If A and B are invertible matrices of order 3 then match List-I with List-II

List-I	List-II
(A) adj(A)	(I) \(B^{-1} A^{-1}\)
(B) \((A B)^{-1}\)	(II) \(|A|^{-1}\)
(C) \(\left|A^{-1}\right|\)	(III) \(|A|^2\)
(D) \(|\operatorname{adj} A|\)	(IV) \(|A| A^{-1}\)

Choose the correct answer from the options given below:

If \(A=\left[\begin{array}{cc}1 & 0 \\ -1 & 7\end{array}\right]\) and \(A^2-8 A+K I=O\), then the value of \(K\) is:

"The random variable \(X\) has a probability distribution \(P ( X )\) of the following form, where \(k\) is some number.
\(P(X=x)=\left\{\begin{array}{ll}k, & \text { if } x=0 \\2 k, & \text { if } x=1 \\3 k, & \text { if } x=2 \\0, & \text { otherwise }\end{array}\right.\)
Then \(P(x \leq 2)\) is :"

\(\int_0^1 x e^x d x\) is equal to

Let E and F are events associated with an experiment. If \(P(E)=0.4, P(F)=0.8\) and \(P(F \mid E)=0.6\) then \(P(E \mid F)\) is:

The function \(f(x)=|x-1|, x \in R\) is:

If the random variable \(X\) follows the Poisson distribution such that \(P(X=k)=P(X=k+1)\), then the mean value of \(X\) is :

Which of the following is an example of a sex linked disorder?

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?

If lines \(\frac{x+5}{5 \lambda+2}=\frac{4-2 y}{10}=\frac{1-3 z}{-3}\) and \(\frac{x-2}{1}=\frac{1+2 y}{4 \lambda}=\frac{2+z}{3}\) are perpendicular, then value of ' \(\lambda\) ' is

If the matrix \(A=\left[\begin{array}{ccc}\alpha & \beta & \gamma \\ 0 & 0 & 2 \\ 3 & -2 & 0\end{array}\right]\) is a skew symmetric matrix, then the value of \((\alpha+\beta+\gamma)^2\) is :

Let \(A=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]\), then \(\left(A^{-1}\right)^T\) equals

Read the passage carefully and answer the questions based on the passage:
Alcohols are versatile compounds as they can act as both nucleophile and electrophile. They undergo reactions based on cleavage of O-H and C-O bonds. The cleavage of O-H bond reflects the acidic character of alcohols. However they are weaker acids than water, phenol and carboxylic acids. Alkoxide ion formed by loss of proton from the OH group of alcohols reacts with water to form the corresponding conjugate acid - base pair. They act as Bronsted base due to presence of unshared electron pairs on oxygen.Both alcohols and phenol react with carboxylic acids, acid chlorides and anhydrides to form esters. The introduction of acetyl group in alcohols or phenol is known as acetylation. Alcohols react with hydrogen halides to form alkyl halides which form the basis of Lucas test. They also undergo acid catalyzed dehydration to form alkenes. Alcohols can be easily oxidized with variety of oxidizing agents. The nature of the product depends on the type of oxidizing agent and the nature of alcohol.
Which of the following gives the correct sequential steps for dehydration of alcohol?