for \(|x|<1, \sin \left(\tan ^{-1} x\right)\) equal to:

The sale of ice creams is higher in summer than in winter is an example of:

If \(y=\frac{1}{\sqrt[3]{1-x^3}}\), then \(\frac{d y}{d x}\) is equal to :

A die is thrown 4 times and getting 3 is considered a success. The probability of 2 successes is :

Given that the lines: \(\frac{x-1}{2}=\frac{y+2}{3}=\frac{z}{5}\) and \(\frac{x+2}{1}=\frac{y-1}{2}=\frac{z-\alpha}{2}\) are coplanar. Then the value of \(\alpha\) is:

The value of \(\tan ^{-1} \frac{2}{11}+\tan ^{-1} \frac{7}{24}\) is :

If \(y=2 x(x-1)(2-x)\); then \(\frac{d^2 y}{d x^2}\) is:

Answer the question on basis of passage given below :
In zwitter ionic form, amino acids show amphoteric behaviour as they react both with acids and bases.
Except glycine, all other naturally occurring \(\alpha\) - amino acids are optically active, since the \(\alpha\) -carbon atom is asymmetric. These exist both in 'D' and 'L' forms. Most naturally occurring amino acids have L-configuration. L-Aminoacids are represented by writing the \(-NH_2\) group on left hand side.
Optically inactive amino acid from the following is :

Masses of three wires of copper are in the ratio of \(1: 3: 5\) and their lengths are in the ratio of 5:31. The ratio of their electrical resistance are:

Which of the following process is used in the extractive metallurgy of magnesium?

Identify the incorrect statement about the genetic modification.

If \(A=\left[\begin{array}{ccc}5 & 1 & 0 \\ 6 & 2 & -1\end{array}\right], B^T=\left[\begin{array}{cc}2 & 1 \\ -2 & 0 \\ 1 & 3\end{array}\right]\), then \(B A^T\) is :

Read the following passage carefully and answer the given questions.
Bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. 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. Baculoviruses are pathogens that attack insects and other arthropods. The majority of baculoviruses used as biological control agents are in the genus Nucleopolyhedrovirus. These viruses are excellent candidates for species-specific, narrow spectrum insecticidal applications. They have been shown to have no negative impacts on plants, mammals, birds, fish or even on non-target insects. BOD refers to the amount of the oxygen that would be consumed if all the organic matter in one liter of water were oxidised by bacteria. The sewage water is treated till the BOD is reduced. Cheese, is one of the oldest food items in which microbes were used. Different varieties of cheese are known by their characteristic texture, flavour and taste. For example, the large holes in 'Swiss cheese' are due to production of a large amount of CO₂ by a bacterium named Propionibacterium sharmanii.
Baculoviruses are-