The Total pressure observed by mixing two liquid \(A\) and \(B\) is \(350\,mm\,Hg\) when their mole fractions are \(0.7\) and \(0.3\) respectively.The Total pressure becomes \(410 \,mm\,Hg\) if the mole fractions are changed to \(0.2\) and \(0.8\) respectively for \(A\) and \(B\). The vapour pressure of pure \(A\) is \(...........\,mm\,Hg\). (Nearest integer) Consider the liquids and solutions behave ideally.

Given below are two statements Statement \(I : CeO _{2}\) can be used for oxidation of aldehydes and ketones. Statement \(II :\) Aqueous solution of \(EuSO _{4}\) is a strong reducing agent. In the light of the above statements, choose the correct answer from the options given below

Arrange the following labelled hydrogens in decreasing order of acidity

A constant current was passed through a solution of \(\mathrm{AuCl}_4^{-}\)ion between gold electrodes. After a period of \(10.0\) minutes, the increase in mass of cathode was \(1.314 \mathrm{~g}\). The total charge passed through the solution is _______ \(\times 10^{-2} \mathrm{~F}\). (Given atomic mass of \({\mathrm{Au}}={197}\) )

Choose the correct statements about the hydrides of group \(15\) elements. \(A\). The stability of the hydrides decreases in the order \(\mathrm{NH}_3>\mathrm{PH}_3>\mathrm{AsH}_3>\mathrm{SbH}_3>\mathrm{BiH}_3\) \(B\). The reducing ability of the hydrides increases in the order \(\mathrm{NH}_3<\mathrm{PH}_3<\mathrm{AsH}_3<\mathrm{SbH}_3<\mathrm{BiH}_3\) \(C\). Among the hydrides, \(\mathrm{NH}_3\) is strong reducing agent while \(\mathrm{BiH}_3\) is mild reducing agent. \(D\). The basicity of the hydrides increases in the order \(\mathrm{NH}_3<\mathrm{PH}_3<\mathrm{AsH}_3<\mathrm{SbH}_3<\mathrm{BiH}_3\)
Choose the most appropriate from the option given below.

If \(A_2 B\) is \(30 \%\) ionised in an aqueous solution, then the value of van't Hoff factor (i) is ______ \(\times 10^{-1}\).

Total number of relatively more stable isomer(s) possible for octahedral complex \(\left[ Cu ( en )_{2}( SCN )_{2}\right]\) will be \(.........\)

Let \(f:(1,\infty)\to\mathbb{R}\) be a function defined as \(f(x) = \dfrac{x-1}{x+1}\). Let \(f^{i+1}(x) = f(f^i(x))\), \(i=1, 2, \ldots, 25\), where \(f^1(x)=f(x)\). If \(g(x) + f^{26}(x) = 0\), \(x \in (1, \infty)\), then the area of the region bounded by the curves \(y=g(x)\), \(2y=2x-3\), \(y=0\) and \(x=4\) is:

An electron of mass \(m_{e}\) and a proton of mass \(m_{p}\) are accelerated through the same potential difference. The ratio of the de-Broglie wavelength associated with the electron to that with the proton is

The number of onto functions \(f\) from \(\{1, 2, 3, …, 20\}\) only \(\{1, 2, 3, …, 20\}\) such that \(f(k)\) is a multiple of \(3\), whenever \(k\) is a multiple of \(4\), is

Figure shows a circuit that contains four identical resistors with resistance \(R =2.0\, \Omega,\) two identical inductors with inductance \(L =2.0 \,mH\) and an ideal battery with \(e m f E =9 \,V .\) The current \('i'\) just after the switch \('S'\) is closed will be .... \(A\)

Let \(y=y(x)\) be the solution of the differential equation \(x\frac{dy}{dx}-y=x^{2}\cot x, x\in(0,\pi)\). If \(y(\frac{\pi}{2})=\frac{\pi}{2}\), then \(6y(\frac{\pi}{6})-8y(\frac{\pi}{4})\) is equal to :

Two batteries with e.m.f \(12\ V\) and \(13\ V\) are connected in parallel across a load resistor of \(10\,\Omega\) . The internal resistances of the two batteries are \(1\,\Omega\) and \(2\,\Omega\) respectively. The voltage across the load lies between