Unpolarised light is incident on a medium at an angle of incidence \( 60^{\circ} \). The reflected ray is perpendicular to the refracted ray. Refractive index (\( \mu \)) of the medium is:

In Young's double slit experiment, two slits are 2 mm apart and the screen is 2 m away from the slits. A light source having two wavelengths 4000 \( \text{\AA} \) and 6000 \( \text{\AA} \) is used.
The minimum distance from the centre of the screen where the bright fringes produced by both wavelengths coincide is :

There are two metallic spheres A and B having radii equal to R and 2R respectively. A charge Q is distributed on these two spheres such that the two spheres have equal surface charge densities. The ratio of charge on A to charge on B is :

Which of the following statements are correct?
(A) The current under reverse bias is essentially voltage dependent on a critical reverse bias voltage.
(B) The diode gets destroyed due to overheating if the forward or reverse current exceeds the rated value.
(C) In forward bias measurement, we use a milliammeter since the expected current is large, while a microammeter is used in reverse bias to measure the current.
(D) The drift current is of the order of a few \( \mu \)A
Choose the correct answer from the options given below:

There is a solenoid of length 1 m has a radius 1 cm and is made up of 1000 turns, carrying a current of 10 A. The magnitude of the magnetic field inside the solenoid is

An infinite line of charge has a linear charge density of \(10^{-7} \text{ C m}^{-1}\). The magnitude of the force acting on a charge \(6.4 \times 10^{-19} \text{ C}\) kept at a distance of 8 cm from the line of charge is

Match list-I with list-II

List-I	List-II
(A) Rays used in satellite communication	(I) X rays
(B) Rays produced in nuclear reaction	(II) Gamma rays
(C) Radiation used for studying crystal structure	(III) Ultraviolet rays
(D) Radiation absorbed by ozone layer	(IV) microwave

Choose the correct answer from the options given below:

Let \(A=\left[\begin{array}{ccc}1 & \cos \theta & 1 \\ -\cos \theta & 1 & \cos \theta \\ -1 & -\cos \theta & 1\end{array}\right], 0 \leq \theta \leq 2 \pi\), then :

During lockdown, Amit was suffering from heart problem. After proper check-up it was deducted that he has \(45\%\) chance of having heart attack, but yoga and meditation assumed to reduce the chance of heart attack by \(25\%\) and \(20\%\) respectively. He has option to choose any of the two options with equal probabilities. If Amit choose yoga to reduce the chance of heart attack, then the chance of heart attack is:During lockdown, Amit was suffering from heart problem. After proper check-up it was deducted that he has \(45\%\) chance of having heart attack, but yoga and meditation assumed to reduce the chance of heart attack by \(25\%\) and \(20 \%\) respectively. He has option to choose any of the two options with equal probabilities.
If Amit choose yoga to reduce the chance of heart attack, then the chance of heart attack is:

Answer the question on the basis of passage given below :
There are three kinds of amines which are primary, secondary and tertiary amines. These amines may have alkyl group or aryl group or both alkyl and aryl groups. These amines can be distinguished from one another by various chemical tests.
An amine A on treatment with \(\text{NaNO}_2\) and \(\text{HCl}\) at 273-277 K, followed by treatment with ethyl alcohol, gives a compound B with empirical formula CH and molecular mass 78.
A is :

The magnetic flux density at a point on the axis of a long solenoid having 1000 turns \(/ m\) when it is carrying a current of 3.4 A is nearly,

The value of \(\int\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)^2 d x\) is:

The solubility of a gas in a liquid