Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is xI. The value of \(x\) is ______.

A common example of alpha decay is \({ }_{82}^{238} U \longrightarrow{ }_{80}^{234} Th +{ }_2 He ^4+ Q\).  ( Given : \({ }_{92}^{238} U =238.05060 u ,\) \({ }_{90}^{234} Th =234.04360 u ,\) \({ }_2^4 He =4.00260 u \text {, and }\) \(1 u =931.5 \frac{ MeV }{ c ^2} )\). The energy released \((Q)\) during the alpha decay of \({ }_{92}^{238} U\) is \(......\,MeV\)

Two masses of \(3.4\) kg and \(2.5\) kg are accelerated from an initial speed of \(5\) m/s and \(12\) m/s, respectively. The distances traversed by the masses in the \(5^\text{th}\) second are \(104\) m and \(129\) m, respectively. The ratio of their momenta after \(10\) s is \(\dfrac{x}{8}\). The value of \(x\) is ________.

The ranges and heights for two projectiles projected with the same initial velocity at angles \(42^{\circ}\) and \(48^{\circ}\) with the horizontal are \({R}_{1}, {R}_{2}\) and \({H}_{1}\), \({H}_{2}\) respectively. Choose the correct option:

The net current flowing in the given circuit is_______ A.

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at \(P\), in the region, is found to vary between in the limits \(589.0\,V\) to \(589.8\, V\). What is the potential at a point on the sphere whose radius vector makes an angle of \(60^o\) with the direction of the field ?........\(V\)

The variation of applied potential and current flowing through a given wire is shown in figure. The length of wire is \(31.4 \,cm\). The diameter of wire is measured as \(2.4 \,cm\). The resistivity of the given wire is measured as \(x \times 10^{-3} \,\Omega cm\). The value of \(x\) is_______ [Take \(\pi=3.14]\)

To find the focal length of a convex mirror, a student records the following data

Object Pin	Convex Lens	Convex Mirror	Image Pin
\(22.2\,cm\)	\(32.2\,cm\)	\(45.8\,cm\)	\(71.2\,cm\)

The focal length of the convex lens is \(f_1\)  and that of mirror is \(f_2\). Then taking index correction to be negligibly small, \(f_1\)  and  \(f_2\) are close to

Two identical spherical balls of mass \(M\) and radius \(R\) each are stuck on two ends of a rod of length \(2R\) and mass \(M\) (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is

\(n\) mole a perfect gas undergoes a cyclic process \(ABCA\) (see figure) consisting of the following processes. \(A \rightarrow B :\) Isothermal expansion at temperature \(T\) so that the volume is doubled from \(V _{1}\) to \(V _{2}=2 V _{1}\) and pressure changes from \(P _{1}\) to \(P _{2}\) \(B \rightarrow C :\) Isobaric compression at pressure \(P _{2}\) to initial volume \(V _{1}\) \(C \rightarrow A\) : Isochoric change leading to change of pressure from \(P _{2}\) to \(P _{1}\) Total workdone in the complete cycle \(ABCA\) is