In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance \(C\) will be

The equivalent resistance between \(A\) and \(B\) is \(......\)

The ratio of 10.Powers of two motors is \(\frac{3 \sqrt{x}}{\sqrt{x}+1}\), that are capable of raising \(300\,kg\) water in \(5\) minutes and \(50\,kg\) water in \(2\) minutes respectively from a well of \(100\,m\) deep. The value of \(x\) will be

The figure shows a region of length \('l'\) with a uniform magnetic field of \(0.3\, T\) in it and a proton entering the region with velocity \(4 \times 10^{5}\, ms ^{-1}\) making an angle \(60^{\circ}\) with the field. If the proton completes \(10\) revolution by the time it cross the region shown, \(l\) is close to....... \(m\) (mass of proton \(=1.67 \times 10^{-27} \,kg ,\) charge of the proton \(\left.=1.6 \times 10^{-19}\, C \right)\)

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of \(2: 1\). After disintegration they will move :-

A concave mirror for face viewing has focal length of \(0.4\,m.\) The distance at which you hold the mirror from your face in order to see your image upright with a magnification of \(5\) is......\(m\)

A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed \(v\). The sphere and the cylinder reaches upto maximum heights \(h_1\) and \(h_2\), respectively, above the initial level. The ratio \(h_1: h_2\) is \(\frac{n}{10}\). The value of \(\mathrm{n}\) is __________.

A particle moving in a straight line covers half the distance with speed \(6 \mathrm{~m} / \mathrm{s}\). The other half is covered in two equal time intervals with speeds 9 \(\mathrm{m} / \mathrm{s}\) and \(15 \mathrm{~m} / \mathrm{s}\) respectively. The average speed of the particle during the motion is _______.

A soap bubble is blown to a diameter of \(7 \mathrm{~cm}\). \(36960 \mathrm{erg}\) of work is done in blowing it further. If surface tension of soap solution is \(40 \mathrm{dyne} / \mathrm{cm}\) then the new radius is ______ \(\mathrm{cm}\). Take \(:\left(\pi=\frac{22}{7}\right)\).

The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered by the object between \(t=0\) to \(t=4 \mathrm{~s}\) ?

Seawater at a frequency \(f =9 \times 10^{2} \,Hz ,\) has permittivity \(\varepsilon=80\, \varepsilon_{0}\) and resistivity \(\rho=0.25\, \Omega m.\) Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source \(V ( t )= V _{0} \sin (2 \pi ft ) .\) Then the conduction current density becomes \(10^{x}\) times the displacement current density after time \(t =\frac{1}{800} \,s\). The value of \(x\) is ......... .
\(\left(\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} Nm ^{2} C ^{-2}\right)\)