Which of the following statement is correct?

A direct current of \(4\,A\) and an alternating current of peak value \(4\,A\) flow through resistance of \(3\,\Omega\) and \(2\,\Omega\) respectively. The ratio of heat produced in the two resistances in same interval of time will be.

A uniform solid cylinder of length \(L\) and radius \(R\) has moment of inertia about its axis equal to \(I_1\). A small co-centric cylinder of length \(L / 2\) and radius \(R / 3\) carved from this cylinder has moment of inertia about its axis equals to \(I_2\). The ratio \(I_1 / I_2\) is _________ .

A parallel plate capacitor having capacitance \(12\, pF\) is charged by a battery to a potential difference of \(10\, V\) between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant \(6.5\) is slipped between the plates. The work done by the capacitor on the slab is.......\(pJ\)

Consider a light ray travelling in air is incident into a medium of refractive index \(\sqrt{2 n}\). The incident angle is twice that of refracting angle. Then, the angle of incidence will be

Two particles are located at equal distance from origin. The position vectors of those are represented by \(\bar{A}=2 \hat{i}+3 n \hat{j}+2 \hat{k}\) and \(\bar{B}=2 \hat{i}-2 \hat{j}+4 p \hat{k}\), respectively. If both the vectors are at right angle to each other, the value of \(\mathrm{n}^{-1}\) is _____ .

Two beams, \(A\) and \(B\), of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam \(A\) has maximum intensity ( and beam \(B\) has zero intensity), a rotation of polaroid through \(30 ^o \) makes the two beams appear equally bright. If the initial intensities of the two beams are \(I_A\) and \(I_B\)  respectively, then \(\frac{{{I_A}}}{{{I_B}}}\)=

Assuming the nitrogen molecule is moving with \(r.m.s.\) velocity at \(400\, K\), the de\(-\)Broglie wavelength of nitrogen molecule is close to\(......\mathring {A}\) (Given : nitrogen molecule weight : \(4.64 \times 10^{-26}\, kg ,\) Boltzman constant : \(1.38 \times 10^{-23}\, J / K ,\) Planck constant : \(\left.6.63 \times 10^{-34}\, J . s \right)\)

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.