Relation \(R\) on Real Numbers is defined as \(R =\{( a , b ): a \leq b \}\). The relation is :

\(\int_{-5}^{5} (3x^5 + \sqrt{5} x^3) e^x dx\) is equal to:

The vector equation of the line joining the points \((-2,-3,-4)\) and \((1,-2,4)\) is :

The vector equation of a line passing through the point with position vector \(2 \hat{i}-\hat{j}+\hat{k}\) and parallel to the line joining the points with position vectors \(-\hat{i}+4 \hat{j}+\hat{k}\) and \(\hat{i}+2 \hat{j}+2 \hat{k}\) is:

The function \(f(x) = |x - 1|\) is

\(I=\int a^{5 x+3} d x\) is :

The area bounded by the curve \(|x|+y=1\) and the axis of \(x\) is :

If a person \(A\) speaks the truth in \(80 \%\) cases and the person \(B\) speaks the truth in \(75 \%\) cases, then the probability that they contradict each other in a statement is:

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 micro-organisms in a sample of water and thus, indirectly, BOD is a measure of the organic matter present in the water.
Statins, used as blood-cholesterol lowering agents are produced by -

The values of van't Hoff factors for \(\text{CaCl}_2\), \(\text{Na}_2\text{SO}_4\) and \(\text{KCl}\) respectively are:

A integrating factor of the differential equation \(\frac{d y}{d x}+\frac{y}{x}=\frac{1}{x^2}(x>0)\) is equal to

Where is donor energy level located?

Nucleosome is associated with__________ molecules of histones.