The effective resistance between \(A\) and \(B\), if resistance of each resistor is \(R\) will be _______.

A point charge \(2 \times 10^{-2}\,C\) is moved from \(P\) to \(S\) in a uniform electric field of \(30\,NC ^{-1}\) directed along positive \(x\)-axis. If coordinates of \(P\) and \(S\) are \((1,2\), \(0) m\) and \((0,0,0) m\) respectively, the work done by electric field will be \(.........\,mJ\)

XPQY is a vertical smooth long loop having a total resistance R where PX is parallel to QY and separation between them is \(l\). A constant magnetic field B perpendicular to the plane of the loop exists in the entire space. A rod CD of length L (L > \(l\)) and mass m is made to slide down from rest under the gravity as shown in figure. The terminal speed acquired by the rod is __________ m/s.
(g = acceleration due to gravity)

The internal energy of a monoatomic gas is 3 nRT . One mole of helium is kept in a cylinder having internal cross section area of \(17 cm^2\) and fitted with a light movable frictionless piston. The gas is heated slowly by suppling 126 J heat. If the temperature rises by \(4^{\circ} C\), then the piston will move ___________ cm.
(atmospheric pressure \(=10^5 Pa\) )

The metallic bob of simple pendulum has the relative density \(5\). The time period of this pendulum is \(10\,s\). If the metallic bob is immersed in water, then the new time period becomes \(5 \sqrt{ x } s\). The value of \(x\) will be.

A particle is released from height \(S\) above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.

A current of 5A exists in a square loop of side \(\frac{1}{\sqrt{2}} \mathrm{~m}\). Then the magnitude of the magnetic field \(B\) at the centre of the square loop will be \(p \times 10^{-6} \mathrm{~T}\). where, value of p is _____ .
\(\left[\right.\) Take \(\left.\mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}\right]\).

A body of mass \(2\, kg\) moves under a force of \((2 \hat{ i }+3 \hat{ j }+5 \hat{ k }) \,N\). It starts from rest and was at the origin initially. After \(4 \,s\), its new coordinates are \((8, b, 20)\). The value of \(b\) is ........ . (Round off to the Nearest Integer)