If \(A=\left[\begin{array}{cc}-2 & 3 \\ k & 4\end{array}\right]\) is a singular matrix then value of \(k\) is :

Bag A contains 2 unbiased and 3 biased coins whereas Bag B contains 3 unbiased and 2 biased coins. A bag is selected at random and 2 coins are taken out simultaneously. The probailty, that both coins are unbiased is :

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

The degree of the differential equation \(\left(\frac{d y}{d x}\right)^3+\left(\frac{d^2 y}{d x^2}\right)^2=0\) is:

The plane \(x(1+2 \lambda)+y(2+\lambda)+z(3-\lambda)=0\) passes through the intersection of :

Let \(A=\left[a_{i j}\right]_{2 \times 4}\) and \(B=\left[b_{i j}\right]_{4 \times 2}\), then \(|3 A B|\) is equal to

If the present value for a sequence of payments made at the end of each 6 months and continuing forever is ₹6000. If the money is worth 4% compounded semi-annually, then, the value of sequence of payment made is:

Match List-I with List-II

List-I	List-II
(A) \(S _{ N } 2\)	(I) Racemization
(B) Iodoform	(II) Ozone depletion
(C) \(S _{ N } 1\)	(III) Antiseptic
(D) Carbon tetrachloride	(IV) Inversion

Choose the correct answer from the options given below:

Read the following paragraph and answer the given questions.
Cancer detection is based on biopsy and histopathological studies. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Do you know why mother's milk is considered very essential for the new-born infant? The yellowish fluid colostrum secreted by mother during the initial days of lactation has abundant antibodies (IgA) to protect the infant. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal. The exaggerated response of the immune system to certain antigens present in the environment is called allergy. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused. Morphine is a very effective sedative and painkiller, and is very useful in patients who have undergone surgery.
Malignant malaria is caused by -

The maximum value of \(Z=3 x+4 y\) subject to constraint \(x+y \leq 6, x, y \geq 0\) is:

What is the decreasing order of field strength of given ligands?
(A) S^2-
(B) Ethylenediamine
(C) NCS^-
(D) CN^-
Choose the correct answer from the options given below :

Match List - I with List - II.

List - I	List - II
(A) Plasmid of Salmonella	(I) Join foreign DNA to plasmid
(B) Restriction enzymes	(II) Insertional inactivation
(C) Ligases	(III) Construction of \(1^{s t}\) recombinant DNA
(D) \(\beta\)-galactosidase	(IV) Molecular scissors

Choose the correct answer from the options given below:

A network of five capacitors is shown in the figure. The total charge stored in the network connected between A and B is :