If \(\vec{a}+\vec{b}+\vec{c}=0,|\vec{a}|=3,|\vec{b}|=25,|\vec{c}|=7\), then the angle between \(\vec{a}\) and \(\vec{b}\) is:

If the function \(f(x)=x^4-62 x^2+a x+9\) attains its local maximum value at \(x=1\), then \(a\) is equal to :

If \(A\) and \(B\) are independent events such that \(P(A \mid B)=\frac{1}{3}\) and \(P(B)=\frac{1}{2}\), then the value of \(P(A \cap B)\) is equal to :

Arrange the following as per statistical inferences :
(A) Data Analysis
(B) Population
(C) Making Inferences
(D) Data Collection
Choose the correct answer from the options given below :

Consider the LPP: Minimize \(Z=x+2 y\) subject to \(2 x+y \geq 3, x+2 y \geq 6, x, y \geq 0\). The optimal feasible solution occurs at:

Match List-I with List-II

List-(I) Function	Lis-(II) Derivative
(A) \(y=\sin ^{-1} x+\sin ^{-1} \sqrt{1-x^2},|x|<1\)	(I) \(\frac{d y}{d x}=\frac{1}{2 y-1}\)
(B) \(y=\sqrt{x+y}, x+y>0, y \neq \frac{1}{2}\)	(II) \(\frac{d y}{d x}=10^x \log _e 10\)
(C) \(y=\log _{10} x, x>0\)	(III) \(\frac{d y}{d x}=0\)
(D) \(y=10^*\)	(IV) \(\frac{d y}{d x}=\frac{1}{x \log _e 10}\)

Choose the correct answer from the options given below:

The foot of the perpendicular drawn from the point \((1,6,3)\) to the line \(\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\) is :

Under which of the following conditions the Poisson distribution is the limiting case of, binomial distribution :
(A) The number of trials is indefinitely large.
(B) The probability of success for each trial is indefinitely small.
(C) The product of the number of trials and the probability of success for each trial is finite.
(D) The probability of success for each trial is indefinitely large.
Choose the correct answer from the options given below :

What is the product of nitration of Benzoic acid?

The sum of the products of elements of any row with the cofactors of corresponding elements is equal to:

The decomposition of ammonia on platinum surface is a zero order reaction. How much time it will take for \(1 \times 10^{-4}\ mol\ L^{-1}\) of ammonia to reduce into half of its concentration ?
(\(K = 0.5 \times 10^{-4}\ mol\ L^{-1}\ s^{-1}\))

The central dogma was proposed by:

Read the passage carefully and answer:
Organic compounds derived from NH3 by replacing one or more H-atoms with alkyl or aryl groups will form primary, secondary and tertiary amines. The common methods which include their preparations are reduction of nitro group, amide group and nitrile group, Gabriel phthalimide synthesis and ammonolysis of alkyl halides. Amines are basic in nature due to the presence of a lone pair of electrons on the nitrogen atom. Important chemical properties of amines include acylation, alkylation and their interaction with nitrous acid. There are various tests which can distinguish different types of amines from each other, for e.g. carbylamine test, Hinsberg's test, coupling reaction etc. Another important class of compounds which can be derived from primary amines is azo compounds. These compounds are intensely colored and widely used as dyes in textile, leather and food industries.
Conversion of nitro group into primary amine is preferred using