\(0.01\, M\, KMnO _{4}\) solution was added to \(20.0\, mL\) of \(0.05\, M\) Mohr's salt solution through a burette. The initial reading of \(50\, mL\) burette is zero. The volume of \(KMnO _{4}\) solution left in the burette after the end point is \(.....\,mL\). (nearest integer)

Molecules of benzoic acid \((C_6H_5COOH)\) dimerise in benzene. \(‘w’\,g\) of the acid dissolved in \(30\,g\) of benzene shows a depression in freezing point equal to \(2\,K.\) If the percentage association of the acid to form dimer in the solution is \(80,\) then \(w\) is : ............. \(\mathrm{g}\) (Given that \(K_f = 5\,K\, kg\,mol^{-1},\) Molar mass of benzoic acid \(= 122\,g\,mol^{-1}\) )

The standard Gibbs energy change at \(300\, K\) for the reaction \(2A \rightleftharpoons  B+C\) is \(2494.2\,J.\) At a given time, the composition of the reaction mixture is \([A] = \frac{1}{2}, [B] = 2\) and \([C] = \frac{1}{2} .\) The reaction proceeds in the : \([R = 8.314 \,J/K/mol, e= 2.718]\)

The number of correct statement/s from the following is _____ .
Larger the activation energy, smaller is the value of the rate constant.
The higher is the activation energy, higher is the value of the temperature coefficient.
At lower temperatures, increase in temperature causes more change in the value of  k  than at higher temperature.
A plot of \(\ln k\) vs \(\frac{1}{T}\) is a straight line with slope equal to \(-\frac{ Ea }{ R }\)

An organic compound (P) on treatment with aqueous ammonia under hot condition forms compound (Q) which on heating with \(Br_2\) and KOH forms compound (R) having molecular formula \(C _9 H _7 N\). Names of P, Q and R respectively are:

The rate of a certain biochemical reaction at physiological temperature \((T)\) occurs \(10^{6}\) times faster with enzyme than without. The change in the activation energy upon adding enzyme is

To inhibit the growth of tumours, identify the compounds used from the following: \((A)\) \(EDTA\)  \((B)\) Coordination Compounds of \(Pt\)  \((C)\) \(D-\)Penicillamine  \((D)\) Cis - Platin Choose the correct answer from the option given below:

In an experiment of determine the Young's modulus of wire of a length exactly \(1\; m\), the extension in the length of the wire is measured as \(0.4\,mm\) with an uncertainty of \(\pm 0.02\,mm\) when a load of \(1\,kg\) is applied. The diameter of the wire is measured as \(0.4\,mm\) with an uncertainty of \(\pm 0.01\,mm\). The error in the measurement of Young's modulus \((\Delta Y)\) is found to be \(x \times 10^{10}\,Nm ^{-2}\). The value of \(x\) is \(\left[\right.\) Take \(\left.g =10\,m / s ^{2}\right]\)

When radiation of wavelength \(\lambda\) is used to illuminate a metallic surface, the stopping potential is \(V.\) When the same surface is illuminated with radiation of wavelength \(3 \lambda,\) the stopping potential is \(\frac{ V }{4} .\) If the threshold wavelength for the metallic surface is \(n \lambda\) then value of \(n\) will be......

Suppose for a differentiable function \(h, h(0)=0\), \(\mathrm{h}(1)=1\) and \(\mathrm{h}^{\prime}(0)=\mathrm{h}^{\prime}(1)=2\). If \(\mathrm{g}(\mathrm{x})=\mathrm{h}\left(\mathrm{e}^{\mathrm{x}}\right) \mathrm{e}^{\mathrm{h}(\mathrm{x})}\), then \(g^{\prime}(0)\) is equal to :

Let \([t]\) denote the greatest integer function. If \(\int \limits_0^{2.4}\left[x^2\right] d x=\alpha+\beta \sqrt{2}+\gamma \sqrt{3}+\delta \sqrt{5}\), then \(\alpha+\beta+\gamma+\) \(\delta\) is equal to \(..............\).

All five letter words are made using all the letters \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}\) and arranged as in an English dictionary with serial numbers. Let the word at serial number \(n\) be denoted by \(W_n\). Let the probability \(\mathrm{P}\left(\mathrm{W}_{\mathrm{n}}\right)\) of choosing the word \(\mathrm{W}_{\mathrm{n}}\) satisfy \(\mathrm{P}\left(\mathrm{W}_{\mathrm{n}}\right)=2 \mathrm{P}\left(\mathrm{W}_{\mathrm{n}-1}\right), \mathrm{n} \gt 1\).
If \(\mathrm{P}(\mathrm{CDBEA})=\frac{2^\alpha}{2^\beta-1}, \alpha, \beta \in \mathbb{N}\), then \(\alpha+\beta\) is equal to : _______

A particle is released on a vertical smooth semicircular track from point \(X\) so that \(OX\) makes angle \(\theta \) from the vertical ( see figure). The normal reaction of the track on the particle vanishes at point \(Y\) where \(OY\) makes angle \(\phi \) with the horizontal. Then