Some of the commonly known ideas regarding magnetism are:
(A) It is possible to make magnets out of iron and its alloys
(B) It is possible to isolate the north or south pole of a magnet
(C) A bar magnet suspended freely, points in the north-south direction
(D) The earth behaves as a magnet with the magnetic field pointing approximately from the geographic south to the north
Choose the correct answer from the options given below:

Three charges, +Q, q and +Q are placed with q at mid point of the line joining the other two charges. For the system of charges to be in equilibrium, the value of q is

Displacement current (\( i_{d} \)) = \( \epsilon_{0} \frac{d\phi_{E}}{dt} \)
Where symbols have their usual meanings.
Which of the following options gives correct equation for displacement current ?

If 'n' identical resistors, each of value 'R' are first connected in series to a battery of emf 'E' and internal resistance 'R', the current drawn is 'I'. Now if they are connected in parallel, then the current drawn is '5 I'. The value of n is

The radius of curvature of the path of a charged particle in a uniform magnetic field is directly proportional to the

Two long coaxial solenoids of the same length L have inner and outer coils with diameters \( D_1 \) and \( D_2 \) and number of turns \( N_1 \) and \( N_2 \), respectively. What will be the ratio of the self-inductance of the inner solenoid to the mutual inductance of both the solenoids?

Identify the correct statement(s).
(A) In any lens, the optical centre is always at the centre of the lens.
(B) In a lens, if the curvature of its two surfaces is equal, the optical centre is at the centre of the lens.
(C) A light ray passing through the optical centre of a lens never shifts from the direction of the incident ray.
(D) A ray of light incident perpendicularly on a lens passes through its focus after refraction.
Choose the correct answer from the following given options.

Read the passage carefully and answer
When a metal is placed in a solution of its ions, the metal can lose electron and can go in the solution as ion or the metal ion in the solution can take electron from the electrode and get deposited as metal. Thus, the electrode acquires either positive or negative charge with respect to the solution leading to the development of a potential difference between the metal electrode and the solution. This potential difference is called the electrode potential of the metal. The electrode potential of a metal is a measure of relative tendency to undergo oxidation (loss of electron) or reduction (gain of electron). When the concentration of the ions in the solution is unity, the electrode potential is called standard electrode potential. The magni of potential depends upon the nature of electrode, concentration of ions in solution and the temperature. In a galvanic cell, the electrode at which oxidation occurs is known as anodic half-cell and the electrode at which reduction occurs is known as cathodic half cell. The emf of the cell in terms of standard reduction potential is given by \(E_{\text {cell }}^{\circ}=E_{\text {cathode }}^{\circ}-E_{\text {anode. }}^{\circ}\).The standard free energy change of the redox reaction taking place in the cell is related to \(E_{\text {cell }}^{\circ}\) by \(\Delta G^{\circ}=-n F E^{\circ}\). A redox reaction would occur spontaneously if the free energy change is negative. The equilibrium constant of the reaction is related to the standard free energy change by \(\Delta G^{\circ}=-R T \ln K\).
The equillibrium constant of a feasible cell reaction is

For \(x<\frac{1}{2}\), derivative of \(\tan ^{-1}\left(\frac{1+2 x}{1-2 x}\right)\) with respect to \(\sqrt{1+4 x^2}\) is:

Which of the following genes encode protein to control Cotton bollworms?
A. cry|Ac
B. cryllAb
C. crylAb
D. cryllAc
Choose the correct answer from the options given below:

An oxidation of phenol with chromic acid produces

Darwin's finches of Galapagos Islands are the examples of:

Arrange the metal ions of the following compounds in increasing order of oxidation number:
(A) \(TiCl _3\)
(B) \(CrF _6\)
(C) ZnO
(D) \(Mn _2 O _7\)
Choose the correct answer from the options given below: