The speed of sound in oxygen at \(S.T.P. \)will be approximately _______. (Given, \(\mathrm{R}=8.3 \mathrm{JK}^{-1}, \gamma=1.4\) )

Three particles \({P}, {Q}\) and \({R}\) are moving along the vectors \({A}=\hat{{i}}+\hat{{j}}, {B}=\hat{{j}}+\hat{{k}}\) and \({C}=-\hat{{i}}+\hat{{j}}\) respectively. They strike on a point and start to move in different directions. Now particle \(P\) is moving normal to the plane which contains vector \(\vec{A}\) and \(\vec{B} .\) Similarly particle \(Q\) is moving normal to the plane which contains vector \(\vec{A}\) and \(\vec{C} .\) The angle between the direction of motion of \(P\) and \(Q\) is \(\cos ^{-1}\left(\frac{1}{\sqrt{x}}\right)\). Then the value of \(x\) is ...... .

A block of mass \(m\) slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is : Given \({m}=8 \,{kg}, {M}=16\, {kg}\) Assume all the surfaces shown in the figure to be frictionless.

A particle executes SHM of amplitude A. The distance from the mean position when its's kinetic energy becomes equal to its potential energy is on

Consider an electromagnetic wave propagating in vacuum . Choose the correct statement

The electric field in a region is given \(\overrightarrow{ E }=\left(\frac{3}{5} E _{0} \hat{ i }+\frac{4}{5} E _{0} \hat{ j }\right) \frac{ N }{ C } .\) The ratio of flux of reported field through the rectangular surface of area \(0.2\, m ^{2}\) (parallel to \(y - z\) plane) to that of the surface of area \(0.3\, m ^{2}\) (parallel to \(x - z\) plane \()\) is \(a : b ,\) where \(a =\) ............. [Here \(\hat{ i }, \hat{ j }\) and \(\hat{ k }\) are unit vectors along \(x , y\) and \(z-\)axes respectively]

Refer to the figure given below. The values of \(I_1\), \(I_2\) and \(I_3\) are __________.

\(5\, beats/ second\) are heard when a turning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either \(0.95\,m\) or \(1\,m\) . The frequency of the fork will be ... \(Hz\)

Primary side of a transformer is connected to \(230 \mathrm{~V}, 50 \mathrm{~Hz}\) supply. Turns ratio of primary to secondary winding is \(10: 1\). Load resistance connected to secondary side is \(46\  \Omega\). The power consumed in it is :

When a coil is connected across a \(20 \mathrm{~V}\) DC supply, it draws a current of \(5 \mathrm{~A}\). When it is connected across \(20 \mathrm{~V}, 50 \mathrm{~Hz}\) AC supply, it draws a current of \(4 \mathrm{~A}\). The self inductance of the coil is _______ \(\mathrm{mH}\). (Take \(\pi=3\) )