A bag contains 8 blue and 12 green balls. Two balls are drawn in succession without replacement.
The probability that first is blue and second is green is

For \(x \in R -\{0\}\), the function \(f(x)=\frac{3}{x}+7\) is decreasing when

The function \(f(x)=x^3+1\) is:

The Greatest Integer Function \(f: R \rightarrow R\) given by \(f(x)=[x], x \in R\) and \([x]\) denotes the greatest integer less than or equal to \(x\) is :

\(\int_{\sqrt{\log _e 2}}^{\sqrt{\log _e 4}} x e^{x^2} d x\) is equal to

The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is :

The value of a for which \(\int_1^a x^2 d x=\frac{7}{3}\) is:

Area of the region bounded by the curve \(y^2=4 x, y\)-axis and the line \(y=3\) is equal to:

Intermolecular hydrogen bonding is observed between chloroform and acetone.
Therefore, their binary solution will_
(A) Show positive deviation from Raoult's law
(B) Show negative deviation from Raoult's law
(C) Obey Raoult's law
(D) Show decrease in vapor pressure
Choose the correct answer from the options given below:

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 -

Match List-I with List-II :

List - I	List - II
(A) Electric potential due to point charge	(I) \( \propto \frac{1}{r^2} \)
(B) Electric potential due to a dipole on axial line	(II) \( \propto \frac{1}{r^3} \)
(C) Electric field intensity due to a dipole on axial line	(III) \( \propto \frac{1}{r} \)
(D) Electric field intensity due to a quadrapole	(IV) \( \propto \frac{1}{r^4} \)

Choose the correct answer from the options given below :

The value of \(\frac{3}{2}(\hat{i} \cdot \hat{i})+\frac{1}{2}(\hat{j} \cdot \hat{j})+\frac{|\hat{i} \times \hat{i}|}{(\hat{k} \cdot \hat{k})}+\frac{(\hat{k} \cdot \hat{i})}{|\hat{i} \times \hat{j}|}\) is:

Identify the correct options with respect to the salient features of DNA.
(A) The two polynucleotide chains are coiled in a left-handed fashion
(B) Adenine forms three hydrogen bonds with thymine
(C) The distance between a base pair in a DNA helix is approximately 0.34 nm
(D) The plane of one base pair stacks over the other in double helix
Choose the correct answer from the options given below: