In Young's double slits experiment, if the ratio of the width of the two slits is 25 : 1, what is the ratio of intensity at the maxima and minima in the interference pattern?

Arrange the following electromagnetic waves in decreasing order of their respective wavelengths.
(A) UV-rays
(B) X-rays
(C) Radio waves
(D) Visible light
Choose the correct answer from the options given below:

A 50 cm long air core solenoid has a 2 cm radius and 500 turns. The self-inductance of the solenoid would be (given \(\mu_0=4 \pi \times 10^{-7} \operatorname{Tm} * A^{-1}\) and \(\pi^2=10\) )

Two point charges of 2 C each are separated from each other by a distance of 1 m in water (K = 80). The force between the charges is:

In an AC circuit, the power factor :

Match List-I with List-II

List-I	List-II
(A) Power of concave lens	(I) Concave lens
(B) Power gets algebraically added	(II) Refraction of light
(C) Image formation by lens	(III) Negative
(D) Always virtual image	(IV) combination of lenses

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An electric dipole of moment P is placed along the direction of electric field E. The work done in deflecting the dipole through 180° is equal to

Which of the following complexes will show absorbance of light at the lowest wavelength?

Choose the correct option from the following:
(A) The internal resistance of a cell depends on its distance between electrodes and on the area of the electrodes.
(B) The emf of a cell is measured when it is used in series in an electrical circuit carrying current I.
(C) If a cell of emf E and of internal resistance r is providing current/through a resistance R then the potential difference across the cell is V = I(R + r).
(D) The emf of a cell is 1 V, if 1 J of work is done by the cell to drive 1 C of charge in the whole circuit.
Choose the correct answer from the options given below:

Two coaxial solenoids having number of turns per unit length 50 and 200, respectively, have same length 50 cm. The area of cross-section of the two solenoids are \( 4 \, \text{cm}^2 \) and \( 6 \, \text{cm}^2 \), respectively. The mutual inductance of the two solenoids is:

Solution of differential equation \(x d y-y d x=0\) represents :

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:

\(\int \frac{x}{(x-1)(x-2)} d x\) is equal to (where C is a constant of integration)