If a person \(A\) speaks the truth in \(80 \%\) cases and the person \(B\) speaks the truth in \(75 \%\) cases, then the probability that they contradict each other in a statement is:

A relation \(f: N \rightarrow N\) be defined by \(f(x)=x^2, x \in N\) (Set of Natural numbers), Then \(f(x)\) is

Let \(f(x)=|x|\) and \(g(x)=[x]\), then the value of \(f \circ g\left(-\frac{9}{2}\right)-g \circ f\left(-\frac{9}{2}\right)\) is :

Let \(|\vec{a}|=5,|\vec{b}|=2\) and \(\vec{a} \cdot \vec{b}=6\), then the value of \(|\vec{a} \times \vec{b}|\) is equal to

If \(A X=B\) where \(A , X\) and B are matrices and \(A^{-1}, B^{-1}\) exist, then matrix X is

Let the matrix \(A=\left[\begin{array}{ll}2 & 3 \\ 1 & 4\end{array}\right]\). Then which of the following are true?
(A) \(\operatorname{adj} A =\left[\begin{array}{cc}4 & -3 \\ -1 & 2\end{array}\right]\)
(B) \(\operatorname{det}( A )=5\)
(C) \(\operatorname{det}(\operatorname{adj} A )=25\)
(D) If \(A^3=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\), then \(a+b=c+d\)
Choose the correct answer from the options given below :

A random variable \(X\) has the following probability distribution

x	-2	-1	0	1	2	3
p	0.1	k	0.2	2k	0.3	k

Then the mean of X is :

In a double slit experiment, the distance between slits is increased 10 times whereas their distance from screen is halved, then what is the fringe width ?

A bar magnet is cut into two equal halves along a plane parallel to the magnetic axis. The one parameter which remains unchanged is

A strong magnetic field is applied on a stationary electron :

Match List I with List II

List I (Terms)	List ll (Features)
(A) Natality	(I) Exit of individuals
(B) Mortality	(II) Entry of individuals
(C) Immigration	(III) Death rate
(D) Emigration	(IV) Birth rate

Choose the correct answer from the options given below:

Identify the correct statements for the behavior of ethane-1,2-diamine as a ligand.
(A) it is a neutral ligand
(B) it is a bidentate ligand
(C) it is an ambidentate ligand
(D) it is a chelating ligand
Choose the correct answer from the options given below:

We use microbes and microbially derived products almost every day. Bacteria called lactic acid bacteria (LAB) grow in milk to convert it into curd. The dough, which is used to make bread, is fermented by yeast called Saccharomyces cerevisiae. Microbes are used to produce industrial products like lactic acid, acetic acid and alcohol, which are used in a variety of processes in the industry. However, certain bacteria, which grow anaerobically on cellulosic material, produce large amount of methane along with CO2 and H2. These bacteria are collectively called methanogens, and one such common bacterium is Methanobacterium. These bacteria are commonly found in the anaerobic sludge during sewage treatment. Microbes are also used for commercial and industrial production of certain chemicals like organic acids, alcohols and enzymes.
Examples of acid producers are Aspergillus niger (a fungus) of citric acid. You are familiar with the commonly used antibiotic Penicillin. Do you know that Penicillin was the first antibiotic to be discovered, and it was a chance discovery? Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol.
A boy wants to set curd from milk. Suggest which of the following microbes can be useful for him?