Let y be a discrete random variable, taking values \(y_1, y_2, y_3, ..., y_n\) with probabilities \(p_1, p_2, p_3, ..., p_n\) respectively. Then the standard deviation of y is given by:

Let A = {1, 2, 3} Consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} Then R is:

Let \(R =\left\{\left(L_1, L_2\right) : L_1 \perp L_2\right.\) where \(L_1, L_2 \in L\) (set of straight line in a plane), then

If \(\left[\begin{array}{ll}x-y & 0 \\ x+y & 1\end{array}\right]\) is an identity matrix and \(\left[\begin{array}{ll}x & y \\ x & x\end{array}\right]\) is a singular matrix then :

If \(A\) and \(B\) are symmetric matrices of order \(3 \times 3\) then the matrix \(2 A B-B A\) is :

Let \(A=\left[\begin{array}{ccc}1 & \cos \theta & 1 \\ -\cos \theta & 1 & \cos \theta \\ -1 & -\cos \theta & 1\end{array}\right], 0 \leq \theta \leq 2 \pi\), then :

The solution set of the inequality \(3 x+5 y<15\) is :

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:

If A and B are two non-singular matrices of order n, then which of the following statement / statements is/are not correct?
(A) AB is non-singular.
(B) AB is singular.
(C) \((A B)^{-1}=A^{-1} B^{-1}\)
(D) \((A B)^{-1}\) does not exist.
Choose the correct answer from the options given below :

Camphor in nitrogen gas is a type of solution:

Consider the line \(\vec{r}=\hat{i}-2 \hat{j}+4 \hat{k}+\lambda(-\hat{i}+2 \hat{j}-4 \hat{k})\)
Match List-I with List-II

List-I	List-II
(A) A point on the given line	(I) \(\left(\frac{-1}{\sqrt{21}}, \frac{2}{\sqrt{21}}, \frac{-4}{\sqrt{21}}\right)\)
(B) direction ratios of the line	(II) \((4,-2,-2)\)
(C) direction cosines of the line	(III) \((1,-2,4)\)
(D) direction ratios of a line perpendicular to given line	(IV) \((-1,2,-4)\)

Choose the correct answer from the options given below:

Match List-I with List-II

List-I (Reaction)	List-II (Type of reaction)
(A) Hydrolysis of Ethyl Chloride	(I) Substitution reaction
(B) 2-Propanol is treated with Conc. Sulphuric acid	(II) Addition reaction
(C) Reaction of HCN with Acetone	(III) Degradation reaction
(D) Treatment of acetamide with NaOH and Br2	(IV) Elimination reaction

Choose the correct answer from the options given below:

A compound is formed by 2 elements P and Q. Atoms of element Q (as anions) makes ccp and those of P (as cations) fill all tetrahedral voids and also occupy half of the octahedral voids. What is the correct formula of this compound?