Match List-I with List-II

List-I	List-II
(A) If A is a non singular matrix of order n, then \(| A (\operatorname{adjA})|\) is equal to	(I) \(|A|^{n-1}\)
(B) If A is a non singular matrix of order n, then |adj(adj A)| is equal to	(II) \(|A|^{n-2} A\)
(C) If A is a non singular matrix of order n, then \(\operatorname{adj}(\operatorname{adj} A )\) is equal to	(III) \(|A|^n\)
(D) if A is a non singular matrix of order n, then \(|(\operatorname{adj} A)|\) is equal to	(IV) \(|A|^{(n-1)^2}\)

Choose the correct answer from the options given below :

A person can row a boat in still water at the rate of \(5 km / hr\). It takes him \(4\) times as long to row upstream of a river as to row downstream to cover same distance in the same river. The speed of flow of the stream is:

The value of \(k\) for which the following system of equations does not possess a unique solution is:
\(\begin{array}{l}k x+3 y-z=1 \\ x+2 y+z=2 \\ -k x+y+2 z=-1\end{array}\)

If \(\vec{a}, \vec{b}, \vec{c}\) are three mutually perpendicular unit vectors, then \(|\vec{a}+\vec{b}+\vec{c}|\) is equal to:

The value of \(c\) for which \(f(x)=x(x-3)^2, 0 \leq x \leq 3\), satisfies Rolle's theorem is:

The value of \(\left|\begin{array}{ccc}1 & x & y \\ 1 & x+y & y \\ 1 & x & x+y\end{array}\right|\) is

The co-ordinates of the point at which the line \(\frac{x-3}{3}=\frac{y+1}{2}=\frac{z-4}{-2}\) crosses \(x y\) plane, are

A slab of material of dielectric constant \( k \), having the same area as the plate of a parallel plate capacitor but has a thickness \( \frac{3}{5} \) of the distance between the plates \( d \), is inserted between the plates of the capacitor. When there is air between the plates, the potential difference is \( V_0 \). What is the potential difference between the plates of the capacitor after inserting the dielectric?

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.

Which of these is not present in mature insulin?

Which of the following reactions are involved in preparation of aldehydes?
(A) Gatterman-Koch reaction
(B) Etard Reaction
(C) Stephen Reaction
(D) Rosenmund Reaction
Choose the correct answer from the options given below:

Two points A and B in a plane are related if OA = OB, where O is a fixed point. This relation is:

Wavelength of matter wave is independent of :

Sulphur molecule at room temperature is