The position vector of \(1\,kg\) object is \(\overrightarrow{ r }=(3 \hat{ i }-\hat{ j })\,m\) and its velocity \(\overrightarrow{ v }=(3 \hat{ j }+ k )\,ms ^{-1}\). The magnitude of its angular momentum is \(\sqrt{ x } Nm\) where \(x\) is

For the network shown below, the value \(V _{ B }- V _{ A }\) is_______ \(V\)

Light travels in two media \(M _{1}\) and \(M _{2}\) with speeds \(1.5 \times 10^{8} ms ^{-1}\) and \(2.0 \times 10^{8} ms ^{-1}\) respectively. The critical angle between them is.

In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative \(z\)-axis and magnetic field is along the positive \(x\)-axis. Then the direction of propagation of electromagnetic wave is

A body of mass \(2\, kg\) moves under a force of \((2 \hat{ i }+3 \hat{ j }+5 \hat{ k }) \,N\). It starts from rest and was at the origin initially. After \(4 \,s\), its new coordinates are \((8, b, 20)\). The value of \(b\) is ........ . (Round off to the Nearest Integer)

Two persons \(A\) and \(B\) perform same amount of work in moving a body through a certain distance \({d}\) with application of forces acting at angle \(45^{\circ}\) and \(60^{\circ}\) with the direction of displacement respectively. The ratio of force applied by person \(A\) to the force applied by person \(B\) is \(\frac{1}{\sqrt{x}}\). The value of \(x\) is ...... .

Electrons are accelerated through a potential difference \(V\) and protons are accelerated through a potential difference \(4\, V\). The de-Broglie wavelengths are \(\lambda_e \) and \(\lambda_p \) for electrons and protons respectively. The ratio of \(\frac{{{\lambda _e}}}{{{\lambda _p}}}\) is given by : (given \(m_e\) is mass of electron and \(m_p\) is mass of proton).

In the below circuit, \(C\, = \,\frac{{\sqrt 3 }}{2}\,\mu F,\,R = 20\,\,\Omega ,\,L = \frac{{\sqrt 3 }}{{10}}H\) and \({R_1} = 10\,\,\Omega .\) Current in \(L-R_1\) path is \(I_1\) and \(C-R_2\) path is \(I_2.\) The voltage of \(A.C\) source is given by, \(V\, = \,200\sqrt 2 \,\sin \,(100\,t)\,volts.\) The phase difference between \(I_1\) and \(I_2\) is