Match List - I with List - II.

LIST-I	LIST-I
(A) \(\csc ^{-1} x\)	(I) \((0, \pi)\)
(B) \(\sec ^{-1} x\)	(II) \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}\)
(C) \(\tan ^{-1} x\)	(III) \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)
(D) \(\cot ^{-1} x\)	(IV) \([0, \pi]-\left\{\frac{\pi}{2}\right\}\)

Choose the correct answer from the options given below:

If \(y=\sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}\), then

The area (in sq. units) of the region bounded by the curve \(y=\cos x\) between \(x=-\frac{\pi}{2}, x=\frac{\pi}{2}\) and the \(x\)-axis is

If \(x \sqrt{1+y}+y \sqrt{1+x}=0\), where \(|x|<1,|y|<1\) and \(x \neq y\), then

The feasible region for an LPP is shown by shaded region in the figure. Then the minimum value of Z = 11x + 7y is

\(\int \frac{\sqrt{\tan x}}{\sin x \cos x} d x\) equals :

Given equation of the plane is \(5x + 2y - 3z = 17\). Then,
A. A point \((2, 2, -1)\) lies on the plane
B. The direction cosines of normal to plane are \((2, 2, -1)\)
C. Coordinates of foot of perpendicular from origin are \((5, 2, -3)\)
D. The plane does not pass through the origin
Choose the correct answer from the options given below:

Match List-I with List-II

List-I (Terms)	List-II (Applications)
(A) RNA interference	(I) ADA deficiency
(B) Genetically engineered insulin	(II) \(\alpha\)-1-antitrypsin
(C) Gene therapy	(III) Meloidegyne incognitia
(D) Biological product	(IV) Eli Lilly

Choose the correct answer from the options given below:

Read the following passage carefully.
Restriction enzyme
Restriction enzymes cut the strand of DNA a little away from the center of the palindrome sites, but between the same two bases on the opposite strands. This leaves single stranded portions at the ends. There are overhanging stretches called sticky ends on each strand. These are named so because they form hydrogen bonds with their complementary cut counterparts. This stickiness of the ends facilitates the action of the enzyme DNA ligase. The word palindromes refer to group of letters that forms the same words when read both forward and backward. Restriction endonucleases are used in genetic engineering as molecular scissors.
Which one of the following option is correct about restriction enzyme?

The value of \(|\text{adj}(2A)|\), if \(A = [a_{ij}]_{3 \times 3}\) and \(|A| = 2\) is:

What is the product of nitration of Benzoic acid?

\(\mathrm{CuSO}_4\) is colorless but \(\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}\) is blue in color. Which of the following statements is incorrect about the color of \(\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}\)?

The correct relation for determining the molar mass of solute (\(\text{M}_2\))
using osmotic pressure measurement, is