The depression in freezing point observed for a formic acid solution of concentration \(0.5\,mL\,L ^{-1}\) is \(0.0405^{\circ}\,C\). Density of formic acid is \(1.05\,g\,mL ^{-1}\). The Van't Hoff factor of the formic acid solution is nearly: (Given for water \(k _{ f }=1.86\,K\,kg\,mol ^{-1}\) )

In compound \(( Q )\), the percentage of oxygen is __________ %. (Nearest integer)

Match List -\(I\) with List \(II\): (Image) Choose the correct answer from the options given below :

The stepwise formation of \(\left[ Cu \left( NH _{3}\right)_{4}\right]^{2+}\) is given below \(Cu ^{2+}+ NH _{3} \stackrel{ K _{1}}{\rightleftharpoons}\left[ Cu \left( NH _{3}\right)\right]^{2+}\) \(\left[ Cu \left( NH _{3}\right)\right]^{2+}+ NH _{3} \stackrel{ K _{2}}{\rightleftharpoons}\left[ Cu \left( NH _{3}\right)_{2}\right]^{2+}\) \(\left[ Cu \left( NH _{3}\right)_{2}\right]^{2+}+ NH _{3} \stackrel{ K _{3}}{\rightleftharpoons}\left[ Cu \left( NH _{3}\right)_{3}\right]^{2+}\) \(\left[ Cu \left( NH _{3}\right)_{3}\right]^{2+}+ NH _{3} \stackrel{ K _{4}}{\rightleftharpoons}\left[ Cu \left( NH _{3}\right)_{4}\right]^{2+}\) The value of stability constants \(K _{1}, K _{2}, K _{3}\) and \(K _{4}\) are \(10^{4}, 1.58 \times 10^{3}, 5 \times 10^{2}\) and \(10^{2}\) respectively. The overall equilibrium constants for dissociation of \(\left[ Cu \left( NH _{3}\right)_{4}\right]^{2+}\) is \(x \times 10^{-12}\) The value of \(x\) is ............... (Rounded off to the nearest integer)

Given below are two statements :
Statement I : Ozonolysis followed by treatment with \(\mathrm{Zn}, \mathrm{H}_2 \mathrm{O}\) of cis-2-butene gives ethanal.Statement II : The production obtained by ozonolysis followed by treatment with \(\mathrm{Zn}, \mathrm{H}_2 \mathrm{O}\) of 3, 6-dimethyloct-4-ene has no chiral carbon atom.
In the light of the above statements, choose the correct answer from the options given below

An organic compound "\(x\)" where molar ratio of C, O and H are equal, on treatment with \(50\%\) KOH under reflux followed by acidification produced "\(y\)". The most likely structure of "\(y\)" is:
[Molar mass of '\(x\)' is \(58\) g mol\(^{-1}\)]

Chlorine undergoes disproportionation in alkaline medium as shown below : \( \text { a } \mathrm{Cl}_2(\mathrm{~g})+\mathrm{b} \mathrm{OH}^{-}(\mathrm{aq}) \rightarrow \mathrm{c} \mathrm{ClO}^{-}(\mathrm{aq})+\mathrm{d} \mathrm{Cl}^{-}(\mathrm{aq})  +\mathrm{e} \mathrm{H}_2 \mathrm{O}(l)\) The values of \(a, \ b,\  c\) and \(d\) in a balanced redox reaction are respectively :

When \(XO_2\)  is fused with an alkali metal hydroxide in presence of an oxidizing agent such as \(KNO_3,\) a dark green product is formed which disproportionates in acidic solution to afford a dark purple solution. \(X\)  is

Let \(A\) be a \(3 \times 3\) matrix of non-negative real elements such that \(A\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]=3\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]\). Then the maximum value of \(\operatorname{det}(\mathrm{A})\) is ...........

If the functions are defined as \(f(x)=\sqrt{x}\) and \(g ( x )=\sqrt{1- x },\) then what is the common domain of the following functions: \(f+g, f-g, f / g, g / f, g-f\) where \((f \pm g)(x)=\) \(f(x) \pm g(x),(f / g)(x)=\frac{f(x)}{g(x)}\)

A circular hole of radius \(\frac{R}{4}\) is made in a thin uniform disc having mass \(M\) and radius \(R\), as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point \(O\) and perpendicular to the plane of the disc is

Figure shows a part of an electric circuit. The potentials at points \(a , b\) and \(c\) are \(30\,V , 12\,V\) and \(2\,V\) respectively. The current through the \(20 \Omega\) resistor will be \(........\,A\)

A body having specific charge \(8\,\mu {C} / {g}\) is resting on a frictionless plane at a distance \(10\, {cm}\) from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of \(100 \,{V} / {m}\) is applied horizontally toward the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be \(....\, S.\)