In the reported figure, heat energy absorbed by a system in going through a cyclic process is \(......\,\pi J\)

Refer the figure given below. \(\mu_1\) and \(\mu_2\) are refractive indices of air and lens material. The height of image will be _______ cm.

Distance between an object and three times magnified real image is 40 cm . The focal length of the mirror used is _________ cm .

To measure the temperature coefficient of resistivity \(\alpha\) of a semiconductor, an electrical arrangement shown in the figure is prepared. The arm BC is made up of the semiconductor. The experiment is being conducted at \(25^{\circ} \mathrm{C}\) and resistance of the semiconductor arm is \(3 \mathrm{~m} \Omega\). Arm BC is cooled at a constant rate of \(2^{\circ} \mathrm{C} / \mathrm{s}\). If the galvanometer \(\mathrm{G}\) shows no deflection after \(10 \mathrm{~s}\), then \(\alpha\) is _______.

Moment of Inertia \((M.I.)\) of four bodies having same mass ' \(M\) ' and radius ' \(2 R^{\prime}\) are as follows \(I _{1}=\) \(M.I.\) of solid sphere about its diameter \(I _{2}=\) \(M.I.\) of solid cylinder about its axis \(I _{3}=\) \(M.I.\) of solid circular disc about its diameter \(I _{4}=\) \(M.I.\) of thin circular ring about its diameter If \(2\left(I_{2}+I_{3}\right)+I_{4}=x\). \(I_{1}\) then the value of \(x\) will be.......

A pendulum is executing simple harmonic motion and its maximum kinetic energy is \(K_1\). If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is \(K_2\) then

As shown in figures, three identical polaroids \(P_1\), \(P _2\) and \(P _3\) are placed one after another. The pass axis of \(P_2\) and \(P_3\) are inclined at angle of \(60^{\circ}\) and \(90^{\circ}\) with respect to axis of \(P _1\). The source \(S\) has an intensity of \(256 \frac{ W }{ m ^2}\). The intensity of light at point \(O\) is \(...........\frac{ W }{ m ^2}\).

Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius of curvature of the common surface, in cm , is ______ .

If electric field intensity of a uniform plane electro magnetic wave is given as \(E =-301.6 \sin ( kz -\omega t ) \hat{a}_{ x }+452.4 \sin ( kz -\omega t )\) \(\hat{a}_{y} \frac{V}{m}\) Then, magnetic intensity \(H\) of this wave in \(Am ^{-1}\) will be [Given: Speed of light in vacuum \(c =3 \times 10^{8} ms ^{-1}\), permeability of vacuum \(\mu_{0}=4 \pi \times 10^{-7} NA ^{-2}\) ]

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) \(\left[M L^3 T^{-3} A^{-2}\right]\)

A particle starts from the origin at \(\mathrm{t}=0\) with an initial velocity of \(3.0 \hat{\mathrm{i}} \;\mathrm{m} / \mathrm{s}\) and moves in the \(x-y\) plane with a constant acceleration \((6.0 \hat{\mathrm{i}}+4.0 \hat{\mathrm{j}}) \;\mathrm{m} / \mathrm{s}^{2} .\) The \(\mathrm{x}\) -coordinate of the particle at the instant when its \(y-\)coordinate is \(32\;\mathrm{m}\) is \(D\) meters. The value of \(D\) is

The difference between threshold wavelengths for two metal surfaces \(A\) and \(B\) having work function \(\phi_A=9\,eV\) and \(\phi_{ B }=4.5\,eV\) in \(nm\) is:(Given, \(hc =1242\,eV\,nm\))