A uniform metallic wire carries a current \(2\,A\). when \(3.4\,V\) battery is connected across it. The mass of uniform metallic wire is \(8.92 \times 10^{-3} \,kg\). density is \(8.92 \times 10^3\,kg / m ^3\) and resistivity is \(1.7 \times 10^{-8} \Omega- m\). The length of wire is \(l=............\,m\)

An \(npn\) transistor operates as a common emitter amplifier with a power gain of \(10^{6} .\) The input circuit resistance is \(100\, \Omega\) and the output load resistance is \(10\, K \Omega\). The common emitter current gain ' \(\beta\) ' will be............. (Round off to the Nearest Integer)

Match List - I with List - II.

List-I	List-II
(A) Angular Impulse	(I) \(\left[M^0 L^2 T^{-2}\right]\)
(B) Latent Heat	(II) \(\left[M L^2 T^{-3} A^{-1}\right]\)
(C) Electrical resistivity	(III) \(\left[M L^2 T^{-1}\right]\)
(D) Electromotive force	(IV) \(\left[M L^3 T^{-3} A^{-2}\right]\)

If the kinetic energy of a moving body becomes four times its initial kinetic energy, then the percentage change in its momentum will be \(...\%\)

A thin circular disc of mass \(M\) and radius \(R\) is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity \(\omega\). If another disc of same dimensions but of mass \(\mathrm{M} / 2\) is placed gently on the first disc co-axially, then the new angular velocity of the system is _______.

A capacitor of capacitance \(150.0\,\mu F\) is connected to an alternating source of \(emf\) given by \(E =36\) \(\sin (120 \pi t ) V\). The maximum value of current in the circuit is approximately equal to \(......\,A\)

A current of \(30\) A each flows in opposite directions in two conducting wires, placed parallel to each other at a distance of \(8\) cm. The magnetic field at the mid point between the two wires is __________ \(\mu\)T. \(\left(\dfrac{\mu_0}{4\pi} = 10^{-7}\text{ N/A}^2\right)\)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.
Reason (R): Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa.
In the light of the above statements, choose the most appropriate answer from the options given below :

A moving coil galvanometer has \(100\) turns and each turn has an area of \(2.0 \mathrm{~cm}^2\). The magnetic field produced by the magnet is \(0.01 \mathrm{~T}\) and the deflection in the coil is \(0.05\) radian when a current of \(10 \mathrm{~mA}\) is passed through it. The torsional constant of the suspension wire is \(\mathrm{x} \times 10^{-5} \mathrm{~N}-\mathrm{m} / \mathrm{rad}\). The value of \(\mathrm{x}\) is _______.

A quantity \(f\) is given by \(f=\sqrt{\frac{{hc}^{5}}{{G}}}\) where \(c\) is speed of light, \(G\) universal gravitational constant and \(h\) is the Planck's constant. Dimension of \(f\) is that of

A line charge of length \(\frac{\text { ' } a \text { ' }}{2}\) is kept at the center of an edge \(B C\) of a cube \(A B C D E F G H\) having edge length ' \(a\) ' as shown in the figure. If the density of line charge is \(\lambda\) C per unit length, then the total electric flux through all the faces of the cube will be _______. (Take, \(\epsilon_0\) as the free space permittivity)

Escape velocity of a body from earth is \(11.2 \mathrm{~km} / \mathrm{s}\). If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is _______.