The given graph represent the variations of compressibility factor \((Z)=\frac{P V}{n R T}\) versus \(P\), for three real gases \(A, B\) and \(C\). Identify the only incorrect statement

In the nuclear transmutation ${}_4^9\text{Be}+\text{X}⟶{}_4^8\text{Be}+\text{Y}$, identify $\left(\mathrm{X}, \mathrm{Y}\right)$.

Among the following, the number of aromatic compound (s) is/are

According to Molecular Orbital Theory,

An aqueous solution of X is added slowly to an aqueous solution of Y as shown in List I. The variation in conductivity of these reactions is given in List II. Match List I with List II and select the correct using answer the code given below the lists :

List - I	List - II
a. \(\underset{\quad\quad~~ X }{( C _2 H _5)_3 N}+\underset{ Y }{CH _3 COOH}\)	p. Conductivity decreases and then increases
b. \(\underset{\quad\quad~~ X }{KI (0.1 M )}+\underset{ Y }{AgNO _3(0.01 M )}\)	q. Conductivity decreases and then does not change much
c. \(\underset{\text X }{CH _3 COOH}+\underset{\text Y }{KOH}\)	r. Conductivity increases and then does not change much
d. \(\underset{\text X }{NaOH}+\underset{\text Y }{HI}\)	s. Conductivity does not change much and then increases

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Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogeneous solution. These are called colligative properties. Applications of colligative properties are very useful in day-to-day life. One of its examples is the use of ethylene glycol and water mixture as anti-freezing liquid in the radiator automobiles.
A solution \(M\) is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixtrue is \(0.9\)
Given Freezing point depression constant of water \(\left(k^{\text {water }}\right)=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\)
Freezing point depression constant of ethanol \(\left(k_f^{\text {ethanol }}\right)=2.0 \mathrm{Kkg} \mathrm{mol}^{-1}\)
Boiling point elevation constant of water \(\left(k_b^{\text {water }}\right)=0.52 \mathrm{Kkg} \mathrm{mol}^{-1}\)
Boiling point elevation constant of ethanol \(\left(k_b^{\text {ethanol }}\right)=1.2 \mathrm{Kkg} \mathrm{mol}^{-1}\)
Standard freezing point of water \(=273 \mathrm{~K}\)
Standard freezing point of ethanol \(=155.7 \mathrm{~K}\)
Standard boiling point of water \(=373 \mathrm{~K}\)
Standard boiling point of ethanol \(=351.5 \mathrm{~K}\)
Vapour pressure of pure water \(=328 \mathrm{~mm}\) of \(\mathrm{Hg}\)
Vapour pressure of pure ethanol \(=40 \mathrm{~mm}\) of \(\mathrm{Hg}\)
Molecular weight of water \(=18 \mathrm{~g} \mathrm{~mol}^{-1}\)
Molecular weight of ethanol \(=46 \mathrm{~g} \mathrm{~mol}^{-1}\)
In answering the following questions, consider the solutions to be ideal dilute solutions and solutes to be non-volatile and non-dissociative.

Question:
The freezing point of the solution \(M\) is

In the following reaction sequence, the amount of $\text{D}$ (in g) formed from $10$ moles of acetophenone is ____.
(Atomic weights in $\text{g}\text{m}\text{o}{\text{l}}^{-1}:\text{H}=1,\text{C}=12,\text{N}=14,\text{O}=16,\text{B}\text{r}=80.$ The yield (%) corresponding to the product in each step is given in the parenthesis)

Among the following options, select the option in which each complex in Set-I shows geometrical isomerism and the two complexes in Set-II are ionization isomers of each other.
\(\text { [en } \left.=\mathrm{H}_2 \mathrm{NCH}_2 \mathrm{CH}_2 \mathrm{NH}_2\right]\)

Consider the matrix, \(P=\left(\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3\end{array}\right)\)
Let the transpose of a matrix \(X\) be denoted by \(\mathrm{X}^T\). Then the number of \(3 \times 3\) invertible matrices Q with integer entries, such that \(Q^{-1}=Q^T\) and \(P Q=Q P\) is

Let $n \ge 2$ be an integer. Take n distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of n is ________

A charge is kept at the central point \(\mathrm{P}\) of a cylindrical region. The two edges subtend a half-angle \(\theta\) at \(\mathrm{P}\), as shown in the figure. When \(\theta=30^{\circ}\), then the electric flux through the curved surface of the cylinder is \(\Phi\). If \(\theta=60^{\circ}\), then the electric flux through the curved surface becomes \(\Phi / \sqrt{n}\), where the value of \(n\) is _______ .

Let $S$ be the set of all complex numbers $z$ satisfying $\left|z^2+z+1\right|=1$. Then which of the following statements is/are TRUE?

The reagent(s) that can selectively precipitate ${\mathrm{S}}^{2-}$ from a mixture of ${\mathrm{S}}^{2-}$ and $\mathrm{S}{\mathrm{O}}_4^{2-}$ in aqueous solution is (are)