Number of compounds giving \((i)\) red colouration with ceric ammonium nitrate and also \((ii)\) positive iodoform test from the following is \(...........\).

Considering acetic acid dissociates in water, its dissociation constant is \(6.25 \times 10^{-5}\). If \(5 \mathrm{~mL}\) of acetic acid is dissolved in \(1\) litre water, the solution will freeze at \(-\mathrm{x} \times 10^{-2}{ }^{\circ} \mathrm{C}\), provided pure water freezes at \(0^{\circ} \mathrm{C}\). \(\mathrm{x}=\) _______ (Nearest integer) Given : \(\left(\mathrm{K}_{\mathrm{r}}\right)_{\text {water }}=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\). density of acetic acid is \(1.2 \mathrm{~g} \mathrm{~mol}^{-1}\) molar mass of water \(=18 \mathrm{~g} \mathrm{~mol}^{-1}\). molar mass of acetic acid \(=60 \mathrm{~g} \mathrm{~mol}^{-1}\). density of water \(=1 \mathrm{~g} \mathrm{~cm}^{-3}\) Acetic acid dissociates as \(\mathrm{CH}_3 \mathrm{COOH} \rightleftharpoons \mathrm{CH}_3 \mathrm{COO}^{\oplus}+\mathrm{H}^{\oplus}\)

The value of \(K _{ C }\) is \(64\) at \(800\, K\) for the reaction \(N _{2}( g )+3 H _{2}( g ) \rightleftharpoons 2 NH _{3}( g )\) The value of \(K _{ C }\) for the following reaction is : \(NH_{3}(g) \rightleftharpoons \frac{1}{2} N _{2}(g)+\frac{3}{2} H_{2}(g)\)

Hydrogen peroxide acts both as an oxidising and as a reducing agent depending upon the nature of the reacting species . In which of the following cases \(H_2O_2\) acts as a reducing agent in acid medium?

Which one of the following statements is not true about enzymes ?

The sum of oxidation state of the metals in \(Fe ( CO )_5, VO ^{2+}\) and \(WO _3\) is \(.........\).

The number of stereoisomers possible for \(1,2-\) dimethyl cyclopropane is :

If \(A = \left[ {\begin{array}{*{20}{c}}2&{ - 3}\\{ - 4}&1\end{array}} \right],\) then \(adj\;\left( {3{A^2} + 12A} \right) = \) . . . .

The line \(x =8\) is the directrix of the ellipse \(E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) with the corresponding focus \((2,0)\). If the tangent to \(E\) at the point \(P\) in the first quadrant passes through the point \((0,4 \sqrt{3})\) and intersects the \(x\)-axis at \(Q\), then \((3PQ)^2\) is equal to \(........\)

Let \(f: R \rightarrow R\) be a function defined \(f(x)=\frac{2 e^{2 x}}{e^{2 x}+\varepsilon}\). Then \(f\left(\frac{1}{100}\right)+f\left(\frac{2}{100}\right)+f\left(\frac{3}{100}\right)+\ldots .+f\left(\frac{99}{100}\right)\) is equal to

The dimension of \(\sqrt{\frac{\mu_0}{\epsilon_0}}\) is equal to that of :
( \(\mu_0=\) Vacuum permeability and \(\epsilon_0=\) Vacuum permittivity)

The number of real roots of the equation \(\tan ^{-1} \sqrt{x(x+1)}+\sin ^{-1} \sqrt{x^{2}+x+1}=\frac{\pi}{4}\) is:

The increasing order of the boiling points for the following compounds is \(\mathop {{C_2}{H_5}OH}\limits_{\left( I \right)} \)    \(\mathop {{C_2}{H_5}Cl}\limits_{\left( {II} \right)} \)   \(\mathop {{C_2}{H_5}C{H_3}}\limits_{\left( {III} \right)} \)   \(\mathop {{C_2}{H_5}OC{H_3}}\limits_{\left( {IV} \right)} \)