\(\int_{-\pi}^\pi \frac{e^{\sin x}}{e^{\sin x}+e^{-\sin x}} d x\) is equal to:

If a line makes angles \(\alpha, \beta\) and \(\gamma\) with the positive directions of coordinate axes respectively, then \(\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma\) is equal to

Let A be a non-singular square matrix of order n, then
Match List - I with List - II

List - I	List - II
(A) A (adj A)	(I) \(\frac{1}{|A|}\)
(B) |adj A|	(II) \(|A|^n\)
(C) \(\left|A^{-1}\right|\)	(III) \(|A| I\)
(D) \(|A(\operatorname{adj} A)|\)	(IV) \(|A|^{n-1}\)

Choose the correct answer from the options given below:

The common region determined by all constraints of a Linear programming problem is called:

Match List-l with List-ll

List-l (Statement)	List-ll (Its value)
(A) Degree of the differential equation \(\frac{d^2 y}{d x^2}=e^{d y / d x}\) is	(I) 2
(B) Order of the differential equation \(\left(\frac{d y}{d x}\right)^2+\frac{d^3 y}{d x^3}=0\) is	(II) not defined
(C) Degree of the differential equation \(\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2-5 x^2=0\)	(III) 3
(D) If \(p\) is the order and \(q\) is the degree of the differential equation \(\frac{d y}{d x}+3 y=e^x\), then \(p+q\) is	(IV) 1

Choose the correct answer from the options given below :

Two cards are drawn simultaneously at random from a well shuffled pack of 52 Cards.
Let X be the random variable which denotes number of kings in the draw. Then the probability distribution of X is

The probability distribution of number of heads in two tosses of a coin is:

Arrange the given steps of menstrual cycle in correct sequence.
(A) Menstruation
(B) Luteal phase
(C) Follicular phase
(D) Next cycle starts
Choose the correct answer from the options given below:

Arrange the following ligands in increasing order of their field strength:
(A) SCN-
(B) F-
(C) H2O
(D) CO
Choose the correct answer from the options given below :

\(\left[\begin{array}{cc}2 x+1 & 4 x \\ y+3 & 2 y-5\end{array}\right]=\left[\begin{array}{cc}x+2 & 4 \\ 7 & 3\end{array}\right]\)

The sides of an equilateral triangle are increasing at the rate of \(5 cm / sec\). The rate at which the area increases when the side is 20 cm , is

Answer the question on the basis of passage given below :
Adsorption is a surface phenomenon and it differs from absorption which occurs throughout the body of the substance that absorbs. In physiosorption the attractive forces are mainly van der Waal's forces while in chemisorption ionic/covalent bonds are formed between particles of adsorbent and adsorbate. The catalytic activity of finely divided iron in Haber's process of ammonia manufacture can be explained by adsorption theory. Adsorption being an exothermic process, the heat of adsorption is utilised in enhancing the rate of the reaction. Adsorption has many applications being used in gas masks, control of humidity, chromatograph separation, curing diseases etc.
The modern adsorption theory lists the following steps for heterogeneous catalysis
(A) Adsorption of reactant molecules on the surface of a catalyst
(B) Occurrence of chemical reaction on the surface of a catalyst
(C) Desorption of products from a catalyst surface
(D) Diffusion of reactants to the surface of the catalyst
Choose the correct sequences of steps from the options given below:

"Toddy" is a traditional drink which is made by-