Choose the wrong statement.

\(\int_0^2 \frac{\sqrt{x}}{\sqrt{x}+\sqrt{2-x}} d x\) is equal to:

The value of a determinant is unaltered if:

A 50 Hz AC current of crest 1 A flows through a transformer primary. With mutual inductance \(0 . 5 ~ H\), the crest voltage induced in secondary is :

Let \(A\) be a square matrix of order \(3 \times 3\), then \(|K A|\) is equal to :

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 matrix \(A=\left[\begin{array}{cc}p & -3 \\ -4 & p\end{array}\right]\) and \(\left|A^3\right|=64\), then the value of \(p\) is :

When a charged particle moves in a uniform magnetic field, its kinetic energy:

A. General solution of \(\frac{d y}{d x}=\frac{1+y^2}{1+x^2}\) is \(\tan ^{-1} y=\tan ^{-1} x+c\); Where c is a constant
B. General solution of \(\frac{d y}{d x}+\frac{\sqrt{1-y^2}}{\sqrt{1-x^2}}=0\) is \(\sin ^{-1} y-\sin ^{-1} x=c\); Where c is a constant
C. General solution of \(\frac{y d x-x d y}{y}=0\) is \(y=c x\); Where c is a constant
D. General solution of \(\frac{d y}{d x}=e^{x+y}\) is \(e^x+e^y=c\); Where c is a constant
E. \(\left(x^2+x y\right) d y=\left(x^2+y^2\right) d x\) is a homogeneous differential equation
Choose the correct answer:

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 enzyme helps to join DNA?

Which of the following statements are correct?
(A) The mean and variance of the Poisson distribution are equal.
(B) The mean and variance of a Binomial distribution are equal.
(C) An unbiased die is thrown again and again until two sixes are obtained, then the probability of obtaining the second six in the 3rd throw is \(\frac{5}{108}\).
(D) If the variance of a Poisson distribution is 2 , then \(P(X=2)=2 e^{-2}\).
Choose the correct answer from the options given below :

The refractive index of the material of an equilateral prism is \(\sqrt {2}\). The angle of minimum deviation of that prism is

Match List-l with List-ll

List-l (Abbreviation)	List-II (Relation)
(A) MTP	(I) Infertility
(B) AIDS	(II) Artificial insemination
(C) IUI	(III) Legal
(D) ART	(IV) Careless exchange of body fluids

Choose the correct answer from the options given below: