A plane electromagnetic wave is travelling along +y-axis. The value of electric field at a point is \( \vec{E} = 12.3 \hat{i} \frac{N}{C} \). The magnitude and direction of magnetic field \( \vec{B} \) at this point is:

The light from a point source placed in air is incident on a convex spherical glass surface of radius of curvature 30 cm.
The refractive index of the glass is 1.5. The distance of light source from the glass surface is 120 cm. The distance of the image formed from the glass surface is

A radioactive source (Phosphorus-32) has an initial activity 10 \(\mu\)Ci, its half life is 14 days. What time elapses before the activity falls to 1.25 \(\mu\)Ci ?

Match List-I with List-II

List-I (Motion of a charge particle)	List-II (Path)
(A) Initial velocity of charge particle parallel to B	(I) Circular Path
(B) Initial velocity of charge particle perpendicular to B	(II) Helical Path
(C) Initial velocity of charge particle inclined to B	(III) Straight Path
(D) Initial velocity of charge particle perpendicular to E	(IV) Parabolic Path

Choose the correct answer from the options given below :

If a copper rod carries a direct current, the magnetic field due to it will be:

A short bar magnet of magnetic moment \(m =0.45 J / T\) is placed in a uniform magnetic field of 0.22 T . If the bar is free to rotate in the plane of the field, what is the potential energy of the magnet in stable and unstable equilibrium respectively?

Match List-I with List-II

List-I (Electromagnetic waves)	List-II (Wavelength range)
(A) X-rays	(I) 1 mm to 700 nm
(B) Radio waves	(II) 0.1 m to 1 mm
(C) Infrared waves	(III) 1 nm to \( 10^{-3} \) nm
(D) Microwaves	(IV) >0.1 m

Choose the correct answer from the options given below:

The differentiation of \(\frac{x^3}{1-x^3}\) w.r.t. \(x^3\) is:

At one place on earth, the resultant magnetic field is 0.25 G and the angle of dip is 45°. The horizontal component of earth's magnetic field will be

Flower colour in Antirrhinum sp. is an example of:

Answer the question on basis of passage given below:
Organic compounds containing carbon -oxygen double bonds ( \(C = O\) ) are called carbonyl compounds. These are highly polar molecules. Hence, their boiling points are higher than hydrocarbons and ethers. Aldehydes can be prepared from dehydrogenation or oxidation of alcohols and by reduction of acylhalides. Ketones are prepared by oxidation of secondary alcohols or by hydration of alkynes etc. Aldehydes and ketones undergo nucleophilic addition reaction with the number of nucleophiles such as HCN , NaHSO3 ammonia derivatives. Carboxylic acids are prepared by the oxidation of primary alcohols, aldehydes and alkenes, by hydrolysis of nitriles. Carboxylic acids are more acidic than alcohols and phenols.
Which of the following is most reactive towards nucleophilic addition reaction ?

Order and degree of the differential equation \(\left[1+\left(\frac{d y}{d x}\right)^3\right]^{\frac{5}{4}}=\frac{d^2 y}{d x^2}\) are:

Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on 10 cm length of wire B: