Determine the charge on the capacitor in the following circuit ................ \(\mu  C\)

The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of \(2 \,\Omega\). The value of internal resistance of each cell is ............ \(\Omega\)

A block of \(\sqrt{3}\,kg\) is attached to a string whose other end is attached to the wall. An unknown force \(F\) is applied so that the string makes an angle of \(30^{\circ}\) with the wall. The tension \(T\) is \(...........\,N\) :(Given \(g =10\,ms ^{-2}\) )

The current \(I\) in the given circuit will be \(......A\)

The three charges \(q / 2, q\) and \(q / 2\) are placed at the corners \(A , B\) and \(C\) of a square of side ' \(a\) ' as shown in figure. The magnitude of electric field \((E)\) at the comer \(D\) of the square, is

Two point charges \(2 q\) and \(q\) are placed at vertex \(A\) and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is :

Two radioactive substances \(X\) and \(Y\) originally have \(N _{1}\) and \(N _{2}\) nuclei respectively. Half life of \(X\) is half of the half life of \(Y\). After three half lives of \(Y\), number of nuclei of both are equal. The ratio \(\frac{ N _{1}}{ N _{2}}\) will be equal to

Match List\(-I\) with List\(-II.\)

List\(-I\)	List\(-II\)
\((a)\) Torque	\((i)\) \({MLT}^{-1}\)
\((b)\) Impulse	\((ii)\) \({MT}^{-2}\)
\((c)\) Tension	\((iii)\) \({ML}^{2} {T}^{-2}\)
\((d)\) Surface Tension	\((iv)\) \({MI} {T}^{-2}\)

Choose the most appropriate answer from the option given below :

Two known resistance of \(R \Omega\) and \(2 R \Omega\) and and one unknown resistance \(X \Omega\) are connected in a circuit as shown in the figure. If the equivalent resistance between points A and B in the circuit is \(X \Omega\), then the value of X is _________ \(\Omega\).

A \(220 \; V , 50 \; Hz\) AC source is connected to a \(25 \; V\), \(5 \; W\) lamp and an additional resistance \(R\) in series (as shown in figure) to run the lamp at its peak brightness, then the value of \(R\) (in ohm) will be

An electron is moving along \(+x\) direction with a velocity of \(6 \times 10^{6}\, ms ^{-1}\). It enters a region of uniform electric field of \(300 \,V / cm\) pointing along \(+ y\) direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the \(x\) direction will be

A cylinder of mass \(M_c\) and sphere of mass \(M_s\) are placed at points \(A\) and \(B\) of two inclines, respectively (See Figure). If they roll on the incline without sipping such that their accelerations are the same, then the ratio \(\frac{{\sin \,{\theta _c}}}{{\sin \,{\theta _s}}}\) is

Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is