Three charges \(+Q, q, +Q\) are placed respectively, at distance, \(0, \frac d2\) and \(d\) from the origin, on the \(x-\) axis. If the net force experienced by \(+Q\), placed at \(x = 0\), is zero, then value of \(q\) is

A transformer operating at primary voltage \(8\,kV\) and secondary voltage \(160\,V\) serves a load of \(80\,kW\). Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be.

The ratio of intensities at two points \(P\) and \(Q\) on the screen in a Young's double slit experiment where phase difference between two wave of same amplitude are \(\pi / 3\) and \(\pi / 2\), respectively are

The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass \(4\;kg\). (The coordinates of the same are shown in figure) are

A planar loop made of wire is rotating in a uniform magnetic field. At time \(t=0\), the plane of the loop is perpendicular to the magnetic field. If the loop is rotating about an axis passing through its plane with a period of \(10\) seconds, at which of the following times will the induced electromotive force (emf) be maximum and minimum, respectively?

A charged particle going around in a circle can be considered to be a current loop. A particle of mass \(m\) carrying charge \(q\) is moving in a plane with speed \(v\) under the influence of magnetic field \(\overrightarrow{ B }\). The magnetic moment of this moving particle

When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is 3.2 V . If a second light having wavelength twice of first light is used, the stopping potential drops to 0.7 V . The wavelength of first light is _________ m .
\(\left( h =6.63 \times 10^{-34} J . s , e =1.6 \times 10^{-19} C , c =3 \times 10^8 m / s \right)\)

Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm , at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is :

Proton with kinetic energy of \(1\;MeV\) moves from south to north. It gets an acceleration of \(10^{12}\; \mathrm{m} / \mathrm{s}^{2}\) by an applied magnetic field (west to east). The value of magnetic field :.......\(mT\) (Rest mass of proton is \(1.6 \times 10^{-27} \;\mathrm{kg}\) )

An \(n.p.n\) transistor with current gain \(\beta=100\) in common emitter configuration is shown in figure. The output voltage of the amplifier will be\(.....V\)

A particle is executing simple harmonic motion \((SHM)\) of amplitude \(A,\) along the \(x-\) axis, about \(x = 0.\) When its potential energy \((PE)\) equals kinetic energy \((KE),\) the position of the particle will be

Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is \(M,\) radius of its top, \(R\) and height, \(H\), then its moment of inertia about its axis is