 + 2t + 3)\text{ T}\). At \(t = 0\), for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at \(t = 3\text{ s}\) is \(\dfrac{\alpha}{50}\text{ A}\). The value of \(\alpha\) is _______.
(Take \(\pi = 22/7\))

A parallel beam of electrons travelling in \(x-\) direction falls on a slit of width \(d\) (see figure) . If after passing the slit, an electron acquires momentum \(P_y\) in the \(y-\) direction then for a majority of electrons passing through the slit ( \(h\) is Planck's constant)

An unpolarised light is incident at an interface of two dielectric media having refractive indices of 2 (incident medium) and \(2 \sqrt{3}\) (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is _________ .

Which one of the following is the correct dimensional formula for the capacitance in F ? \(\mathrm{M}, \mathrm{L}, \mathrm{T}\) and C stand for unit of mass, length, time and charge,

The \(SI\) unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be ..............

The root mean square speed of molecules of a given mass of a gas at \(27^{\circ} C\) and \(1\) atmosphere pressure is \(200\, ms ^{-1}\). The root mean square speed of molecules of the gas at \(127^{\circ} C\) and \(2\) atmosphere pressure is \(\frac{ x }{\sqrt{3}}\, ms ^{-1} .\) The value of \(x\) will be ......\(ms ^{-1} .\)

A thin biconvex lens is prepared from the glass (\(\mu=1.5\)) both curved surfaces of which have equal radii of \(20\) cm each. Left side surface of the lens is silvered from outside to make it reflecting. To have the position of image and object at the same place, the object should be placed, from the lens at a distance of ________ cm.

A proton, a deuteron and an \(\alpha-\)particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is

Radiation coming from transition \(n = 2\) to \(n = 1\) of hydrogen atoms fall of \(He^+\) ions in \(n = 1\) and \(n = 2\) states. The possible. Transition of helium ions as they absorb energy from the radiation is

A particle is moving in a circle of radius \(50 \mathrm{~cm}\) in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at \(t=0\) is \(4 \mathrm{~m} / \mathrm{s}\), the time taken to complete the first revolution will be \(\frac{1}{\alpha}\left[1-\mathrm{e}^{-2 \pi}\right] \mathrm{s}\), where \(\alpha=\) _______.