A simple random sample consists of three observations \(1,3,5\). The point estimate of the population standard deviation is :

The value of \(\int \frac{\left(x^4-x\right)^{1 / 4}}{x^5} d x\) is equal to (where \(C\) is an arbitrary constant) :

Find the maximum value of the function sin x(1 + cos x) is:

Match List-I with List-II

List - I (Function)	List - II (Points of discontinuity)
(A) \(f(x)=\frac{x^2+1}{x}\)	(I) x = 4
(B) \(f(x)=\frac{|x-1|}{x-1}\)	(II) x = 2
(C) \(f(x)=\{x-1\), if \(x<2 ; x+1\), if \(x \geq 2\}\)	(III) x = 0
(D) \(f(x)=\frac{1-x}{x-4}\)	(IV) x = 1

Choose the Correct answer from the options given below :

Interval in which the function \(f\) given by \(f(x)=\tan x-4 x, x \in\left(0, \frac{\pi}{2}\right)\) is strictly decreasing is

The function \(f(x)=x+\cot ^{-1} x\) is increasing in the interval:

Let \(\vec{a}=3 \hat{i}+\hat{j}-4 \hat{k}\) and \(\vec{b}=6 \hat{i}+5 \hat{j}-2 \hat{k}\) be two vectors.
Then a vector perpendicular to both \(\vec{a}\) and \(\vec{b}\) with magnitude 3 units is :

Inlet pipe A can fill a tank in 30 minutes and outlet pipes B and C can empty the tank in 2 hours each. If all three pipes operate together, the tank will be filled in

In eukaryotes, the regulation could be exerted at -
(A) Transcriptional level (formation of primary transcript)
(B) Processing level (regulation of splicing)
(C) Transport of mRNA from nucleus to the cytoplasm
(D) Translational level

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

Identify the codon with dual function.

Low oxygen concentration in the human body at high altitudes is due to the __________ .

Identify the correct order of organic compounds in the following chemical reaction: ? + Mg → ? → ? → ?
(A) CH 3 MgBr
(B) CH 3 B
(B) CH 3 B
(D) CH 4
Choose the correct answer from the options given below :