Consider the function \(f: R \rightarrow R\) defined by \(f(x)=\frac{x}{x^2+1}\) then

If the probability that an individual suffers a bad reaction from an injection of a given serum is 0.001, the probability that out of 2000 individuals, more than two individuals suffer from bad reaction.
[Given that \(e^{-2}=0.13534\) ]

Consider the LPP, Max Z = x + y subject to the conditions
\(x+y \leq 3, \quad x-y \geq 1, \quad x \geq 0, y \geq 0\),
then which of the following is not the corner point of the feasible region of above LPP.

If \(e^x+e^y=e^{x+y}\), then \(\frac{d y}{d x}\) equals

What sum of money is needed to invest now so as to get Rs. 5000 at the beginning of every month forever, if the money is worth 6% per annum compounded monthly?

According to the graph drawn here, identify the constraints of the associated linear programming problem :

Let A be a non-singular square matrix of order n, then
Match List - I with List - II

List - I	List - II
(A) A (adj A)	(I) \(\frac{1}{|A|}\)
(B) |adj A|	(II) \(|A|^n\)
(C) \(\left|A^{-1}\right|\)	(III) \(|A| I\)
(D) \(|A(\operatorname{adj} A)|\)	(IV) \(|A|^{n-1}\)

Choose the correct answer from the options given below:

Read the passage carefully and answer the questions
Carbohydrates are naturally formed organic compounds from various plants. The common chemical formula, \(C _x\left( H _2 O \right)_y\), was considered as hydrates of carbon to derive the various carbohydrates. For instance, the general formula for glucose ( \(C _6 H _{12} O _6\) ) easily fits into the above formula. Carbohydrates also called saccharides are classified on the basis of their behavior towards hydrolysis. Monosaccharides cannot be hydrolyzed further to simpler units of polyhydroxy aldehyde or ketones. About 20 monosaccharides are known to occur in nature. Carbohydrates that yield large number of monosaccharide units are called polysaccharides. Amino acids contain ( \(- NH _2\) ) and ( - COOH ), which can be classified in various forms. Proteins are polymers of alpha amino acids which are connected to each other by a peptide bond or peptide linkage. When a native protein is subjected to physical change, its globules unfold and helix get uncoiled and the protein loses its biological activity. The protein is said to be denaturated.
The two monosaccharides units are joined together through which linkage ?

Which of the following statement(s) is correct ?
(A). Keratin is an example of fibrous protein.
(B). Fibrous proteins are water-soluble, while globular proteins are water-insoluble.
(C). Polypeptide chains in fibrous proteins run parallel and are held together by hydrogen and disulphide bonds.
(D). Insulin and albumins are common examples of globular proteins.
Choose the correct answer from the options given below:

A uniform electric field of 20 V m -1 exists in the vertically downward direction. What will be the increase in the electric potential as one goes up through a height of 60 cm?

Let \(A, B, C\) be matrices of order \(p \times k, 3 \times k\) and \(n \times 3\) respectively, then the conditions on \(n, k\) and \(p\) so that \(A B+C B\) will be defined are :

The area of the region enclosed between the two circles \(x^2+y^2=1\) and \((x-1)^2+y^2=1\) is

Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on 10 cm length of wire B: