Unpolarised light of intensity \(32\,Wm ^{-2}\) passes through the combination of three polaroids such that the pass axis of the last polaroid is perpendicular to that of the pass axis of first polaroid. If intensity of emerging light is \(3\,Wm ^{-2}\), then the angle between pass axis of first two polaroids is \(............\,^{\circ}\)

A monkey of mass \(50\,kg\) climbs on a rope which can withstand the tension \((T)\) of \(350\,N\). If monkey initially climbs down with an acceleration of \(4\,m / s ^{2}\) and then climbs up with an acceleration of \(5\,m / s ^{2}\). Choose the correct option \(\left( g =10\,m / s ^{2}\right)\)

The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is

An electron moving with speed \(v\) and a photon moving with speed \(c,\) have same D-Broglie wavelength. The ratio of kinetic energy of electron to that of photon is -

The magnetic susceptibility of a material of a rod is \(499 .\) Permeability in vaccum is \(4 \pi \times 10^{-7}\; {H} / {m}\). Absolute permeability of the material of the rod is \(....\,\pi \times 10^{-4} {H} / {m}\)

Eight mercury drops, each of radius \(r\), coalesce to form a bigger drop. The surface energy released in this process is _______. (\(S\) is the surface tension of mercury).

Consider an equilateral prism (refractive index \( \sqrt{2} \)). A ray of light is incident on its one surface at a certain angle i. If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to __________ .

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 :

The measured value of the length of a simple pendulum is \(20 \mathrm{~cm}\) with \(2 \mathrm{~mm}\) accuracy. The time for \(50\) oscillations was measured to be \(40\) seconds with \(1\) second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is \(\mathrm{N} \%\). The value of \(\mathrm{N}\) is _______.

A parallel beam of light of wavelength \(900\,nm\) and intensity \(100\,Wm ^{-2}\) is incident on a surface perpendicular to the beam. Tire number of photons crossing \(1\,cm ^{2}\) area perpendicular to the beam in one second is :

In \(1^{\text {st }}\) case, Carnot engine operates between temperatures \(300\,K\) and \(100\,K\). In \(2^{\text {nd }}\) case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in \(2^{\text {ad }}\) case) will be.

A heavy box of mass \(50 \mathrm{~kg}\) is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is \(0.3\) then force of kinetic friction is _______.