Let R be the relation in the set \(\{a, b, c\}\) given by \(R=\{(a, b),(b, b),(a, a),(a, c),(c, c),(c, b)\}\) Choose the correct answer from the options below :

The interval(s), where the function \(f(x)=\left\{\begin{array}{l}\frac{1-e^x}{e^{2 x}-1}: x \neq 0 \\ -\frac{1}{2}: x=0\end{array}\right.\) is increasing, is/are:

A random variable X has the following distribution:

X	0	1	2	3	4	5	6	7
P(X)	0	3k	k	2k	\(3k^2\)	\(k^2\)	\(6k^2\)	3k

The value of k is:

If \(A=\left[\begin{array}{ccc}\cos \theta & \sin \theta & 0 \\ -\sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right]\) and B is a square matrix of order 3, then |AB| is equal to:

If \(f(x)=|x|+|x-5|\), then which of the following statements are TRUE?
(A) \(f\) is a continuous function everywhere
(B) \(f\) is a continuous function except x = 5 and x = 0
(C) \(f\) is a continuous function except x = 0 but not differentiable at x = 5
(D) \(f\) is a continuous function everywhere but not differentiable at x = 0 and x = 5
Choose the correct answer from the options given below:

Match List-I with List-II

List-I (Equationof Lines)	List-II (Information)
(A) \(\vec{r}=(3 \hat{i}-2 \hat{j}+\hat{k})+\lambda(\hat{j}-2 \hat{k})\)	(I) Direction ratios are \(2,4,-1\)
(B) \(\frac{2-x}{1}=\frac{2 y+1}{4}, z=2\)	(II) Perpendicular to \(2 \hat{i}-\hat{j}+\hat{k}\)
(C) \(\frac{x}{1}=\frac{y-3}{2}=\frac{3-4 z}{2}\)	(III) Passing through the point \((3,-2,1)\)
(D) \(\vec{r}=(3 \hat{i}+2 \hat{j}+\hat{k})+\lambda(2 \hat{i}+\hat{j}-3 \hat{k})\)	(IV) Direction ratios are \(-1,2,0\)

Choose the correct answer from the options given below :

The marks obtained by five students in a test of Applied Mathematics carrying 100 marks are 49,58,67,92,99. Then the point estimate of the population mean is

Which of the following represents Fehling solution B?

Read the following paragraph and answer the given questions.
RNAi takes place in all eukaryotic organisms as a method of cellular defense. The source of this complementary RNA could be from an infection by viruses having RNA genomes or mobile genetic elements (transposons) that replicate via an RNA intermediate. Insulin from an animal source, though caused some patients to develop allergy or other types of reactions to the foreign protein. Insulin consists of two short polypeptide chains: chain A and chain B, that are linked together by disulphide bridges. Transgenic mice are being developed for use in testing the safety of vaccines before they are used on humans. Transgenic mice are being used to test the safety of the polio vaccine. If successful and found to be reliable, they could replace the use of monkeys to test the safety of batches of the vaccine. Specific Bt toxin genes were isolated from Bacillusthuringiensis} and incorporated into the several crop plants such as cotton. The choice of genes depends upon the crop and the targeted pest, as most Bt toxins are insect-group specific. The toxin is coded by a gene cryIAc named cry. There are a number of them, for example, the proteins encoded by the genes cryIAc and cryIIAb control the cotton bollworms, that of cryIAb controls corn borer.

Identify the incorrect fact about the genetic modification?

Identify the term (s) which is/are not associated with post transcriptional processing of RNA.
A. Termination factor
B. Splicing
C. Capping
D. Tailing
Choose the correct answer from the options given below:

When a nucleotide from DNA containing adenine is hydrolyzed, the products obtained are

According to the Biot- Savart law, the magnetic field due to a current element is
(A) inversely proportional to the square of the distance from the current element to the point of interest.
(B) produced by a vector source.
(C) perpendicular to the plane containing the displacement vector and the current element.
(D) non-zero at any point in the direction of the current element.
Choose the correct answer from the options given below:

The instantaneous magnetic flux linked with a coil is given by \(\phi = (15t^3 - 100t^2 + 40)\) Wb. The emf induced in the coil at time \(t = 1\) s is :