Area bounded by the curve \(y=\cos ^{-1} x\) and the lines \(x=0, x=1\) is:

If \(\vec{a}=5 \hat{i}+\hat{j}+3 \hat{k}\) then the sum of projections of \(\vec{a}\) on \(x\)-axis, \(y\)-axis and \(z\)-axis is:

If \(A=\left[\begin{array}{cc}4 & 3 \\ 2 & -1 \\ 1 & 0\end{array}\right]\) and \(B^T=\left[\begin{array}{ccc}1 & 2 & 3 \\ 2 & 1 & -1\end{array}\right]\), then \(A-B\) is equal to

The probability distribution of a random variable X is given below:

x	-5	-4	-3	-2	-1	0	1	2	3	4	5
P(X)	p	2p	3p	4p	5p	7p	8p	9p	10p	11p	12p

A bag contains 8 blue and 12 green balls. Two balls are drawn in succession without replacement.
The probability that first is blue and second is green is

Match List-I with List-II

List-I (Inverse Trigonometric Function)	List-II (Principal Value)
(A) \(\sin ^{-1}\left(-\frac{1}{2}\right)\)	(I) \(\pi / 6\)
(B) \(\cos ^{-1}\left(-\frac{1}{2}\right)\)	(II) \(-\pi / 6\)
(C) \(\tan ^{-1}(-\sqrt{3})\)	(III) \(2 \pi / 3\)
(D) \(\cot ^{-1}(\sqrt{3})\)	(IV) \(-\pi / 3\)

Choose the correct answer from the options given below :

The slope of the normal to the curve \(y=x^3-4 \sin x\) at \(x=0\) is:

Choose the incorrect statements from the options given below:
(A) If a monochromatic source is replaced by a source of white light in Young's experiment, then interference fringes will be coloured,
(B) If the screen is moved away from the plane of slits, then the angular width of the fringe will not remain the same,
(C) If separation between slits in Young's experiment is halved, the fringe width becomes double,
(D) The fringe width in Young's experiment is \( \lambda d/D \)
Choose the correct answer from the options given below:

The condition on \(a\) and \(b\), such that for \(y=\frac{a}{x}-\frac{b}{x^2}, \frac{d y}{d x}=0\) at \(x=1\) is :

Read the passage carefully and answer the given questions.
DNA Fingerprinting
Polymorphism in DNA sequence is the basis of genetic mapping of the human genome as well as of DNA fingerprinting. DNA fingerprinting involves identification of differences in some specific regions in the DNA sequence called repetitive DNA. It works on the principle of polymorphisms in DNA sequences. The repetitive DNA are separated from bulk genomic DNA. The bulk DNA forms a major peak and the other small peaks are referred to as satellite DNA. These repetitive/satellite DNA sequences show a high degree of polymorphisms and form the basis of DNA fingerprinting.
Which one of the following techniques is involved in DNA fingerprinting?

A resistor develops 200 J of thermal energy in 5 s when a current of 2 A is passed through it. If the current is measured to 5 A, what will be the energy developed in 12 s ?

Arrange the following electrolytes in the increasing order of van't Hoff factor (i) for complete dissociation of solute.
(A) \(\left[ Co \left( NH _3\right)_6\right] Cl _3\)
(B) \(MgCl _2\)
(C) \(K _4\left[ Fe ( CN )_6\right]\)
(D) KCl
Choose the correct answer from the options given below:

A first order reaction is 50% completed in \(1.26 \times 10^{14}\) s.
How much time would it take for 100% completion?