If \( \vec{M} \) is the magnetic moment and \( \vec{B} \) is the magnetic field, then the torque is given by

A slab of material of dielectric constant \( k \), having the same area as the plate of a parallel plate capacitor but has a thickness \( \frac{3}{5} \) of the distance between the plates \( d \), is inserted between the plates of the capacitor. When there is air between the plates, the potential difference is \( V_0 \). What is the potential difference between the plates of the capacitor after inserting the dielectric?

In a region of constant potential,

The speed of light in a medium depends on:

\( \alpha, \beta \) and \( \gamma \) rays emitted by a radioactive substance are allowed to pass through a region containing a magnetic field at right angles to their path. The energy gained will be

A very long solenoid has 800 turns per unit length. A current of 1.6 A flows through it. Then the magnetic induction in the middle of the solenoid on its axis is approximately :
(1) \( 16 \times 10^{-4} \text{ T} \)
(2) \( 8 \times 10^{-4} \text{ T} \)
(3) \( 32 \times 10^{-4} \text{ T} \)
(4) \( 4 \times 10^{-4} \text{ T} \)

An a.c. source of 200 V is connected through a diode 'D' to a capacitor as shown in figure. Find the maximum potential difference across the capacitor :

A polythene piece rubbed with wool is found to have a negative charge of \( 8 \times 10^{-10} \, \text{C} \). What is the number of electrons transferred ?

Biofertilisers are the organisms that enrich the nutrient quality of the soil.
Which of the following is not a source of biofertiliser?

Steps of replication of retrovirus (HIV) in the host cell are given below. Arrange the steps in correct sequence.
(A) Viral RNA is introduced in host cell
(B) New viruses with new RNA are produced
(C) Viral DNA is produced by reverse transcription
(D) Viral DNA incorporates into host genome
(E) Virus infects the normal cell
Choose the correct answer from the options given below:

Light ray travels from an rarer medium to an denser medium. Which of the following is incorrect if \( (0^{\circ} < i < 90^{\circ}) \).

Read the passage carefully and answer the Questions
In the formation of coordination complexes, if the inner \(d\) orbital \((n-1) d\) is used in hybridisation, the complex, is called an inner orbital or low spin or spin paired complex. And if it uses outer \(d\) orbital ( \(n d\) ) in hybridisation (like \(s p^3 d^2\) ), it is called outer orbital or high spin or spin free complex. The degeneracy of the \(d\) orbitals has been removed due to ligand electron-metal electron repulsions in the complex. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting. For coordination complexes, the magnetic moment is determined by the number of unpaired electrons and is calculated by using the 'spin-only' formula, \(\mu=\sqrt{n(n+2)}\) where \(n\) is the number of unpaired electrons and \(\mu\) is the magnetic moment in units of Bohr magneton (BM). The coordination compounds are of great importance. These compounds are widely present in the mineral, plant and animal worlds and are known to play many important functions in the area of analytical chemistry, metallurgy, biological systems, industry and medicine.
Which of the following metals belongs to Wilkinson catalyst?

The value of a determinant is unaltered if: