Figure here shows \(P\) and \(Q\) as two equally intense coherent sources emitting radiations of wavelength \(20 \,m\). The separation \(PQ\) is \(5.0 \,m\) and phase of \(P\) is ahead of the phase of \(Q\) by \(90^{0}\). \(A, B \) and \( C\) are three distant points of observation equidistant from the mid-point of \(PQ\). The intensity of radiations at \(A, B, C\)  will bear the ratio

A square shaped coil of area \(70\,cm ^2\) having \(600\) turns rotates in a magnetic field of \(0.4\,wbm ^{-2}\), about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes \(500\) revolution in a minute, the instantaneous emf when the plane of the coil is inclined at \(60^{\circ}\) with the field, will be \(..........V\). (Take \(\pi=\frac{22}{7}\) )

A square loop of area \(25\,cm ^2\) has a resistance of \(10\,\Omega\). The loop is placed in uniform magnetic field of magnitude \(40.0 T\). The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in \(1.0 sec\), will be \(..........\times 10^{-3}\)

The displacement equations of two interfering waves are given by \(y_1  =10 \sin \left(\omega t+\frac{\pi}{3}\right) cm\) \(y_2 =5[\sin (\omega t)+\sqrt{3} \cos \omega t] \;cm\) respectively. The amplitude of the resultant wave is \(.............cm\).

Which of the following phenomena does not explain by wave nature of light? \((A)\) reflection \((B)\) diffraction \((C)\) photoelectric effect \((D)\) interference \((E)\) polarization Choose the most appropriate answer from the options given below :

In the following circuit, the battery has an emf of \(2\mathrm{V}\) and an internal resistance of \(\frac{2}{3}\  \Omega\). The power consumption in the entire circuit is _______ \(W\).

The mean free path of a molecule of diameter \(5\times10^{-10}\) m at the temperature \(41^{\circ}C\) and pressure \(1.38\times10^{5}Pa\), is given as ___________ m.
(Given \(k_{B}=1.38\times10^{-23}J/K\)).

The number of terms in the expansion of \((1 +x)^{101}  (1 +x^2 - x)^{100}\) in powers of \(x\) is

A \(10\,\mu C\) charge is divided into two parts and placed at \(1\,cm\) distance so that the repulsive force between them is maximum. The charges of the two parts are :

Let \({a_1},{a_2},\;.\;.\;.\;.,{a_{49}}\) be in \(A.P.\) such that \(\mathop \sum \limits_{k = 0}^{12} {a_{4k + 1}} = 416\) and \({a_9} + {a_{43}} = 66\). If \(a_1^2 + a_2^2 + \ldots + a_{17}^2 = 140m,\) then \(m = \;\;..\;.\;.\;.\;\)

Young's modulus is determined by the equation given by \(\mathrm{Y}=49000 \frac{\mathrm{m}}{\ell} \frac{\text { dyne }}{\mathrm{cm}^2}\) where \(\mathrm{M}\) is the mass and \(\ell\) is the extension of wre used in the experiment. Now error in Young modules \((\mathrm{Y})\) is estimated by taking data from \(M-\ell\) plot in graph paper. The smallest scale divisions are \(5 \mathrm{~g}\) and \(0.02\) \(\mathrm{cm}\) along load axis and extension axis respectively. If the value of \(M\) and \(\ell\) are \(500 \mathrm{~g}\) and \(2 \mathrm{~cm}\) respectively then percentage error of \(\mathrm{Y}\) is _______.

The de Broglie wavelength of a proton and \(\alpha\) -particle are equal. The ratio of their velocities is ...... .

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : In Young's double slit experiment, the fringes produced by red light are closer as compared to those produced by blue light.
Reason (R): The fringe width is directly proportional to the wavelength of light.
In the light of the above statements, choose the correct answer from the options given below.