Two radioactive elements \(E_1\) and \(E_2\) with their half lives \(T_1\) and \(T_2\) have undecayed atoms \(n_1\) and \(n_2\) respectively present at a given instant. What will be the ratio of their activities at this instant?

Electric field at a point due to a uniformly charged infinite plane sheet is

Which of the following statements are correct?
(A) Electrostatic lines of force may be curved or straight in an electric field.
(B) Number of lines of force per unit perpendicular area represents the intensity of the electric field at the point.
(C) Two electric field lines can not intersect each other.
(D) Electric field lines are directed from negative to positive charge for an electric dipole.
Choose the correct answer from the options given below:

The magnitude of the electric and magnetic fields in an electromagnetic wave are related as :

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.

A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be

A long straight wire carries a current of 35 A. The magnitude of the field \( \vec{B} \) at a point 20 cm from the wire would be:

In aldehydes, the carbonyl group is bonded to a carbon and hydrogen, while in ketones it is bonded to two carbon atoms. The carbonyl compounds in which carbonyl group is bonded to oxygen are known as carboxylic acid and their derivatives.
1,3-Diphenylprop-2-en-1-one is produced by the following.

Below given are some statements about electronic devices:
(A) Diodes can be used for rectifying an ac voltage.
(B) For semiconductors, band gap energy \( E_g > 3 \, eV \).
(C) By changing the external applied voltage, junction barriers can be changed.
(D) p-n junction is the 'key' to all semiconductor devices.
Choose the correct answer from the options given below:

Identify the set of cells which have haploid number of chromosomes ?

A bar magnet of magnetic moment 5.0 \( A \, m^2 \) has poles 20 cm apart. The pole strength would be

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 complex has the highest magnetic moment?

The area of the region bounded by the curve \(y^2=x\) and the lines \(x=1, x=4\) is: