An e.m.f. \( e_s = 50 \sin(314t) \) is applied across a pure capacitor of \( 637 \ \mu\text{F} \).
The instantaneous current \( I \) is:

For an ac source rated at 220 V, 50 Hz, which of the following statements is correct?

The density of a nucleus of mass number A is proportional to :

In a double slit experiment, if the distance between the slits be reduced to half, then the new fringe width will be

The radius of a wire having resistance R is made half and its length reduced to one - fourth of its original length. The new resistance of the wire will be

A charged particle enters a uniform magnetic field at an angle of \(45 ^\circ\) with the field. The path along which the particle moves in the field will be

A Fraunhofer diffraction pattern due to a single slit of width 0.2 mm is being obtained on a screen placed at a distance of 2 m from the slit. The first minimum lies at 5 mm on either side of the central maximum on the screen. The wavelength of light is:

Osmotic pressure of solution formed by mixing 50 ml of 0.2 M urea and 50 ml of 0.4 M glucose aqueous solution at 298 K will be : (\(R = 0.083\text{ L atm K}^{-1}\text{ mol}^{-1}\))

Which of the following is a vertex of the positive region bounded by the inequalities:
\(4 x+y \geq 80 ; \quad 2 x+y \geq 60 ; \quad x, y \geq 0\)

Read the following passage carefully and answer the given questions.
Insulin consists of two short polypeptide chains- chain A and chain B, that are linked together by disulphide bridges. Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans, coleopterans and dipterans. Bt toxin protein is converted into an active form of toxin due to the alkaline pH of the gut which solubilise the crystals. Transgenic animals that produce useful biological products can be created by the introduction of the portion of DNA (or genes) which codes for a particular product such as human protein (alpha-1-antitrypsin) used to treat emphysema. Plants, bacteria, fungi and animals whose genes have been altered by manipulation are called Genetically Modified Organisms (GMO). GM plants have been useful in many ways. Genetic modification has: (i) made crops more tolerant to abiotic stresses. (ii) reduced reliance on chemical pesticides (pest-resistant crops). (iii) helped to reduce post harvest losses. (iv) increased efficiency of mineral usage by plants (this prevents early exhaustion of fertility of soil). (v) enhanced nutritional value of food.
Transgenic animals that produce useful biological products such as human protein (alpha-1-antitrypsin) used to treat the disorder:

A money lender charges Rs 10 for Rs 100 per month in advance then effective rate of interest per annum charged by money lender is : \(\left[\right.\) given \(\left.\left(\frac{10}{9}\right)^{12}=3.541\right]\)

Identify the incorrect feature of human genome.

The angle between the vectors \(\hat{i}-2 \hat{j}+\hat{k}\) and \(3 \hat{i}+2 \hat{j}+\hat{k}\) is: