Consider the cell \(Pt ( s )\left| H _2( s )( latm )\right| H ^{+}\left( aq ,\left[ H ^{+}\right]=1\right)|| Fe ^{3+}( aq ), Fe ^{2+}( aq ) \mid \operatorname{Pt}( s )\) Given : \(E _{ Fe ^{3+} / e ^{2 *}}^0=0.771\,V\) and \(E _{ H ^{+}+\frac{1}{2} H _2}^0=0 V , T =298\,K\) If the potential of the cell is \(0.712\,V\) the ratio of concentration of \(Fe ^{2+}\) to \(Fe ^{2+}\) is \(........\).(Nearest integer)

Match List \(I\) with List \(II\)

\(LIST-I\) \((Substances)\)	\(LIST-II\) \((Element Present)\)
\(A\). Ziegler catalyst	\(I\). Rhodium
\(B\). Blood pigment	\(II\). Cobalt
\(C\) .Wilkinson catalyst	\(III\). Iron
\(D\). Vitamin \(\mathrm{B}_{12}\)	\(IV\). Titanium

Choose the correct answer from the options given below:

Tischenko reaction is a modification of

Which of the following statements is false ?

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.]

Consider that a \(d ^{6}\) metal ion \(\left( M ^{2+}\right)\) forms a complex with aqua ligands, and the spin only magnetic moment of the complex is \(4.90\) \(BM.\) The geometry and the crystal field stabilization energy of the complex is:

Which of the following series correctly represents relations between the elements from \(X\) to \(Y\) ? \(X \to Y\)

For the reaction \(H _{2} F _{2( g )} \rightarrow H _{2( g )}+ F _{2( g )}\) \(\Delta U =-59.6\,kJ\,mol ^{-1} \text { at } 27^{\circ}\,C\). The enthalpy change for the above reaction is (-) \(kJ mol ^{-1}\) [nearest integer] Given : \(R =8.314\,JK ^{-1}\,mol ^{-1}\)

In a Young's double slit experiment, the slits are separated by 0.2 mm. If the slits separation is increased to 0.4 mm , the percentage change of the fringe width is _______.

Given below are two statements :
Statement \(I\): Nitration of benzene involves the following step -

Statement \(II\): Use of Lewis base promotes the electrophilic substitution of benzene.
In the light of the above statements, choose the most appropriate answer from the options given below:

Let the equation of the plane \(P\) containing the line \(x+10=\frac{8-y}{2}=z\) be \(a x+b y+3 z=2(a+b)\) and the distance of the plane \(P\) from the point \((1,27,7)\) be c. Then \(a^2+b^2+c^2\) is equal to \(.............\).

If \(\int \mathrm{e}^x\left(\frac{x \sin ^{-1} x}{\sqrt{1-x^2}}+\frac{\sin ^{-1} x}{\left(1-x^2\right)^{3 / 2}}+\frac{x}{1-x^2}\right) \mathrm{d} x=\mathrm{g}(x)+\mathrm{C}\), where C is the constant of integration, then \(g\left(\frac{1}{2}\right)\) equals :

In the above conversion of compound \(( X )\) to product \((Y)\), the sequence of reagents to be used will be: