In which of the following interference is possible?

The phenomenon of polarisation of light confirmed that light waves are

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:

Match List-I with List-II

List-I	List-II
(A) Electric potential V due to a single charge	(I) \(\propto r^0\)
(B) Electric flux due to a positive point charge through sphere of radius r	(II) \(\propto \frac{1}{r^2}\)
(C) Electric intensity E due to a point charge	(III) \(\propto \frac{1}{r}\)
(D) Electric intensity E due to dipole	(IV) \(\propto \frac{1}{r^3}\)

Choose the correct answer from the options given below :

A moving coil galvanometer has N number of turns in the coil with area A. It carries a current I and the magnetic field is B. The torque acting on the coil is :

An element \( \Delta \vec{l} = 0.5 \hat{j} \text{ cm} \) is placed at the origin and carries a large current \( I = 10 \text{ A} \). The magnetic field at point (50 cm, 0) is

A cell of emf E and internal resistance r gives current of 0.5 A with external resistance of 12 \(\Omega\) and a current of 0.25 A with an external resistance 25 \(\Omega\). What is the value of internal resistance?

A spherical conducting shell of inner radius \( r_1 \) and outer radius \( r_2 \) has a charge \( Q \). A charge \( q \) is placed at the centre of the shell. The surface charge density on outer surface of the shell is :

A uniformly charged sphere of \( 80 \text{ } \mu\text{C} \) and radius 2 cm is placed in air.
The electric field intensity at a point 20 cm from the center of the sphere is:

Read the passage carefully and answer the questions based on the passage:
Pest Resistance Plants
Various nematodes parasitize a wide variety of plants and animals, including human beings. A nematode, Meloidogyne incognitia, infects the roots of tobacco plants and causes a great reduction in yield. A noval strategy was adopted to prevent this infestation which was based on the process of RNA interference (RNAi). RNAi takes place in all eukaryotic organisms as a method of cellular defense. This method involves silencing of a specific mRNA due to a complementary dsRNA molecule that binds to and prevents translation of the mRNA (silencing). 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 (cold, drought, salt, heat). (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, e.g., golden rice, i.e., Vitamin 'A' enriched rice. Genetic modification of organisms can have unpredicatable results when such organisms are introduced into the ecosystem. Therefore, the Indian Government has set up organisations such as GEAC (Genetic Engineering Approval Committee), which will make decisions regarding the validity of GM research and the safety of introducing GM-organisms for public services. Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans (tobacco budworm, armyworm), coleopterans (beetles) and dipterans (flies, mosquitoes).
The Indian Government organization GEAC stands for -

What is the order of hydrolysis of methyl acetate in acidic medium?

The function \(f(x)=x^x\) has a critical point at :

A vector of magnitude 9, which is perpendicular to both the vectors \((4 \hat{i}-\hat{j}+8 \hat{k})\) and \((-\hat{j}+\hat{k})\) is