The conjugate base of hydrazoic acid is

For the cell \(Zn(s)|\,Z{n^{2 + }}(aq)\,||\,{M^x+} \,(aq)|\,M(s),\) different half cells and their standard electrode potentials are given below

\(M^{x+}\,  (aq)\,/M(s)\)	\(A{u^{3 + }}(aq)/\) \(Au(s)\)	\(A{g^ + }(aq)/\) \(Ag(s)\)	\(F{e^{3 + }}(aq)/\) \(F{e^{2 + }}(aq)\)	\(F{e^{2 + }}(aq)/\) \(Fe(s)\)
\(E^o\,M^{x+}\) \(\,/M(V)\)	\(1.40\)	\(0.80\)	\(0.77\)	\(-0.44\)

If \(E_{Z{n^{2 + }}/Zn}^o =  - 0.76\,V,\) which cathode will given a maximum value of  \(E_{cell}^o\) per electron transferred?

The equilibrium constant for the reaction \(Zn ( s )+ Sn ^{2+}( aq ) \rightleftharpoons Zn ^{2+}( aq )+ Sn ( s )\) is \(1 \times 10^{20}\) at \(298 K\). The magnitude of standard electrode potential of \(Sn / Sn ^{2+}\) if \(E _{ Zn ^{2+/ / nn }}^0=-0.76 V\) is \(............\times 10^{-2}\,V\). (Nearest integer) Given : \(\frac{2.303 RT }{ F }=0.059\,V\)

\(KClO _3+6 FeSO _4+3 H _2 SO _4 \rightarrow KCl +3 Fe _2\left( SO _4\right)_3+3 H _2 O\) The above reaction was studied at \(300\,K\) by monitoring the concentration of \(FeSO _4\) in which initial concentration was \(10\,M\) and after half an hour became \(8.8\,M\). The rate of production of \(Fe _2\left( SO _4\right)_3\) is \(........\times 10^{-6}\,mol\,L ^{-1}\,s ^{-1}\).

Low oxidation state of metals in their complexes are common when ligands.

Among the following, the CORRECT combinations are :
A. \( IF_{3} \) → T-shaped \( (sp^{3}d) \)
B. \( IF_{5} \) → Square pyramidal \( (sp^{3}d^{2}) \)
C. \( IF_{7} \) → Pentagonal bipyramidal \( (sp^{3}d^{3}) \)
D. \( ClO_{4}^{-} \) → Square planar \( (sp^{3}d) \)
Choose the correct answer from the options given below :

The total pressure of a mixture of non-reacting gases \(X (0.6\,g )\) and \(Y (0.45\,g )\) in a vessel is \(740\,mm\) of \(Hg\). The partial pressure of the gas \(X\) is \(........mm\) of \(Hg\). (Nearest Integer)(Given : molar mass \(X =20\) and \(Y =45\,g\,mol ^{-1}\) )

For a diatomic gas, if \(\gamma_1=\left(\frac{C p}{C v}\right)\) for rigid molecules and \(\gamma_2=\left(\frac{C p}{C v}\right)\) for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct ? (Cp and Cv are specific heats of the gas at constant pressure and volume)

A current carrying circular loop of radius \(2\) cm with unit normal \(\hat{n} = \dfrac{\hat{k}+\hat{i}}{\sqrt{2}}\) is placed in a magnetic field, \(\vec{B} = B_0(3\hat{i}+2\hat{k})\). If \(B_0 = 4\times 10^{-3}\) T and current \(I=100\sqrt{2}\) A, the torque experienced by the loop is ________ Wb·A. (\(\pi=3.14\))

In an experiment the values of two spring constants were measured as \(k _1=(10 \pm 0.2) N / m\)
and \(k _2=(20 \pm 0.3) N / m\). If these springs are connected in parallel, then the percentage error in equivalent spring constant is :

The number of elements in the set
\( S=\{x:x\in[0,100] \text{ and } \int_{0}^{x}t^{2}sin(x-t)dt=x^{2}\} \) is:

Given below are two statements:
Statement I: In the oxalic acid vs \(\mathrm{KMnO}_4\) (in the presence of dil \(\mathrm{H}_2 \mathrm{SO}_4\) ) titration the solution needs to be heated initially to \(60^{\circ} \mathrm{C}\), but no heating is required in Ferrous ammonium sulphate (FAS) vs \(\mathrm{KMnO}_4\) titration (in the presence of dil \(\mathrm{H}_2 \mathrm{SO}_4\) )
Statement II: In oxalic acid vs \(\mathrm{KMnO}_4\) titration, the initial formation of \(\mathrm{MnSO}_4\) takes place at high temperature, which then acts as catalyst for further reaction. In the case of FAS vs \(\mathrm{KMnO}_4\), heating oxidizes \(\mathrm{Fe}^{2+}\) into \(\mathrm{Fe}^{3+}\) by oxygen of air and error may be introduced in the experiment.
In the light of the above statements, choose the correct answer from the options given below

A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is \(\sqrt{\frac{x}{5}}\) where \(\mathrm{x}=\) _____