When an object is kept at a distance of \(30\, cm\) from a concave mirror, the image is formed at a distance of \(10\, cm\) from the mirror. If the object is moved with a speed of \(9\, cms ^{-1}\), the speed (in \(cms ^{-1}\) ) with which image moves at that instant is\(....m/s\)

A nucleus with mass number \(184\) initially at rest emits an \(\alpha\)-particle. If the \(Q\) value of the reaction is \(5.5\, {MeV}\), calculate the kinetic energy of the \(\alpha-\) particle. (In \({MeV}\))

A point charge \(q_1=4 q_0\) is placed at origin. Another point charge \(q_2=-q_0\) is placed at \(x =12\,cm\). Charge of proton is \(q_0\). The proton is placed on \(x\)-axis so that the electrostatic force on the proton in zero. In this situation, the position of the proton from the origin is \(..........cm\).

A proton and an \(\alpha -\) particle (with their masses in the ratio of \(1 : 4\) and charges in the ratio of \(1:2\) are accelerated from rest through a potential difference \(V\). If a uniform magnetic field \((B)\) is set up perpendicular to their velocities, the ratio of the radii \(r_p : r_{\alpha }\) of the circular paths described by them will be

A thin strip \(10\, cm\) long is on a \(U\) shaped wire of negligible resistance and it is connected to a spring of spring constant \(0.5\,Nm^{-1}\) (see figure). The assembly is kept in a uniform magnetic field of \(0.1\, T\). If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of \(e\) is \(N\). If the mass of the strip is \(50\, grams\), its resistance \(10\,\Omega \) and air drag negligible, \(N\) will be close to

Given below are two statements : Statement \(I\) : When the white light passed through a prism, the red light bends lesser than yellow and violet. Statement \(II\) : The refractive indices are different for different wavelengths in dispersive medium.
In the light of the above statements, choose the correct answer from the options given below :

The wavelength of the photon emitted by a hydrogen atom when an electron makes a  transition from \(n =2\) to \(n =1\) state is ...... \(nm.\)

An antenna is placed in a dielectric medium of dielectric constant \(6.25\). If the maximum size of that antenna is \(5.0\, mm\). it can radiate a signal of minimum frequency of \(GHz .\) (Given \(\mu_{ r }=1\) for dielectric medium)

A uniform disc of mass \(0.5\,kg\) and radius \(r\) is projected with velocity \(18\,m / s\) at \(t =0\,s\) on a rough horizontal surface. It starts off with a purely sliding motion at \(t =0\,s\). After \(2\,s\) it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after \(2\,s\) will be \(..............J\) (given, coefficient of friction is \(0.3\) and \(\left.g =10\,m / s ^2\right)\)

A circular loop ofradius \(0.3\ cm\) lies parallel to amuch bigger circular loop ofradius \(20\ cm\). The centre of the small loop is on the axis of the bigger loop. The distance between their centres is \(15\ cm\). If a current of \(2.0\ A\) flows through the smaller loop, then the flux linked with bigger loop is