If \(\left[\begin{array}{cc}a b & c d \\ a+c & b+d\end{array}\right]=\left[\begin{array}{cc}2 & -3 \\ 4 & 1\end{array}\right]\) where \(a, b, c, d\) are integers, then which of the following are true?
(A) \(a+d=0\)
(B) \(b+d=3\)
(C) \(b+d=1\)
(D) \(c+d=2\)
Choose the correct answer from the options given below :

If \(A=\left[\begin{array}{ccc}-1 & 2 & 3 x \\ 2 y & 4 & -1 \\ 6 & -1 & 0\end{array}\right]\) is a symmetric matrix, then the value of 22 - y is:

Let \(A\) and \(B\) be two events in a random experiment with sample space such that \(P(B) \neq 0\) and \(P(A \mid B)=1\).
Which of the following is true?

A cistern can be filled by an inlet pipe in 20 hours and can be emptied by an outlet pipe in \(2 5\) hours. Both the pipes are opened. After \(1 0\) hours, the outlet pipe is closed, the total time to fill the tank is :

A doctor is to visit a patient.
The probabilities that he comes by train, bus, scooter or other means are
\(\frac{3}{10}, \frac{1}{5}, \frac{1}{10}\) and \(\frac{2}{5}\) respectively.
The probabilities that he will be late are
\(\frac{1}{4}\) if he comes by train,
\(\frac{1}{3}\) if he comes by bus,
\(\frac{1}{12}\) if he comes by scooter.
If he comes by other means of transport, he will not be late.
When he arrives, he arrives late.
The probability that he comes by bus is:

The projection of \(\hat{i}-\hat{j}\) on the vector \(\hat{i}+\hat{j}\) is :

The corner points of the feasible region determined by the following system of linear inequalities \(2 x+y \leq 10, x+3 y \leq 15, x, y \geq 0\) are \((0,0),(5,0),(3,4)\) and \((0,5)\). Let \(z=p x+q y\) where \(p\) and \(q>0\). The condition on \(p\) and \(q\) so that the maximum of \(z\) occurs at both \((3,4)\) and \((0,5)\) is :

Correct IUPAC name of
CH3-CH2-CH=CH-CO-H
is:

A thermal power plant produces electric power of 1000 kW at 10000 V, which is to be transmitted 20 km away from the power plant. The transmission line has resistance of 0.5 ohm per kilometre, the percentage power dissipation during transmission is :

Observe the illustration and answer the following question:

Arrange the following in order of their occurance in human female ovary.
A. Formation of secondary follicle
B. Mitotic division of oogonia
C. Formation of mature Graafian follicle
D. Maintenance of corpus luteum
Choose the correct answer from the options given below:

Transgenic animals that produce useful biological products can be created by the introduction of the portion of DNA (or genes) which codes for a particular product such as human protein (α-1-antitrypsin). This protein is used to treat:

If \(\left[\begin{array}{cc}4 x & 5 x-7 \\ 4 x & 2 x+y\end{array}\right]=\left[\begin{array}{cc}x+6 & y \\ 7 y-13 & 7\end{array}\right]\) then the value of \(2 x+y\) is:

DNA recombinant technology involves the use of restriction endonucleases. After having cloned the gene of interest and having optimised the conditions to induce the expression of the target protein, one has to consider producing it on a large scale. The cells harbouring cloned genes of interest may be grown on a small scale in the laboratory. In order to link the alien DNA, the vector needs to have very few, preferably single, recognition sites for the commonly used restriction enzymes. Presence of more than one recognition sites within the vector will generate several fragments, which will complicate the gene cloning. In Biolistics or gene gun method cells are bombarded with high velocity micro particles of gold or tungsten coated with DNA. The ligation of alien DNA is carried out at a restriction site present in one of the two antibiotic resistance genes. For example, you can ligate a foreign DNA at the BamH I site of tetracycline resistance gene in the vector pBR322. Since the DNA is enclosed within the membranes, we have to break the cell open to release DNA along with other macromolecules such as RNA, proteins, polysaccharides and also lipids. The RNA can be removed by treatment with ribonuclease whereas proteins can be removed by treatment with protease. Other molecules can be removed by appropriate treatments and purified DNA ultimately precipitates out after the addition of chilled ethanol.
Which one of the following enzymes should be used to break the bacterial cells for isolation of DNA?