An electromagnetic wave travels in a medium at a speed of \( 2 \times 10^8 \text{ m/s} \). If the relative permeability (\( \mu_r \)) of the medium is 1.0, then the relative permittivity (\( \varepsilon_r \)) of the medium is equal to

Match List I with List II

LIST I (Phenomenon)	LIST II (Scientists)
A.Dispersion of white light	I.Cassegrain
B.Reflecting type telescope	II.Huygens
C.Double slit experiment	III.Newton
D.Wavefront	IV.Thomas Young

Choose the correct answer from the options given below:

Which of the following statements about electromagnetic waves is/are correct?
A. Visible Light can be polarised but X-rays cannot.
B. X-rays in vacuum travel faster than visible light waves in vacuum.
C. The energy of X-ray photon is greater than that of a visible light photon.
D. Radio waves are produced by the accelerated motion of charges in conducting wires.
E. An electric dipole is a basic source of electromagnetic waves.
Choose the correct answer from the options given below:

A set of n equal resistors, each of resistance R are connected in series to a battery of emf E and internal resistance R. The current drawn is I. Now, the n resistors are connected in parallel to the same battery. The current drawn from the battery is 20 I. The value of n is

The height of transmitting antenna and receiving antenna are 45 m and 80 m. If the radius of earth is \( 6.4 \times 10^6 \text{ m} \), then the maximum distance between the two antennas for satisfactory communication in LOS mode is:

The internal resistance of a cell of emf 2 V is 0.1 \( \Omega \). It is connected to an external resistance of 3.9 \( \Omega \). The terminal potential difference across the cell will be

The magnetic flux passing perpendicular to the plane of a coil is changing according to the equation \( \Phi = 6t^2 + 7t + 1 \) where \( \Phi \) is in mWb and t is in seconds. The magnitude of induced emf at t = 2 s is:

A galvanometer has a resistance of 8 \( \Omega \). It is shunted by a wire of resistance 2 \( \Omega \). If the total current is 2 A, the current passing through the shunt is

Two similar coils of radius r are placed concentrically with their planes at right angles to each other. The currents flowing in them are I and 3I, respectively. The resultant magnetic induction at the centre is

The S.I unit of mutual inductance, the 'henry' can be written as

If A is a square matrix and I is the identity matrix of same order such that \(A^2=I\), then \((A-I)^3+(A+I)^3-3 A\) is equal to:

Read the passage carefully and answer:
Organic compounds derived from NH3 by replacing one or more H-atoms with alkyl or aryl groups will form primary, secondary and tertiary amines. The common methods which include their preparations are reduction of nitro group, amide group and nitrile group, Gabriel phthalimide synthesis and ammonolysis of alkyl halides. Amines are basic in nature due to the presence of a lone pair of electrons on the nitrogen atom. Important chemical properties of amines include acylation, alkylation and their interaction with nitrous acid. There are various tests which can distinguish different types of amines from each other, for e.g. carbylamine test, Hinsberg's test, coupling reaction etc. Another important class of compounds which can be derived from primary amines is azo compounds. These compounds are intensely colored and widely used as dyes in textile, leather and food industries.
How many different structural isomers that correspond to the molecular formula \(\mathrm{C}_3 \mathrm{H}_9 \mathrm{~N}\) are possible? Out of these, how many will give a positive carbylamine test?

If the difference between mean and variance of a Binomial distribution is 1 and the difference of their squares is 5 , then the probability of success is