A wire of resistance \( 18 \, \Omega \) is bent in the form of an equilateral triangle. The effective resistance between any two corners of the triangle is :

In a transistor :
(A) one of the outer layers is heavily doped and is called collector
(B) one of the outer layers is heavily doped and is called emitter
(C) the middle layer is very lightly doped and is called base
(D) one of the outer layer is moderately doped and is called emitter
(E) one of the outer layer is moderately doped and is called collector
Choose the correct answer from the options given below :

If the least distance of distinct vision for a person is 50 cm, what should be the focal length of the reading spectacles for him ?

Assume an electric field \( \vec{E} = 30x \, \hat{i} \) exists in space. If \( V_0 \) is the potential at the origin and \( V_A \) is the potential at \( x = 2 \) m, then the potential difference \( V_A - V_0 \) is:

In a Young's double-slit experiment, the slits are separated by 0.28 mm and the wavelength of light used is 6000 A. The fringes are observed on a screen placed 1.4 m away from the slits. The distance between the central bright fringe and the fourth bright fringe will be

Two circular coils of diameter 10 cm and 20 cm, carrying equal currents have the same number of turns. The ratio of magnetic fields produced at the center of coils, respectively will be

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:

Which of the following option shows the Brewster's law in polarisation of light ?

Match List - I with List - II

List - I	List - II
(A) Simple microscope	(I) A concave mirror is used as an objective
(B) Compound microscope	(II) Two convex lenses both of small focal length
(C) Refracting Telescope	(III) Two convex lenses, one of small focal length other of large focal length
(D) Reflecting Telescope	(IV) Single convex lens of small focal length

Choose the correct answer from the options given below:

Identify the product \([\text{B}]\) in the following reaction.
\(\text{CH}_3\text{CH}_2-\text{C} \equiv \text{CH} + \text{HCl} \rightarrow \text{A} \xrightarrow{\text{HI}} [\text{B}]\)

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.
The beetles that infest Bt cotton plant are killed:

The projection of the vector \(\vec{a}=2 \hat{i}+3 \hat{j}+2 \hat{k}\) on the vector \(\vec{b}=\hat{i}+2 \hat{j}+\hat{k}\) is:

In a 500 m race, the ratio of speeds of two participants \(A\) and \(B\) is \(4: 5\).
If \(A\) has a start of 180 m , then the distance by which \(A\) wins is :