The region represented by the system of inequalities \(x, y \geq 0, y \leq 6, x+y \leq 3\)

On a multiple choice examination with 4 possible answers (out of which one is correct)
for each of the five questions, the probability that a candidatewould get 4 or more correct answers just by guessing is:

The vector equation of the line passing through the point \((-1,5,4)\) and perpendicular to the plane \(z=0\) is :

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:

The relation \(R\) on set \(A=\{1,2,3,4,5\}\), given by \(R=\{(a, b):|a-b|\) is even \(\}\) is :

The mean of numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is:

\(\int_2^5|x-3| d x\) equals

The first clinical gene therapy was given to treat :

Read the following passage carefully and answer the given questions. During anaerobic sludge digestion, bacteria produce a mixture of gases such as methane, hydrogen sulphide and carbon dioxide. These gases form biogas and can be used as source of energy as it is inflammable. The bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. You must have noticed that bottled fruit juices bought from the market are clearer as compared to those made at home. This is because the bottled juices are clarified by the use of pectinases and proteases. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. The BOD test measures the rate of uptake of oxygen by microorganisms in a sample of water and thus, indirectly, BOD is a measure of the organic matter present in the water.
The bottled juices are clarified by the combination of -

If \(\vec{a}, \vec{b}\) and \(\sqrt{3} \vec{a}+\vec{b}\) are unit vectors, then the angle between \(\vec{a}\) and \(\vec{b}\) is:

The following data is available for two independent samples:

	SAMPLE-1	SAMPLE-2
sample size	8	10
sample mean	191	199
sample standard deviation	10	12

Karyotype of an individual is 47, XXY. The individual is suffering from :

Let \(A=\left[a_{i j}\right]\) be a square matrix of order 3 with each entry either 0 or 1 .
Then the number of all such possible matrices is :