A cyclist starts from the point \(P\) of a circular ground of radius \(2 \mathrm{~km}\) and travels along its circumference to the point \(\mathrm{S}\). The displacement of a cyclist is _______.

The radiation corresponding to \(3 \rightarrow 2\) transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of \(5 \times 10^{-4} \,{T}\). Assume that the radius of the largest circular path followed by these electrons is \(7\, {mm}\), the work function of the metal is \(.....\,{eV}\) (Mass of electron \(=9.1 \times 10^{-31} \,{kg}\) )

\(\vec{A}\) is a vector quantity such that \(|\vec{A}|=\) nonzero constant. Which of the following expressions is true for \(\vec{A}\) \(?\)

move in opposite direction with speed ratio \(1: 2\). The following figure represents two biconvex lenses \(L_1\) and \(L_2\) having focal length \(10 \mathrm{~cm}\) and \(15 \mathrm{~cm}\) respectively. The distance between \(\mathrm{L}_1 \& \mathrm{~L}_2\) is _______.

Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in media \(A\) and \(B\) are \(2.4 \times 10^8 m / s\) and \(2.7 \times 10^8 m / s\) respectively, then the value of critical angle is :

A soap bubble of radius \(3\, {cm}\) is formed inside the another soap bubble of radius \(6\, {cm}\). The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is .......... \({cm}\) 

A particle of mass \(M\) originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation \(F=F_{0}\left(1-\left(\frac{t-T}{T}\right)^{2}\right)\) Where \(F_{0}\) and \(T\) are constants. The force acts only for the time internal \(2 T\). The velocity \(v\) of the particle after time \(2 {T}\) is -

A particle is moving \(5\) times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is \(1.878 \times 10^{-4}\). The mass of the particle is close to

Two sitar strings, \(A\)  and \(B,\)  playing the note \('Dha'\)  are slightly out of tune and produce beats and frequency  \(5\,Hz.\)  The tension of the string \(B\) is slightly increased and the beat frequency is found to decrease by  \(3\,Hz\) . If the frequency of \(A\) is \(425\,Hz,\)  the original frequency of \(B\) is  ... \(Hz\)

An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is ___________. \((\pi=3.14)\)

A particle moving in the \(xy\) plane experiences a velocity dependent force \(\overrightarrow{ F }= k \left( v _{ y } \hat{ i }+ v _{ x } \hat{ j }\right),\) where \(v _{ x }\) and \(v _{ y }\) are the \(x\) and \(y\) components of its velocity \(\overrightarrow{ v } .\) If \(\overrightarrow{ a }\) be the acceleration of the particle, then which of the following statements is true for the particle\(?\)