The resistive network shown below is connected to a \(D.C.\) source of \(16\, V\). The power consumed by the network is \(4\, Watt\). The value of \(R\) is ............. \(\Omega\)

In a series LCR circuit, a resistor of \(300 \Omega\), a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _____ \(\times 10^4\) radians \(\mathrm{s}^{-1}\).

A mass \(0.9\,kg\), attached to a horizontal spring, executes \(SHM\) with an amplitude \(A _{1}\). When this mass passes through its mean position, then a smaller mass of \(124\,g\) is placed over it and both masses move together with amplitude \(A _{2}\). If the ratio \(\frac{ A _{1}}{ A _{2}}\) is \(\frac{\alpha}{\alpha-1}\), then the value of \(\alpha\) will be\(......\)

In Young's double slits experiment, the position of \(5^{\text {th }}\) bright fringe from the central maximum is \(5\,cm\). The distance between slits and screen is \(1\,m\) and wavelength of used monochromatic light is \(600\,nm\). The separation between the slits is \(........\mu m\)

Two equal positive point charges are separated by a distance \(2 a\). The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge \(q_0\) becomes maximum is \(\frac{a}{\sqrt{x}}\). The value of \(x\) is \(................\)

A body of mass \(2\, kg\) is driven by an engine delivering a constant 10.Power \(1\, J / s\). The body starts from rest and moves in a straight line. After \(9\) seconds, the body has moved a distance (in \(m )\)

A solenoid of length \(0.5 \mathrm{~m}\) has a radius of \(1 \mathrm{~cm}\) and is made up of ' \(m\) ' number of turns. It carries a current of \(5 \mathrm{~A}\). If the magnitude of the magnetic field inside the solenoid is \(6.28 \times 10^{-3} \mathrm{~T}\), then the value of \(m\) is _______.

Two soap bubbles coalesce to form a single bubble. If \(V\) is the subsequent change in volume of contained air and \(S\) change in total surface area, \(T\) is the surface tension and \(P\) atmospheric pressure, then which of the following relation is correct?

Two plane polarized light waves combine at a certain point whose electric field components are :
\(\begin{aligned} & \mathrm{E}_1=\mathrm{E}_0 \sin \omega \mathrm{t} \\ & \mathrm{E}_2=\mathrm{E}_0 \sin \left(\omega \mathrm{t}+\frac{\pi}{3}\right)\end{aligned}\)
Find the amplitude of the resultant wave.

\(0.08 \mathrm{~kg}\) air is heated at constant volume through \(5^{\circ} \mathrm{C}\). The specific heat of air at constant volume is \(0.17 \mathrm{kcal} / \mathrm{kg}^{\circ} \mathrm{C}\) and \(\mathrm{J}=4.18\) joule \(/ \mathrm{cal}\). The change in its internal energy is approximately.

Two slits are \(1 \mathrm{~mm}\) apart and the screen is located \(1 \mathrm{~m}\) away from the slits. A light wavelength \(500 \mathrm{~nm}\) is used. The width of each slit to obtain \(10\) maxima of the double slit pattern within the central maximum of the single slit pattern is _______ \(\times 10^{-4} \mathrm{~m}\)

The initial pressure and volume of an ideal gas are \(P_0\) and \(V_0\). The final pressure of the gas when the gas is suddenly compressed to volume \(\frac{ V _0}{4}\) will be (Given \(\gamma=\) ratio of specific heats at constant pressure and at constant volume)