The ratio of speed of light in vacuum to the speed of light in a medium is :
Where \(\mu_{ r }=\) relative permeability of the medium,\(\epsilon_{ r }=\) relative permittivity of the medium

Which of the following statements are correct?
A. In a photon-particle collision number of photons are conserved.
B. The photoelectric current is directly proportional to the intensity of incident light.
C. The photoelectric emission is an instantaneous process.
D. Maximum kinetic energy of photoelectrons depend on the intensity of incident radiation.
E. The threshold frequency is different for different metals.
Choose the correct answer from the options given below:

The susceptibility of a paramagnetic material is \( \chi \) at \( 27^\circ \text{C} \). At what temperature will its susceptibility be \( \chi/3 \)?

The ratio of the wavelengths associated with electrons accelerated with the potentials of 64 V and 81 V, respectively is

Identify the electromagnetic waves as per their following use/ applications.
(A) \( \lambda_1 \) is used to produce heating effect
(B) \( \lambda_2 \) is used in satellite communication
(C) \( \lambda_3 \) is absorbed by the ozone layer
(D) \( \lambda_4 \) is used for studying crystal structure
Choose the correct answer from the options given below:

Which of the following element has highest binding energy per nucleon ?

Which of the following statements are correct?
A. The matter wave picture could not incorporate the Heisenberg's uncertainity principle.
B. The wave properties of electrons have been utilised in the design of electron microscope.
C. Electron diffraction experiments have verified and confirmed the wave nature of electrons.
D. Photons are not deflected by magnetic fields.
E. The photon energy is dependent of intensity of radiation.
Choose the correct answer from the options given below:

A black and a red die are rolled simultaneously. The probability of obtaining a sum greater than \(9\) , given that the black resulted in a \(5\) is:

If the probability distribution of a random variable X is as given below :

X	-1	0	1	2	3
P(X)	K	\(\frac{1}{5}\)	2K	\(\frac{3}{10}\)	K

Then the value of K is:

Read the passage carefully and answer the questions
The osmotic pressure is one of the four colligative properties which depends on the number of particles of solute in the solution, irrespective of their nature. The osmotic pressure is equal to the product of concentration, gas constant and temperature. It is the most commonly used property for the determination of the molar mass of biomolecules. In many situations, the molecules get dissociated or associated when they are dissolved in a solvent, thereby changing the number of molecules in the solution. As a result, an abnormal molecular mass is obtained. The extent of dissociation or association is given by van't Hoff factor (i), which is the ratio of normal molar mass to abnormal molar mass. It is related with the degree of association or ionization. The introduction of van't Hoff factor in the osmotic pressure equation modifies the equation.
\[Itext\{Osmotic pressure\} ((Pi) \text\{of a solution does not depend upon\}\}]

The random variable X has a probability distribution \(P(X=r)=\left\{\begin{array}{ll}r k, & \text { if } r \leq 2, \\ (r-1) k, & \text { if } 2 < r \leq 4, \text { where } r \in N \cup\{0\} \text { and } k \in R . \\ 0, & \text { otherwise },\end{array}\right.\), where \(n\) is the set of natural numbers
(A) \(k=\frac{1}{9}\)
(B) \(P(2 \leq X \leq 3)=\frac{1}{2}\)
(C) \(P(X=4)=\frac{1}{3}\)
(D) \(P(X>1)=\frac{7}{8}\)
Choose the correct answer from the options given below:

A parallel plate capacitor of capacitance 2 \( \mu F \) has energy \( 10 \times 10^{-5} \, J \). The potential difference and the charge on the capacitor are:

A 12 V battery is connected to a \( 6 \text{ } \Omega, 10 \text{ H} \) coil, through a closed switch. The switch is suddenly opened in 1 ms. The average induced emf across the coil will be