Three college graduates Asha, Babita and Cyrus enter into partnership to run an online tea business. After a bumper turnover they divide profits as 80,000, 60,000 and 1 lakh respectively. Which of the following was correct ratio of their investments?

If A and B are two events such that \(P(B) = \frac{3}{5}\), \(P(A|B) = \frac{1}{2}\) and \(P(A \cup B) = \frac{4}{5}\), then P(A) is equal to:

If \(A=\left[\begin{array}{lll}-1 & 2 & 3\end{array}\right], B=\left[\begin{array}{l}3 \\ 2 \\ 2\end{array}\right], C=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]\) and \(D=\left[\begin{array}{l}2 \\ 3 \\ 4\end{array}\right]\) then AB + CD is equal to :

A random variable X has the following probability distribution where k is some number :

X	0	1	2
P(X)	k	2k	3k

Find the value of k.

A random variable X has the following probability distribution

X	2	3	4	5
P(X)	5/k	7/k	9/k	11/k

Then the value of \(\frac{k}{4}\) is

If A is a square matrix of order 3 and \(|A| = -2\) then, \(|-2A^{-1}|\) is:

If \(A=\left[\begin{array}{ccc}a & 4 & -5 \\ d & b & -6 \\ 5 & e & c\end{array}\right]\) is a skew symmetric matrix, then value of \(a+b+c+d+e\) is equal to

The graph given below represents which of the following function?

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:

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Read the following paragraph carefully and answer the given questions.
In the year 1963 the two enzymes responsible for restricting the growth of bacteriophage in E. coli were isolated. The first restriction endonuclease - Hind II, whose functioning depended on a specific DNA nucleotide sequence was characterized five years later. It was found that Hind II always cut DNA molecules at a particular point by recognizing a specific sequence of six base pairs. This specific base sequence is known as the recognition sequence for Hind II. Besides Hind II, today we know more than 900 restriction enzymes that have been isolated from over 230 strains of bacteria, each of which recognize different recognition sequences.
Restriction enzymes are also known as

Which of the following is/are not considered as transition elements?
Ag, Mo, Zn, Hg, W

Cloning of alien DNA by the host involves -