A point charge is kept at the centre of a metallic insulated spherical shell. Then :

The current and voltage in an ac circuit are given by \( I = 5 \sin(100t - \pi/2) \text{ A} \) and \( V = 200 \sin(100t) \text{ V} \). The power dissipated in the circuit is

The atomic mass of \({ }_6^{12} C\) is 12.000000 u and that of \({ }_6^{18} C\) is 13.003354 u . The energy required to remove a neutron from \({ }_6^{13} C\) is
(Given: Mass of neutron is 1.008665 u and \(1 u =931 MeV\) )

Choose the correct relation between focal length f and radius of curvature R of a convex mirror from the following:

In a plane electromagnetic wave, the magnetic field oscillates sinusoidally at a frequency of\(2.0 \times 10^{10} Hz\) and amplitude \(1.6 \times 10^{-7} T\). The amplitude of the oscillating electric field is:

Four double convex lenses, with the following specifications are available:

Lens	Focal Length	Aperture
A	100cm	10cm
B	100cm	5cm
C	10cm	2cm
D	5cm	2cm

Which two of the given four lenses should be selected as the objective and eye-piece to construct an astronomical telescope?

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

Kirchhoff's First Law, \( \sum I = 0 \) at a junction deals with conservation of :

Read the passage carefully and answer the questions
Carbohydrates are naturally formed organic compounds from various plants. The common chemical formula, \(C _x\left( H _2 O \right)_y\), was considered as hydrates of carbon to derive the various carbohydrates. For instance, the general formula for glucose ( \(C _6 H _{12} O _6\) ) easily fits into the above formula. Carbohydrates also called saccharides are classified on the basis of their behavior towards hydrolysis. Monosaccharides cannot be hydrolyzed further to simpler units of polyhydroxy aldehyde or ketones. About 20 monosaccharides are known to occur in nature. Carbohydrates that yield large number of monosaccharide units are called polysaccharides. Amino acids contain ( \(- NH _2\) ) and ( - COOH ), which can be classified in various forms. Proteins are polymers of alpha amino acids which are connected to each other by a peptide bond or peptide linkage. When a native protein is subjected to physical change, its globules unfold and helix get uncoiled and the protein loses its biological activity. The protein is said to be denaturated.
During denaturation process of protein which structure(s) remain intact ?

Match List-I with List-II

List-I (Name Reaction)	List-II (Reaction)
(A) Stephen Reaction	(i)
(B) Gatterman-Koch Reaction	(ii)
(C) Etard Reaction	(iii)
(D) Rosenmund reduction	(iv)

Choose the correct answer from the options given below:

A measure of an average yearly growth of an investment over a certain time period when returns are reinvested is

If \(x=\frac{a}{1+t}\) and \(y=\frac{a}{(1+t)^2}\) where \(a>0\), then \(\frac{d^2 y}{d x^2}\) at \(t=1\) is:

The degree of the differential equation \(\left(\frac{d^3 y}{d x^3}\right)^2+x\left(\frac{d^2 y}{d x^2}\right)^3+x^2\left(\frac{d y}{d x}\right)^4=x+y\) is: