Match List - I with List - II.

List - I	List - II
(A) If A and B are mutually exclusive events, then \(P ( A \cup B )=\)	(I) \(\frac{ P ( A \cap B )}{ P ( B )}, P ( B ) \neq 0\)
(B) If A and B are independent events, then \(P ( A \cap B )=\)	(II) \(\frac{ P ( A \cap B )}{ P ( A )}, P ( A ) \neq 0\)
(C) If A and B are two events of a sample space of an experiment, then \(P ( A / B )=\)	(III) \(P ( A ) \cdot P ( B )\)
(D) If A and B are two events of a sample space of an experiment, then \(P ( B / A )=\)	(IV) \(P ( A )+ P ( B )\)

Choose the correct answer from the options given below :

The domain of the function \(f(x)=\sin ^{-1}(2 x-3)\) is :

The maximum value of the \(f(x)=\frac{1}{4 x^2+2 x+1}\) is :

A random variable X has the following probability distribution

X	2	3	4	5
P(X)	5/k	7/k	9/k	11/k

Then the value of \(\frac{k}{4}\) is

Ishita is rowing a boat. She takes 24 hours to row 72 km against the stream and she takes 9 hours to return to the starting point in the direction of the stream. The speed of the boat in still water is :

The area enclosed by the ellipse \(\frac{x^2}{9^2}+\frac{y^2}{6^2}=1\) is :

Consider a L.P.P, Maximize \(Z=3 x+5 y\) subject to constraints \(2 x+6 y \leq 6, x-y \geq 0, x \geq 0, y \geq 0\). Then which of the following are true?
(A) The feasible region of L.P.P is bounded region
(B) The corner points of the feasible region are \((0,0),(2,2),(0,1)\)
(C) Maximum value of Z is 9
(D) Point \((1,3)\) lies in the feasible region
Choose the correct answer from the options given below :

The intervals in which the function \(f(x) = 2x^3 + 9x^2 + 12x + 20\) is increasing is given by:

Read the passage carefully and answer the questions
Carbohydrates are naturally formed organic compounds from various plants. The common chemical formula, \(C _x\left( H _2 O \right)_y\), was considered as hydrates of carbon to derive the various carbohydrates. For instance, the general formula for glucose ( \(C _6 H _{12} O _6\) ) easily fits into the above formula. Carbohydrates also called saccharides are classified on the basis of their behavior towards hydrolysis. Monosaccharides cannot be hydrolyzed further to simpler units of polyhydroxy aldehyde or ketones. About 20 monosaccharides are known to occur in nature. Carbohydrates that yield large number of monosaccharide units are called polysaccharides. Amino acids contain ( \(- NH _2\) ) and ( - COOH ), which can be classified in various forms. Proteins are polymers of alpha amino acids which are connected to each other by a peptide bond or peptide linkage. When a native protein is subjected to physical change, its globules unfold and helix get uncoiled and the protein loses its biological activity. The protein is said to be denaturated.
The two monosaccharides units are joined together through which linkage ?

Which was the first discovered antibiotic ?

In the grass family the cotyledon is called:

If A and B are invertible matrices of the same order, then

The area (in sq. units) of the region bounded by the line \(y=x+2, x=0, x=1\) and \(y=0\) is: