Boiling point of a \(2 \%\) aqueous solution of a nonvolatile solute \(A\) is equal to the boiling point of \(8 \%\) aqueous solution of a non-volatile solute \(B\). The relation between molecular weights of \(A\) and \(B\) is.

What is the ratio of wave number of first line (lowest energy line) of Balmer series of H atomic spectrum to first line of its Brackett series?

The correct order of the spin-only magnetic moments of the following complexes is \((I)\) \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Br}_{2}\) \((II)\) \( \mathrm{Na}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) \((III)\) \(\mathrm{Na}_{3}\left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]\left(\Delta_{0}>\mathrm{P}\right)\) \((IV)\) \(\left(\mathrm{Et}_{4} \mathrm{N}\right)_{2}\left[\mathrm{CoCl}_{4}\right]\)

Some \(\mathrm{CO}_2\) gas was kept in a sealed container at a pressure of 1 atm and at 273 K . This entire amount of \(\mathrm{CO}_2\) gas was later passed through an aqueous solution of \(\mathrm{Ca}(\mathrm{OH})_2\). The excess unreacted \(\mathrm{Ca}(\mathrm{OH})_2\) was later neutralized with 0.1 M of 40 mL HCl . If the volume of the sealed container of \(\mathrm{CO}_2\) was \(x\), then \(x\) is ________ \(\mathrm{cm}^3\) (nearest integer).
[Given : The entire amount of \(\mathrm{CO}_2(\mathrm{~g})\) reacted with exactly half the initial amount of \(\mathrm{Ca}(\mathrm{OH})_2\) present in the aqueous solution.]

The effect of addition of helium gas to the following reaction in equilibrium state, is : \(PCI _5( g ) \rightleftharpoons PCl _3( g )+ Cl _2( g )\)

Consider the reaction \(N _{2} O _{4}( g ) \rightleftharpoons 2 NO _{2}( g )\) The temperature at which \(K _{ C }=20.4\) and \(K _{ P }=600.1,\) is ....... \(K\). (Round off to the Nearest Integer). [Assume all gases are ideal and \(R =0.0831\, L\,bar \, K ^{-1} mol ^{-1}]\)

Identify the correct statements.
A. Glucose exists in two anomeric forms.
B. Anomers of glucose differ in configuration at C\(-1\) in cyclic hemiacetal structure.
C. Melting point of \(\alpha\)-anomer of glucose is greater than \(\beta\)-anomer.
D. Specific rotation of \(\alpha\)-anomer is \(+19°\) while for \(\beta\)-anomer is \(+112°\)
E. \(\alpha\) and \(\beta\)-anomers of glucose are prepared by crystallization of saturated glucose solution at \(303\) K and \(371\) K respectively.
Choose the correct answer from the options given below:

A beam of plane polarised light of large cross sectional area and uniform intensity of \(3.3 \,Wm ^{-2}\) falls normally on a polariser (cross sectional area \(3 \times 10^{-4}\, m ^{2}\) ) which rotates about its axis with an angular speed of \(31.4\, rad/s.\) The energy of light passing through the polariser per revolution, is close to ........ \( \times 10^{-4} \,J\)

Let \(f ( x )\) and \(g ( x )\) be two real polynomials of degree \(2\) and \(1\) respectively. If \(f ( g ( x ))=8 x ^{2}-2 x\), and \(g(f(x))=4 x^{2}+6 x+1\), then the value of \(f(2)+g(2)\) is

For \(\mathrm{x} \geq 0\), the least value of \(\mathrm{K}\), for which \(4^{1+\mathrm{x}}+4^{1-\mathrm{x}}\), \(\frac{\mathrm{K}}{2}, 16^{\mathrm{x}}+16^{-\mathrm{x}}\) are three consecutive terms of an \(A.P.\) is equal to :

Which one of the following arrangements represents the correct order of solubilities of sparingly soluble salts \(Hg_2Cl_2,\,\,Cr_2(SO_4 )_3,\,\,BaSO_4\) and \(CrCl_3\) respectively ?

In an experiment to measure the focal length ( \(f\) ) of a convex lens, the magnitude of object distance \((x)\) and the image distance \((y)\) are measured with reference to the focal point of the lens. The \(y-x\) plot is shown in figure. The focal length of the lens is _______ \(\mathrm{cm}\).

Given below are two statements :
1 M aqueous solution of each of \(\mathrm{Cu}\left(\mathrm{NO}_3\right)_2, \mathrm{AgNO}_3\), \(\mathrm{Hg}_2\left(\mathrm{NO}_3\right)_2 ; \mathrm{Mg}\left(\mathrm{NO}_3\right)_2\) are electrolysed using inert electrodes,
\(\begin{aligned} & \text { Given : } \mathrm{E}_{\mathrm{Ag}^{+} / \mathrm{Ag}}^\theta=0.80 \mathrm{~V}, \mathrm{E}_{\mathrm{Hg}_2^{2+} / \mathrm{Hg}}^\theta=0.79 \mathrm{~V}, \\ & \mathrm{E}_{\mathrm{Cu}^{2+} / \mathrm{Cu}}^\theta=0.24 \mathrm{~V} \text { and } \mathrm{E}_{\mathrm{Mg}^{2+} / \mathrm{Mg}}^\theta=-2.37 \mathrm{~V}\end{aligned}\)
Statement (I) : With increasing voltage, the sequence of deposition of metals on the cathode will be \(\mathrm{Ag}, \mathrm{Hg}\) and Cu
Statement (II) : Magnesium will not be deposited at cathode instead oxygen gas will be evolved at the cathode.
In the light of the above statement, choose the most appropriate answer from the options given below