A point source of light \(S\), placed at a distance \(60 \,cm\) infront of the centre of a plane mirror of width \(50 \,cm\), hangs vertically on a wall. A man walks infront of the mirror along a line parallel to the mirror at a distance \(1.2\, m\) from it (see in the \(figure\)). The distance between the extreme points where he can see the image of the light source in the mirror is \(\ldots \ldots \ldots\, cm.\)

A disc of radius \(R\) and mass \(M\) is rolling horizontally without slipping with speed \(v\). It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is _______.

A battery of \(6\,V\) is connected to the circuit as shown below. The current I drawn from the battery is:

The galvanometer deflection, when key \(K_1\) is closed but \(K_2\) is open, equals \(\theta_0\) (see figure). On closing \(K_2\) also and adjusting \(R_2\) to \(5\,\Omega \) , the deflection in galvanometer becomes \(\frac{{\theta _0}}{5}\). The resistance of the galvanometer is, then, given by [Neglect the internal resistance of battery]: .................. \(\Omega\)

Match List \(- I\) (Fundamental Experiment) with List \(- II\) (its conclusion) and select the correct option from the choices given below the list \(\begin{array}{|||} \hline List\,\,-1  & List\,\,-II\,\,  \\ \hline a\,\,Franck-Hertz\,\,Experiment & i\,\,Particle\,\,nature\,\,of\,\,light \\ \hline b\,\,Photo\,\,-electric\,\,Experiment & ii\,\,Discrete\,\,energy \,\, levels\,\,of\,\,atom \\ \hline c\,\,Davison-Germer\,\,Experiment & iii\,\,Wave\,\,nature\,\,of\,\,electron \\ \hline  & iv\,\,Structure\,\,of\,\,atom  \\ \hline \end{array}\)

Identify the logic operation performed by the given circuit

Three solid spheres each of mass \(\mathrm{m}\) and diameter \(d\) are stuck together such that the lines connecting the centres form an equilateral triangle of side of length \(d\). The ratio \(\mathrm{I}_{0} / \mathrm{I}_{\mathrm{A}}\) of moment of inertia \(\mathrm{I}_{0}\) of the system about an axis passing the centroid and about center of any of the spheres \(\mathrm{I}_{\mathrm{A}}\) and perpendicular to the plane of the triangle is

The magnetic flux \(\phi\) (in weber) linked with a closed circuit of resistance \(8\  \Omega\) varies with time (in seconds) as \(\phi=5 t^2-36 t+1\). The induced current in the circuit at \(t=2 \mathrm{~s}\) is _______ \(\mathrm{A}\).

A thin smooth rod of length \(L\) and mass \(M\) is rotating freely with angular speed \({\omega _0}\) about an axis perpendicular to the rod and passing through its centre. Two beads of mass \(m\) and negligible size are at the centre of the rod initially. The beads are free to slide along the rod. The angular speed of the system, when the beads reach the opposite ends of the rod will be

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A\): The phase difference of two light waves change if they travel through different media having same thickness, but different indices of refraction. Reason \(R:\) The wavelengths of waves are different in different media. In the light of the above statements, choose the most appropriate answer from the options given below

Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance \(2000 \,\Omega\) is used to measure the potential difference across \(500 \,\Omega\) resister, the reading of the voltmeter will be ............... \(V\)

A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be \(......km\) (Take radius of earth \(=6400\,km\) and \(g =10\,ms^{-2}\) )

A capacitor of capacitance \(50 \; pF\) is charged by \(100 \; V\) source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is \(\dots \; nJ\).