If average depth of an ocean is \(4000 \mathrm{~m}\) and the bulk modulus of water is \(2 \times 10^9 \mathrm{Nm}^{-2}\), then fractional compression \(\frac{\Delta V}{V}\) of water at the bottom of ocean is \(\alpha \times 10^{-2}\). The value of \(\alpha\) is ___________(Given, \(\mathrm{g}=10 \mathrm{~ms}^{-2}, \rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}\) )

An antenna is placed in a dielectric medium of dielectric constant \(6.25\). If the maximum size of that antenna is \(5.0\, mm\). it can radiate a signal of minimum frequency of \(GHz .\) (Given \(\mu_{ r }=1\) for dielectric medium)

If \(\in\), \( E \) and \( t \) represent the free space permittivity, electric field and time respectively, then the unit of \( \frac{eE}{t} \) will be :

A short bar magnet is placed in the magnetic meridian of the earth with north pole pointing north . Neutral points are found at a distance of \(30\, cm\) from the magnet on the East - West line, drawn through the middle point of the magnet. The magnetic moment of the magnet in \(Am^2\) is close to: (Given \(\frac{{{\mu _0}}}{{4\pi }}\, = 10^{- 7}\) in \(SI\,units\) and \(B_H\, =\) Horizontal component field \(= 3.6\times10^{-5}\, tesla\))

Young's moduli of the material of wires \(A\) and \(B\) are in the ratio of \(1: 4\), while its area of cross sections are in the ratio of \(1: 3\). If the same amount of load is applied to both the wires, the amount of elongation produced in the wires \(A\) and \(B\) will be in the ratio of [Assume length of wires \(A\) and \(B\) are same]

In a dilute gas at pressure \(P\) and temperature \(T\), the mean time between successive collisions of a molecule varies with \(T\) as

A gas mixture consists of \(3\,moles\) of oxygen and \(5\,moles\) or argon at temperature \(T.\) Considering only translational and rotational modes, the total internal  energy of the system is

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason \(R\). Assertion \(A:\) Alloys such as constantan and manganin are used in making standard resistance coils. Reason \(R:\) Constantan and manganin have very small value of temperature coefficient of resistance.In the light of the above statements, choose the correct answer from the options given below.

A particle is executing simple harmonic motion. Its amplitude is \(A\) and time period is \(5\) sec. The time required by it to move from \(x = A\) to \(x = \dfrac{A}{\sqrt{2}}\) is _______ sec.

In the hydrogen atom, the electron makes a transition from the higher orbit (\(i\)) to a lower orbit (\(f\)). The ratio of the radius of the orbits in given by \(r_i : r_f = 16 : 4\). The wavelength of photon emitted due to this transition is _____ nm.
(Given Rydberg constant \(= 1.0973 \times 10^7\) /m)

The two wires \(A\) and \(B\) of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire \(A\) and wire \(B\) is \(20/11\). When the joined wire is kept under certain tension the elongations in the wires \(A\) and \(B\) are equal. If the length of wire \(A\) is \(2.2\) m, then the length of wire \(B\) is _______ m.

A series \(LR\) circuit connected with an ac source \(E=(25 \sin 1000 t)\  V\) has a power factor of \(\frac{1}{\sqrt{2}}\). If the source of emf is changed to \(E=(20 \sin 2000 t)\ V,\) the new power factor of the circuit will be _______.

Match List-I with List-II.

List-I	List-II
(A) Isothermal	(I) \(\Delta W(\text{work done}) = 0\)
(B) Adiabatic	(II) \(\Delta Q(\text{supplied heat}) = 0\)
(C) Isobaric	(III) \(\Delta U(\text{change in internal energy}) \neq 0\)
(D) Isochoric	(IV) \(\Delta U = 0\)

Choose the correct answer from the options given below :