The area of the region bounded by \(x=y^2\) and the line \(x=4\) in square units is :

Let the matrix \(A=\left[a_{i j}\right]_{3 \times 3}\) be defined by
\(a_{i j}=\left\{\begin{array}{ll}2 i+3 j, & i<j \\5, & i=j \\3 i-2 j, & i>j\end{array}\right.\)
The number of elements in the matrix \(A\) which are greater than 7 , is:

If A is an invertible matrix of order 2 ; then \(\operatorname{det}\left(A^{-1}\right)\) is equal to:

The probability distribution of a discrete random variable x is given below:

\(x\)	\(2\)	\(3\)	\(4\)	\(5\)
\(p(x)\)	\(\frac{5}{k}\)	\(\frac{7}{k}\)	\(\frac{9}{k}\)	\(\frac{10}{k}\)

The value of \(k\) is

Match List I with List II

LIST I	LIST II
A. \(\lim _{x \rightarrow 0} \frac{1-\cos 2 x}{3 x^2}\)	I. 2
B. \(\lim _{x \rightarrow 4} \frac{x^2-16}{x-4}\)	II. 8
C. \(\lim _{x \rightarrow 0} \frac{\sin a x+4 x}{a x+\sin 4 x}\)	III. 1
D. \(\lim _{z \rightarrow 1} \frac{z^{1 / 3}-1}{z^{1 / 6}-1}\)	IV. \(\frac{2}{3}\)

If R and S are two equivalence relations on a set A, then

The function \(f(x)=|x-1|, x \in R\) is:

\(\Lambda_m^{\circ}\) for \(\mathrm{NaCl}, \mathrm{HCl}\), and \(\mathrm{CH}_3 \mathrm{COONa}\) are \(126.4,425.9\), and \(91.0 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}\), respectively. Calculate \(\Lambda_m^{\circ}\) for \(\mathrm{CH}_3 \mathrm{COOH}\).

Answer the question on basis of passage given below :
The noble gases He to Rn have close shell configuration and are monoatomic gases under normal conditions. Though mostly unreactive, but direct reaction of Xe with \(F_2\) leads to a series of compounds with Xe oxidation numbers \(+2,+4\) and +6 . When certain compounds like phenol and quinol are crystallised in the presence of noble gas such as \(Ar , Kr\) and Xe a category of compound called clathrates are formed. In these the noble gas atoms are trapped in the cavities of the crystal lattices. The compounds which crystallise are known as hosts (H) while the noble gas atoms are called guests ( \(G\) ). The general formula of a clathrate compound is \(n H m G\), where \(n\) is the number of host molecules and m is the number of atoms a molecule of guest.
In what molar ratio must Xe and \(F_2\) be taken to give \(XeF _4\) ?

Match List - I with List - II.

LIST I	LIST II
(A) Ribosome	(I) Replication
(B) Histone	(II) Transcription
(C) DNA polymerase	(III) Translation
(D) RNA polymerase	(IV) Nucleosome

Choose the correct answer from the options given below :

Match the type of hybridisation given in List-I with their geometry given in List-II

List-l (Type of hybridisation)	List-II (Geometry)
(A) \(s p^3\)	(I) Trigonal bipyramidal
(B) \(d s p^2\)	(II) Octahedral
(C) \(s p^3 d\)	(III) Square planar
(D) \(s p^3 d^2\)	(IV) Tetrahedral

Choose the correct answer from the options given below :

Match List-I (amino acid) with List-II (Characteristic Side Chain)

List-I  (amino acid)	List-II  (Characteristic Side Chain)
(A) Phenylalanine	(I) \(\left( CH _3\right)_2 CHCH _2-\)
(B) Leucine	(II) \(C _6 H _5 CH _2-\)
(C) Lysine	(III) \(CH _3- CH _2- CH \left( CH _3\right)-\)
(D) Isoleucine	(IV) \(H _2 N-\left( CH _2\right)_4-\)

Choose the correct answer from the options given below:

A coil \(C_1\) is connected to a galvanometer G. Second coil \(C_2\) is connected to a battery through a tapping key. The steady current in the coil \(C_2\) produces a steady magnetic field. As coil \(C_2\) is moved towards the coil \(C_1\), the galvanometer shows a deflection. To obtain a large deflection, one or more of the following steps can be taken:
(A) Use a rod made of soft iron inside the coil \(C_2\)
(B) Connect the coil \(C_2\) to a more powerful battery
(C) Move the arrangement of coil \(C_2\) rapidly towards the coil \(C_1\)
(D) hold the key pressed continuously
Choose the correct answer from the options given below: