The area enclosed between \(y^2=4 x\) and \(x^2=4 y\) is:

Consider the LPP : Maximize \(z=5 x+3 y\) subject to \(3 x+5 y \leq 15,5 x+2 y \leq 10, x, y \geq 0\).
The optimal feasible solution occurs at

If \(A=\left[\begin{array}{ll}5 & 2 \\ 4 & 3\end{array}\right]\) is a given matrix, then which statements are correct?
(A) \(|A|=7\)
(B) minor of \(3=-5\)
(C) co-factor of \(2=-4\)
(D) \(\operatorname{adj}(A)=\left[\begin{array}{cc}3 & -2 \\ -4 & 5\end{array}\right]\)

If A and B are skew-symmetric matrices, then which of the following is not true?

If \(A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]\), then the value of \(A^{20}\) is :

Two slits 0.1 mm apart with screen 2 m away produce fringe separation with 500 nm light. The separation is :

The slope of the normal to the curve \(y=x^3+3 x-2\) at its point of intersection with y-axis is:

RNA interference takes place in all eukaryotic organisms as a method of :

Last year, in a rat population of 600 rats, 600 new rats were added through reproduction in the current year to make a total population of 1200 rats.
Find the birth rate of this rat population.

The rate of a chemical reaction doubled for every \(10^{\circ} C\) rise in temperature. If the temperature is raised by \(50^{\circ} C\), the rate of reactions will be

Match the property given in List-l with the element given in List-Il

List-I (Property)	List-ll (Element)
(A) Lanthanoid, which can show +2 oxidation state	(I) Pm
(B) Radioactive lanthanoid	(II) Lu
(C) Lanthanoid which has \(4 f^{\wedge} 7\) electronic configuration in +3 oxidation state	(III) Eu
(D) Lanthanoid which has \(4 f^{\wedge}\{14\}\) electronic configuration in +3 oxidation state	(IV) Gd

Choose the correct answer from the options given below:

Which one of the following will exhibit maximum paramagnetic character?

Read the passage carefully and answer the questions
Alcohols and phenols are formed when a hydrogen atom in a hydrocarbon, aliphatic and aromatic respectively is replaced by -OH group. These are further classified on the basis of number of hydroxy groups and according to the hybridization of the carbon atom \(sp ^2\) or \(sp ^3\) to which the -OH group is attached. They find applications in industry as well as in day-to-day life. One of the most commercially obtained alcohol also known as wood spirit is obtained by destructive distillation of wood. Both alcohols and phenols are acidic in nature. The acidity of alcohols and phenols vary according to the nature of substituent(s) attached to them. Alcohols and phenols react with carboxylic acids, acid chlorides and acid anhydrides to form esters. Introduction of acetyl group in alcohols and phenols is called acetylation. Phenol undergo electrophilic aromatic substitution reaction because the -OH activates the benzene ring. It undergoes nitration, halogenation and sulphonation reactions.
When phenol is treated with concentrated sulphuric acid, then it gets converted into phenol-2,4-disulphonic acid \(( X )\). On further treatment of X with conc. nitric acid, product Y is formed. Identify Y .