In a Young’s double slit experiment, the path difference, at a certain point on the screen, between two interfering waves is \(1/8^{th}\) of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is close to

A large number of water drops, each of radius \(r\), combine to have a drop of radius \(R\). If the surface tension is \(T\) and mechanical equivalent of heat is \(J ,\) the rise in heat energy per unit volume will be

A Laser light of wavelength \(660\,nm\) is used to weld Retina detachment. If a Laser pulse of width \(60\, ms\) and power \(0.5\, kW\) is used the approximate number of photons in the pulse are : [Take Planck's constant \(h\, = 6.62\times10^{- 34}\, Js\)]

A system consists of two types of gas molecules \(A\) and \(B\) having same number density \(2 \times\) \(10^{25}\, / {m}^{3}\). The diameter of \({A}\) and \({B}\) are \(10\, \stackrel{\circ}{{A}}\) and \(5\, \stackrel{\circ}{{A}}\) respectively. They suffer collision at room temperature. The ratio of average distance covererd by the molecule \(A\) to that of \(B\) between two successive collision is \(.....\,\times 10^{-2}\)

A particle is moving in a circle of radius \(r\) under the action of a force \(F\, = \alpha r^2\) which is directed towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy \(= 0\) for \(r\, = 0\))

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases.
Reason (R): Free expansion of an ideal gas is an irreversible and an adiabatic process.
In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion-(A) : If Young's double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer.
Reason-(R) : The speed of light reduces in an optically denser medium than air while its frequency does not change.
In the light of the above statements, choose the most appropriate answer from the options given below :

A \(27\, mW\) lager beam has a cross -sectional area of \(10\, mm^2\). The magnitude of the maximum electric field in this electromagnetic wave is given by:........\(kV/m\) [Given permittivity of space \({ \in _0} = 9 \times {10^{ - 12}}\, SI\, units\), speed of light \(c = 3 \times 10^8\, m/s\)]

An oscillating \(LC\) circuit consists of a \(75\,mH\) inductor and a \(1.2\,\mu F\) capacitor. If the maximum charge to the capacitor is \(2.7\,\mu C\). The maximum current in the circuit will be \(...........\,mA\).

A person measures mass of 3 different particles as \(435.42 \mathrm{~g}, 226.3 \mathrm{~g}\) and 0.125 g. According to the rules for arithmetic operations with significant figures, the additions of the masses of 3 particles will be.

Two simple harmonic motions, as shown, are at right angles. They are combined to form Lissajous figures \(x\left( t \right) = A\,\sin \,\left( {at + \delta } \right)\) \(y\left( t \right) = B\,\sin \,\left( {bt} \right)\) Identify the correct match below

Light from a point source in air falls on a spherical glass surface (refractive index, \(\mu=1.5\) and radius of curvature \(=50 \mathrm{~cm}\)). The image is formed at a distance of 200 cm from the glass surface inside the glass. The magnitude of distance of the light source from the glass surface is ________ m.

Equation of travelling wave on a stretched string of linear density \(5\,g/m\) is \(y = 0.03\,sin\,(450\,t -9x)\) where distance and time are measured in \(SI\) united. The tension in the string is ... \(N\)