The current \(i\) in the network is.....\(A\)

A block '\(A\)' takes \(2\,s\) to slide down a frictionless incline of \(30^{\circ}\) and length ' \(l\) ', kept inside a lift going up with uniform velocity ' \(v\) '. If the incline is changed to \(45^{\circ}\), the time taken by the block, to slide down the incline, will be approximately \(........\,s\)

The potential energy function (in J) of a particle in a region of space is given as \(U=\left(2 x^2+3 y^3+2 z\right)\). Here \(\mathrm{x}, \mathrm{y}\) and \(\mathrm{z}\) are in meter. The magnitude of \(\mathrm{x}\) - component of force (in \(\mathrm{N}\) ) acting on the particle at point \(\mathrm{P}(1,2,3)\ \mathrm{m}\) is:

In Vander Waals equation \(\left[ P +\frac{ a }{ V ^{2}}\right][ V - b ]= RT\); \(P\) is pressure, \(V\) is volume, \(R\) is universal gas constant and \(T\) is temperature. The ratio of constants \(\frac{a}{b}\) is dimensionally equal to .................

The volume \(V\) of an enclosure contains a mixture of three gases, \(16\, g\) of oxygen, \(28\, g\) of nitrogen and \(44\, g\) of carbon dioxide at absolute temperature \(T\). Consider \(R\) as universal gas constant. The pressure of the mixture of gases is

A rubber ball is released from a height of \(5\, m\) above the floor. It bounces back repeatedly, always rising to \(\frac{81}{100}\) of the height through which it falls. Find the average speed of the ball. (Take \(g =10 ms ^{-2}\) ) (in \(ms ^{-1}\))

A certain charge \(Q\) is divided into two parts \(q\) and \((Q-q) .\) How should the charges \(Q\) and \(q\) be divided so that \(q\) and \((Q-q)\) placed at a certain distance apart experience maximum electrostatic repulsion?

In an experiment with sonometer when a mass of \(180\,g\) is attached to the string, it vibrates with fundamental frequency of \(30\,Hz\). When a mass \(m\) is attached, the string vibrates with fundamental frequency of \(50\,Hz\). The value of \(m\) is \(.........\,g\).

The disc of mass \(M\) with uniform surface mass density \(\sigma\) is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position \(\frac{x}{3} \frac{a}{\pi}, \frac{x}{3} \frac{a}{\pi}\) where \(x\) is ....... . (Round off to the Nearest Integer) \([ a\) is an area as shown in the figure \(]\)

Two magnetic dipoles \(X\) and \(Y\) are placed at a separation \(d\), with their axes perpendicular to each other. The dipole moment of \(Y\) is twice that of \(X\). A particle of charge \(q\) is passing through their mid-point \(P\), at angle \(\theta  = 45^o\) with the horizontal line as shown in the figure. What would be the magnitude of force on the particle at that instant ? (\(d\) is much larger than the dimensions of the dipole)

A parallel plate capacitor of area \(A=16 \mathrm{~cm}^2\) and separation between the plates 10 cm , is charged by a DC current. Consider a hypothetical plane surface of area \(\mathrm{A}_0=3.2 \mathrm{~cm}^2\) inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6A. At the same instant the displacement current through \(\mathrm{A}_0\) is ________ mA .