The following statements are made on the basis of given graph.
(A) OB represents the cost function.
(B) MA represents the cost function.
(C) Loss occurs at x = 5.
(D) Loss occurs at x = 15.
(E) Profit occurs at x = 10.

\(\int_0^2 x(2-x)^n d x\) is equal to

If \(A^2-A+I=0\), then \(A^{-1}\) is equal to :

Let \(\vec{a}=3 \hat{i}+\hat{j}-4 \hat{k}\) and \(\vec{b}=6 \hat{i}+5 \hat{j}-2 \hat{k}\) be two vectors.
Then a vector perpendicular to both \(\vec{a}\) and \(\vec{b}\) with magnitude 3 units is :

If \(y=\sin ^{-1} x+\sin ^{-1} \sqrt{1-x^2}, x \in(-1,0)\), then \(\frac{d y}{d x}\) is equal to

The average salary per head of the entire staff of a small factory including managers and technicians is Rs. 5750.
The average salary per head of a manager is Rs. 20000
and that of a technician is Rs. 5000.
If there are 4 managers, then the number of technicians in the factory is :

The maximum value of \(\frac{\log x^3}{3 x}\) occurs at \(x=\)

IUPAC name of quinol is:

Which of the following statements is true about galvanometer?

In humans, the fertilization takes place at -

Which aldehyde is used to preserve biological specimens?

The values of \(\lambda\) for which the system of equation \(x+2 y+z=14,-x+y+z=10, x+\lambda y+z=2\) has unique solution is :

Answer the question on the basis of passage given below :
Aldehydes and ketones represent two essential classes of organic compounds
which are extensively used in the synthesis of a wide variety of other organic molecules.
Due to the inherent polarity of the central carbonyl group, these substances readily undergo nucleophilic addition reactions.
Broadly speaking, these addition reactions can be categorized into two types:
one in which simple addition of the nucleophilic reagent occurs across the \(> C = O\) bond, and the second type where the initial addition is subsequently followed by the elimination of a water molecule.
A variety of ammonia derivatives, including hydroxylamine, hydrazine, phenylhydrazine,
2, 4-dinitroplhenylhdrasine, and semicarbaside, all belong to this second category of reactions.
These specific derivatives are fundamentally used for the identification and definitive characterization of aldehydes and ketones. Significantly, both types of nucleophilic addition reactions are strongly influenced by both steric and electronic factors.
As a general rule, aliphatic aldehydes exhibit higher reactivity compared to aromatic aldehydes.
The aliphatic aldehydes demonstrate the ability to reduce both Fehling's solution and Tollen's reagent, whereas aromatic aldehydes are limited to reducing only Tollen's reagent.
In a similar manner to aldehydes, aromatic ketones are observed to be less reactive than aliphatic ketones towards all nucleophilic addition reactions.
In a separate context, phenols and carborylic acids both exhibit acidic properties in nature.
Both classes of compounds readily dissolve in NaOH solution and cause blue litmus to turn red.
However, carboxylic acids stand out as much stronger acids than phenols and thus can decompose sodium bicarbonate \(\left( NaHCO _3\right)\) with the distinct evolution of \(CO _2\) gas, a reaction which phenols do not undergo.
It is important to note that both electron- donating and electron- withdrawing substituents significantly influence the acid strength of both aliphatic as well as aromatic carborylic acids.
Furthermore, unlike all other common aliphatic acids, formic acid uniquely possesses reducing properties and simultaneously does not display the typical reactions characteristic of the alkyl group.
Which of the following compound most readily undergoes nucleophilic addition reaction?