Choose the correct statements from the following :
(A) two different solutions of sucrose of same molality prepared in different solventswill have the same depression in freezing point.
(B) the osmotic pressure of a solution is given by the equation \(II = CRT\) (where C is the molarity of the solution)
(C) decreasing order of osmotic pressure for 0.01 M aqueous solution of \(BaCl _2, KCl , CH _3 COOH\), and sucrose is \(BaCl _2 > KCl > CH _3 COOH >\) sucrose
(D) according to Raoult's law the vapor pressure exerted by a volatile component of asolution is directly proportional to its mole fraction in the solution
Choose the correct answer from the options given below :

The degree of dissociation ( \(\alpha\) ) of a weak electrolyte \(A_x B_y\) is related to the van't Hoff factor (i) by the expression:

According to the Raoult's law, vapour pressure of a solution is directly proportional to:

p-block elements are placed in groups 13 to 18 of the periodic table. Group 15 is nitrogen family. Nitrogen makes various compounds like \(NH _3, HNO _3, N_2 O , NO _2\) etc. Phosphorus exists in the form of white and red phosphorus. White phosphorus glows in dark. \(PH _3\) gas is used as smoke screen. Group 16 is called oxygen family. Dry air contains \(21\% O_2\) gas by volume. Combined sulphur exists as sulphates such as gypsum, epsome salt, baryte etc. The allotropic forms of sulphur are Rhombic and monoclinic sulphur. \(S_2\) is paramagnetic like \(O_2\) and it stable at high temperature. Group 17 is Halogen family. \(F_2\) is highly reactive, \(C l_2\) is greenish yellow gas. Both \(S O_2\) and \(C l_2\) are used for bleaching. Group 18 is Noble gas family but some noble gases also form compounds.
Complete hydrolysis of \(XeF _6\) gives HF and \(XeO _3\) as main products.
The product of complete hydrolysis of \(XeF _6\) in the following reaction is
\(XeF _6+ H _2 O \rightarrow ?+ HF\)

Magnetic moment values for \(\left[ Fe \left( H _2 O \right)_6\right]^{3+}\) and \(\left[ Fe ( CN )_6\right]^{3-}\) are:

Reaction occurring at cathode is
\(HgO+H_2 O+2 e^{-} \rightarrow Hg+2 OH^{-}\)
Above reaction is found in :

For a particular reaction taking place at \(\text{T} = 300 \text{ K}\), \(\text{E}_a= 300 \text{ kJ/mol}\) and \(\text{log k} = -3.45\); calculate the temperature at which the rate constant becomes 4 times that of k. (Given \(\text{log } 2 = 0.3010\))

A polaroid sheet \(P _2\) is rotated by an angle \(\theta\) (angle between pass axies of \(P _1\) and \(P _2\) ) between two crossed polaroids \(P _1\) and \(P _3\). The intensity of tranamitted light will be maximum for:

If X, Y, Z, W \& P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 and p × k respectively. The restrictions on n,k \& p so that PY + WY be defined are:

\(\int\left(\frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha}\right) d x=\)
(Given that c is an arbitrary constant )

The shortest distance between the lines \(\frac{x+3}{1}=\frac{y-2}{2}=\frac{z+4}{3}\) and \(\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-6}{4}\) is :

Match List I with List II

List - I	List - II
(A) \(\int x^2 e^{x^3} d x\)	(I) \(\frac{1}{2 a} \log \left|\frac{a+x}{a-x}\right|+C\)
(B) \(\int e^x\left(\tan ^{-1} x+\frac{1}{1+x^2}\right) d x\)	(II) \(\frac{1}{a} \tan ^{-1}\left(\frac{x}{a}\right)+C\)
(C) \(\int \frac{d x}{a^2-x^2}\)	(III) \(\frac{1}{3} e^{x^3}+C\)
(D) \(\int \frac{d x}{x^2+a^2}\)	(IV) \(e^x \tan ^{-1} x+C\)

If X is a random variable with probability distribution as given below:

X	0	1	2	3
P(X)	K	2K	K	3K

Then, the variance of the distribution is: