The area (in sq. units) of the region bounded by \(y=-1, y=2, x=y^3\) and \(x=0\) is equal to

If \(A\) and \(B\) are independent events and \(P(A)=\frac{1}{2}, P(B)=\frac{1}{3}\) then
Match List-I with List-II

List-I	List-II
(A) \(P(A \cap B)\)	(I) \(\frac{1}{2}\)
(B) \(P(\bar{A}) P(B)+P(A) P(\bar{B})\)	(II) \(\frac{1}{3}\)
(C) \(P(A \mid B)+P(B \mid A)\)	(III) \(\frac{1}{6}\)
(D) \(P(\overline{A \cap B})\)	(IV) \(\frac{5}{6}\)

Choose the correct answer from the options given below :

The principle value of \(\cos ^{-1}\left(-\frac{1}{2}\right)\) is :

An asset costing C is expected to have a useful life of 5 years. If the scrap value of the asset is 3,000 and the annual depreciation charge is 2,400, then the value of C is :

If the matrix \(\left[\begin{array}{ccc}3 & 2 a & -5 \\ -4 & 0 & b \\ -5 & 3 & 7\end{array}\right]\) is symmetric, then the value of \((a+b)\) is :

If \(A=\left[\begin{array}{cc}3 & 7 \\ 4 & -2\end{array}\right], X=\left[\begin{array}{c}\alpha \\ -2\end{array}\right], B=\left[\begin{array}{c}7 \\ 32\end{array}\right]\) and \(A X=B\), then the value of \(\alpha\) is:

The area of the region bounded by \(y^2=9 x, x=2, x=4\) and the \(x\)-axis in the first quadrant, is

Three magnetic materials : (A) Paramagnetic, (B) Diamagnetic, (C) Ferromagnetic. The correct order of increasing magnetic susceptibility is :

Read the passage carefully and answer the Questions
Carbonyl compounds such as aldehydes, ketones, and carboxylic acids play an important role in the biochemical process of plants and animal kingdom.
Many aldehydes and ketones find applications in dye, perfumery and other industries.
The carbonyl carbon atom is \(s p^2\)-hybridized forming three sigma and one pi-bond with oxygen.
C-O bonds are polar bond due to high electronegativity of oxygen than carbon.
Hence the carbonyl carbon behaves as an electrophilic center and oxygen as a nucleophilic centre.
Primary and secondary alcohols yield aldehydes and ketones respectively upon oxidation with variety of oxidizing agents.
The boiling points of aldehydes and ketones differ from hydrocarbons and ethers.
Aldehydes and ketones undergo nucleophilic addition reaction due to presence of electrophilic carbonyl carbon.
Nucleophile and a proton add across the carbon oxygen double bond.
The alcohol which cannot be used to prepare carbonyl compound through oxidation is

Answer the question on the basis of passage given below:
Proteins are the polymers of about twenty different a-amino acids which are linked by peptide bonds. Proteins perform various structural and dynamic functions in the organisms. Proteins which contain only a-amino acids are called simple proteins. The secondary or tertiary structure of proteins get disturbed on change of pH or temperature and they are not able to perform their functions. This is called denaturation of proteins. Enzymes are biocatalysts which speed up the reactions in biosystems. Vitamins are accessory food factors required in the diet. They are classified as fat soluble (A, D, E and K) and water soluble (B group and C). Deficiency of vitamins leads to many diseases. Nucleic acids are the polymers of nucleotides which in turn consist of a base, a pentose sugar and phosphate moiety.Nucleic acids are responsible for the transfer of characters from parents to offsprings. There are two types of nucleic acids DNA and RNA. DNA contains a five carbon sugar molecule called 2-deoxyribose whereas RNA contains ribose.
During denaturation of proteins:

Net Primary Productivity (NPP) is given by the formula

Corner points of the feasible region for a linear programming problem are \((0,2),(3,0),(6,0),(6,8)\) and \((0,5)\). Let \(F=4 x+6 y\) be the objective function. Then the minimum value of \(F\) occurs at :

Match List - I with List - II.

List - I (Name of microorganism)	List - II (Chemical)
(A) Aspergillus niger	(I) Citric acid
(B) Acetobacter aceti	(II) Acetic acid
(C) Clostridium butylicum	(III) Butyric acid
(D) Lactobacillus	(IV) Lactic acid