As shown in the figure, the voltmeter reads \(2\,V\) across \(5\,\Omega\) resistor. The resistance of the voltmeter is \(.......\,\Omega\).

A Carnot engine operates between two reservoirs of temperatures \(900\; \mathrm{K}\) and \(300 \;\mathrm{K}\) The engine performs \(1200\; \mathrm{J}\) of work per cycle. The heat energy (in \(\mathrm{J}\) ) delivered by the engine to the low temperature reservoir, in a cycle. is

The dimensional formula of latent heat is _______.

In a medium the speed of light wave decreases to \(0.2\) times to its speed in free space The ratio of relative permittivity to the refractive index of the medium is \(x: 1\). The value of \(x\) is \(...........\) (Given speed of light in free space \(=3 \times 10^8 m s ^{-1}\) and for the given medium \(\mu_{ r }=1\) )

A hollow spherical shell at outer radius \(R\) floats just submerged under the water surface. The inner radius of the shell is \(r\). If the specific gravity of the shell material is \(\frac{27}{8}\) \(w.r.t.\) water, the value of \(r\) is\(......R\)

A cricket player catches a ball of mass \(120 \mathrm{~g}\) moving with \(25 \mathrm{~m} / \mathrm{s}\) speed. If the catching process is completed in \(0.1 \mathrm{~s}\) then the magnitude of force exerted by the ball on the hand of player will be _______ (in SI unit).

A parallel plate capacitor was made with two rectangular plates, each with a length of \(l=3 \mathrm{~cm}\) and breath of \(\mathrm{b}=1 \mathrm{~cm}\). The distance between the plates is \(3 \mu \mathrm{~m}\). Out of the following, which are the ways to increase the capacitance by a factor of 10 ?
A. \(l=30 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m}\)
B. \(l=3 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=30 \mu \mathrm{~m}\)
C. \(l=6 \mathrm{~cm}, \mathrm{~b}=5 \mathrm{~cm}, \mathrm{~d}=3 \mu \mathrm{~m}\)
D. \(l=1 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=10 \mu \mathrm{~m}\)
E. \(l=5 \mathrm{~cm}, \mathrm{~b}=2 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m}\)
Choose the correct answer from the options given below:

A ring of mass \(M\) and radius \(R\) is rotating about its axis with angular velocity \(\omega \). Two identical bodies each of mass \(m\) are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will be

The typical output characteristics curve for a transistor working in the common-emitter configuration is shown in the figure. The estimated current gain from the figure is

When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, \(4^{\text {th}}\) mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes 15 divisions on main scale and \(5^{\text {th}}\) division of vernier scale coincides with a main scale division. Measured length of cylinder is ___________ mm. (Least count of Vernier calliper \(= 0.1\ mm\))

Two long current carrying conductors are placed parallel to each other at a distance of \(8 \,cm\) between them. The magnitude of magnetic field produced at mid-point between the two conductors due to current flowing in them is \(300 \,\mu T\). The equal current flowing in the two conductors is ...............

Two point charges \(Q\) each are placed at a distance \(d\) apart. A third point charge \(q\) is placed at a distance \(x\) from mid-point on the perpendicular bisector. The value of \(x\) at which charge \(q\) will experience the maximum \(Coulomb's force\) is ...............

A particle of charge \(-q\) and mass \(m\) moves in a circle of radius \(r\) around an infinitely long line charge of linear density \(+\lambda\). Then time period will be given as _______. (Consider \(k\) as Coulomb's constant)