Match List I with List II

List - I	List - II
(A) \(|\vec{a} \times \hat{i}|^2+|\vec{a} \times \hat{j}|^2+|\vec{a} \times \hat{k}|^2\)=	(I) \(|\vec{a}|^2\)
(B) \(\frac{(\vec{a} \cdot \vec{b})^2+|\vec{a} \times \vec{b}|^2}{|\vec{b}|^2}=\)	(II) \(\sqrt{3}|\vec{a}|\)
(C) \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three mutually perpendicular vectors of equal magnitude then \(|\vec{a}+\vec{b}+\vec{c}|=\)	(III) \(\frac{1}{2}|\vec{a} \times \vec{b}|\)
(D) Area of parallelogram with diagonals \(\vec{a}\) and \(\vec{b}\)	(IV) \(2|\vec{a}|^2\)

Choose the correct answer from the options given below:

For \(y=x e^x\), which of the following is correct ?

Suppose that A, B and C are matrices of order \(m \times n, n \times 5\) and \(5 \times q\) respectively. The restriction on m, n and q so that AB - BC is defined are

The area of the region bounded by the curve \(x=y^2\), y-axis and the line y = 3 and y = 4 is:

If \(c_{i j}\) denotes the cofactor of element \(c_{i j}\) of the matrix \(A=\left[\begin{array}{ccc}1 & 2 & -1 \\ 0 & -3 & 2 \\ 4 & 2 & 3\end{array}\right]\), then the value of \(c_{21} \cdot c_{33}\) is

If, in a pair of consecutive positive integers, both numbers are greater than 5 and their sum is less than 23, then the number of such pairs is :

A random variable y has the following probability distribution

y	1	2	3	4	5
P(y)	2k	3k	k	4k	5k

Match List-l with List-ll

List - I	List - II
(A) P(y > 2)	(I) \(\frac{2}{5}\)
(B) k	(II) \(\frac{2}{3}\)
(C) \(P(y \leq 3)\)	(II) \(\frac{8}{15}\)
(D) \(P(2 \leq y \leq 4)\)	(II) \(\frac{1}{15}\)

Choose the correct answer from the options given below

Read the following passage carefully and answer the given questions.
Plasmodium, a tiny protozoan is responsible for the disease malaria. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal. Innate immunity consist of four types of barriers. These are – (i) Physical barriers- skin on our body is the main barrier which prevents entry of the micro-organisms. (ii) Physiological barriers- Acid in the stomach, saliva in the mouth, tears from eyes-all prevent microbial growth. (iii) Cellular barriers- Certain types of leukocytes (WBC) of our body like polymorpho-nuclear leukocytes (PMNL-neutrophils) and monocytes and natural killer (type of lymphocytes) in the blood as well as macrophages in tissues can phagocytose and destroy microbes. (iv) Cytokine barriers- virus-infected cells secrete proteins called interferons which protect non-infected cells from further viral infection. Allergy is due to the release of chemicals like histamine and serotonin from the mast cells. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused.
Which one of the followings is not the example of cellular barrier?

The area (in sq. units) of the region bounded by \(y=-2, y=2, x=y^3\) and \(x=0\) is equal to

Inner orbital complex among the following is :
(A) \(\text{[Co(NH}_3)_6\text{]}^{3+}\)
(B) \(\text{[CoF}_6\text{]}^{3-}\)
(C) \(\text{[Ni(CN)}_4\text{]}^{2-}\)
(D) \(\text{[MnCl}_6\text{]}^{3-}\)
(E) \(\text{[FeF}_6\text{]}^{3-}\)
Choose the correct answer from the options given below :

An element has a cubic close packing (ccp) structure with an edge length 297 pm . The density of mass \(=107.9 g / mol\).)
the element is (Given molar mass = \(107.9 g / mol\).)

The angle between the pair of straight lines given by \(\vec{r}=(3 \hat{i}+2 \hat{j}-4 \hat{k})+\lambda(\hat{i}+2 \hat{j}+2 \hat{k})\) and \(\vec{r}=5 \hat{i}-2 \hat{j}+\mu(3 \hat{i}+2 \hat{j}+6 \hat{k})\) is :

A steady current flows in a metallic conductor of non-uniform cross-section. The quantity that is constant along the length is