The equivalent resistance between \(A\) and \(B\) of the network shown in figure

A solid cylinder having radius \(R\) and length \(L\) is slipping on a rough horizontal plane. At time \(t=0\) the cylinder has a translational velocity \(v_0=49\) m/s, perpendicular to its axis and a rotational velocity \(v_0/4R\) about the centre. The time taken by the cylinder to start rolling is ________ seconds. (coefficient of kinetic friction \(\mu_K=0.25\) and \(g=9.8\) m/s\(^2\))

Mach List-\(I\) with List - \(II\) :

List - \(I\)	List - \(II\)
\((a)\) Ultraviolet rays	\((a)\) Study crystal structure
\((b)\) Microwaves	\((b)\) Greenhouse
\((c)\) Infrared waves	\((c)\) sterilizing surgical instrument
\((d)\) \(x\)-rays	\((d)\) Radar system

Choose the correct answer from the options given below

Consider the sound wave travelling in ideal gases of \(\mathrm{He}, \mathrm{CH}_4\), and \(\mathrm{CO}_2\). All the gases have the same ratio \(\frac{P}{\rho}\), where \(P\) is the pressure and \(\rho\) is the density. The ratio of the speed of sound through the gases \(\mathrm{v}_{\mathrm{He}}: \mathrm{v}_{\mathrm{CH}_4}: \mathrm{v}_{\mathrm{CO}_2}\) is given by

Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is ___________.
(Given: \(h=6.63\times10^{-34}\) J.s and \(c=3\times10^{8}m/s\))

A spherically symmetric charge distribution is characterised by a charge density having the following variations \(\rho (r)\, = \,{\rho _0}\left( {1 - \frac{r}{R}} \right)\) for \(r < R\) \(\rho (r)\,=\,0\) for \(r\, \ge \,R\) Where \(r\) is the distance from the centre of the charge distribution \(\rho _0\) is a constant. The electric field at an internal point \((r < R)\) is

Which of the following is not a dimensionless quantity?

A capacitor has air as dielectric medium and two conducting plates of area \(12 \mathrm{~cm}^2\) and they are \(0.6 \mathrm{~cm}\) apart. When a slab of dielectric having area \(12 \mathrm{~cm}^2\) and \(0.6 \mathrm{~cm}\) thickness is inserted between the plates, one of the conducting plates has to be moved by \(0.2 \mathrm{~cm}\) to keep the capacitance same as in previous case. The dielectric constant of the slab is _______. (Given \(\left.\epsilon_0=8.834 \times 10^{-12} \mathrm{~F} / \mathrm{m}\right)\)

In a Young's double slit experiment, the source is white light. One of the slits is covered by red filter and another by a green filter. In this case...

Moment of inertia of a cylinder of mass \(M,\) length \(L\) and radius \(R\) about an axis passing through its centre and perpendicular to the axis of the cylinder is \(I = M \left(\frac{ R ^{2}}{4}+\frac{ L ^{2}}{12}\right) .\) If such a cylinder is to be made for a given mass of material, the ratio \(\frac LR\) for it to have minimum possible \(I\) is