For a square matrix \(A\) of order 3, if \(|A|=2\), then \(|\operatorname{adj}(2 A)|=\)

The area of a triangle with vertices \((0,-3),(0,3)\) and \((k, 0)\) is 27 sq. units. The value of \(k\) is:

Let \(a \leq \tan ^{-1} x+\cot ^{-1} x+\sin ^{-1} x \leq b\). If \(\alpha\) and \(\beta\) denote the minimum and maximum possible values of \(a\) and \(b\) respectively, then :

\(\int \frac{d x}{\left(1+5 \sin ^2 x\right)}\) is equal to

The area enclosed by the curve \(x=8 \cos t, y=4 \sin t\) between the lines \(x=0\) and \(x=4 \sqrt{3}\) is:

If the two lines \(\frac{x-1}{2}=\frac{y-3}{4}=-z\) and \(\frac{x-4}{3}=\frac{y-1}{-2}=z-1\) are contained in a plane then the equation of the plane is :

The value of \(\int_{0}^{\frac{\pi}{2}} \log \left( \frac{5 + 4 \sin x}{5 + 4 \cos x} \right) dx\) is:

If \(A\) and \(B\) are square matrices of the same order 3 , such that \(\operatorname{det}(A)=3\) and \(A B=3 I\), where \(I\) is an identity matrix of order 3. Then the value of \(\operatorname{det}(B)\) 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.
DNA fingerprinting is meant for:

Arrange the following steps of 'Polymerase Chain Reaction' in a correct sequence.
(A) Annealing of primers
(B) Amplified DNA
(C) Denaturation of DNA
(D) Extension of primers
Choose the correct answer from the options given below:

The decomposition of hydrogen peroxide follows the equation:
\(K=\left(2.9 \times 10^{14} s^{-1}\right) e^{-2 \mu o p}\)
The value of Ea is:

Answer the question on the basis of passage given below :
Adsorption is the phenomenon of attracting and retaining the molecules of a substance on the surface of a solid resulting into a higher concentration on the surface than in the bulk. The substance adsorbed is known as adsorbate and the substance on which adsorption takes place is called adsorbent. In physisorption adsorbate is held to the adsorbent by weak van der Waals forces and in chemisorption by strong chemical bond.
Argyrol is a medicine used for

The probability distribution of number of aces when two cards are drawn without replacement from a pack of 52 cards is: