The integral \(\int_0^1 x(1-x)^n d x\) is equal to :

The relation \(R=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}\) on the set \(A=\{1,2,3\}\) is :

Two pipes A and B can fill a tank in 24 minutes and 32 minutes respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 minutes?

The shortest distance between lines \(\frac{-x-3}{4}=\frac{y-6}{3}=\frac{z}{2}\) and \(\frac{-x-2}{4}=\frac{y}{1}=\frac{z-7}{1}\) is :

The value of \(\lambda\) for which the two vectors \((2 \hat{i}-\hat{j}+2 \hat{k})\) and \((3 \hat{i}+\lambda \hat{j}+\hat{k})\) are perpendicular, is :

Consider the following test:
\(H _0: \mu \leq 12\)
\(H _{ a }: \mu>12\)
A sample of 36 provided a sample mean \(\bar{x}\) = 16 and a sample standard deviation S = 4.2 Then the value of the t-test statistic is:

The solution set of the inequality \(\frac{2 x+3}{x-1}<0\) is:

Arrange the following elements of a generalised communication system in the sequencial order :
(A) Channel
(B) Information source
(C) Transmitter
(D) Receiver
(E) User of information
Choose the correct answer from the options given below :

Read the following passage carefully and answer the given questions.
The B-lymphocytes produce an army of proteins in response to pathogens. Each antibody molecule has four peptide chains, two small called light chains and two longer called heavy chains. Virus-infected cells secrete proteins called interferons which protect non-infected cells from further viral infection. Symptoms of allergic reactions include sneezing, watery eyes, running nose and difficulty in breathing. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Lymphoid organs are the organs where origin and/or maturation and proliferation of lymphocytes occur. The primary lymphoid organs are bone marrow and thymus. After maturation the lymphocytes migrate to secondary lymphoid organs like spleen, lymph nodes, tonsils, Peyer's patches of small intestine and appendix. Heroin commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. This is obtained by acetylation of morphine, which is extracted from the latex of poppy plant Papaver somniferum.
Which one of the following is not a feature of an antibody:

A steady current flows in a metallic conductor of non-uniform cross-section. The quantity that is constant along the length is

Let \(A=\left[\begin{array}{ccc}1 & \cos \theta & 1 \\ -\cos \theta & 1 & \cos \theta \\ -1 & -\cos \theta & 1\end{array}\right], 0 \leq \theta \leq 2 \pi\), then :

Bag A contains 2 unbiased and 3 biased coins whereas Bag B contains 3 unbiased and 2 biased coins. A bag is selected at random and 2 coins are taken out simultaneously. The probailty, that both coins are unbiased is :

Match List-l with List-ll

List-l (Terms related to RNA)	List-II (Features)
(A). Capping	(I). Transcribes rRNAs
(B). Polyadenylation	(II). Removal of introns
(C). RNA polymerase I	(III). 5' end-methyl guanosine triphosphate addition
(D). Splicing	(IV). Addition of 200-300 adenylate residues

Choose the correct answer from the options given below: