Let \(X\) denotes the number of hours you study during a randomly selected school day. The random variable \(X\) has the following probability distribution.

X	0	1	2	3	4
P(X)	K	2K	2K	2K	K

Match List - I with List - II.

LIST - I	LIST - II
(A) Value of K	(I) \(\frac{1}{4}\)
(B) Probability you study at least two hours	(II) \(\frac{1}{8}\)
(C) Probability you study exactly two hours	(III) \(\frac{3}{8}\)
(D) Probability you study at most one hour	(IV) \(\frac{5}{8}\)

Choose the correct answer from the options given below:

If \(y=3 e^{2 x}+2 e^{3 x}\), then \(\frac{d^2 y}{d x^2}+6 y\) is equal to

\(\int \frac{e^{2 x}-e^{-2 x}}{e^{2 x}+e^{-2 x}} d x \) is equal to :

If \(a, b, c\) are in A.P., then the value of determinant \(\left|\begin{array}{lll}x+2 & x+3 & x+2 a \\ x+3 & x+4 & x+2 b \\ x+4 & x+5 & x+2 c\end{array}\right|\) is:

The function \(f ( x )=\log (\sin x )\) is ___________

If A is an invertible matrix of order 3, then

List-I	List-II
(A) \(|\operatorname{adj} A|\)	(I) \(8|A|\)
(B) \(|A(\operatorname{adj} A)|\)	(II) \(|A|^2\)
(C) \(|2 A|\)	(III) \(\frac{1}{|A|}\)
(D) \(\left|A^{-1}\right|\)	(IV) \(|A|^3\)

Choose the Correct answer from the options given below :

In an influenza epidemic, the number of cases diagnosed in a week were as follows:

Day	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday
Number of Cases	10	12	8	16	9	14	4

The 3-day moving averages are :

The reaction of two molecules of 1-chlorobenzene with sodium metal in the presence of dry ether to form diphenyl is known as

What product(s) is formed when an Alkyl halide undergoes ammonolysis ?
(A) Primary amine
(B) Secondary amine
(C) Quaternary ammonium salt
(D) Tertiary amine
Choose the correct answer from the options given below:

The reaction in which an amide is treated with bromine in presence of ethanolic solution of sodium hydroxide is called

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.

The suitable example of mobile genetic elements is:

World Summit on 'Sustainable Development' in 2002 was held in :

The variance of the Binomial Distribution \(B\left(5, \frac{1}{4}\right)\) is: