The freezing point of diluted milk sample is found to be \(-\,0.2\,^oC,\) while it should have been \(\,0.5\,^oC,\) for pure milk. How much water been added to pure milk to make the diluted sample?

The pair, in which ions are isoelectronic with \(Al ^{3+}\) is ..... .

Which of the following binary mixture does not show the behaviour of minimum boiling azeotropes?

By usual analysis, 1.00g of compound (X) gave 1.79g of magnesium pyrophosphate. The percentage of phosphorus in compound (X) is: (nearest integer)
(Given, molar mass in \(g~mol^{-1}\); O=16, Mg=24, P=31)

Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below. \(\mathrm{A}+\mathrm{B} \underset{\text { Step } 3}{\text { Step } 1} \mathrm{C} \xrightarrow{\text { Step } 2} \mathrm{P}\) Some details of the above reaction are listed below.

Step	Rate constant\(\left(\sec ^{-1}\right)\)	Activation energy\(\left(\mathrm{kJ} \mathrm{mol}^{-1}\right)\)
\(1\)	\({k}_1\)	\(300\)
\(2\)	\({k}_2\)	\(200\)
\(3\)	\({k}_3\)	\(\mathrm{Ea}_3\)

If the overall rate constant of the above transformation (k) is given as \(\mathrm{k}=\frac{\mathrm{k}_1 \mathrm{k}_2}{\mathrm{k}_3}\) and the overall activation energy \(\left(E_2\right)\) is \(400 \mathrm{~kJ} \mathrm{~mol}^{-1}\), then the value of \(\mathrm{Ea}_3\) is _______ \(\mathrm{kJ} \mathrm{mol}^{-1}\). (nearest integer)

For a \(\mathrm{Mg}\left|\mathrm{Mg}^{2+}(\mathrm{aq})\right|\left|\mathrm{Ag}^{+}(\mathrm{aq})\right| \mathrm{Ag}\) the correct Nernst Equation is _______.

A group \(15\) element, which is a metal and forms a hydride with strongest reducing power among group \(15\) hydrides. The element is

Which of the following represents the correct order of metallic character of the given elements ?

The wavelength of light absorbed for the following complexes are in the order:
\(\underset{\text { (I) }}{\left[ Co \left( NH _3\right)_6\right]^{3+}} ; \underset{\text { (II) }}{\left[ Co \left( H _2 O \right)_6\right]^{3+}} ; \underset{\text { (III) }}{\left[ Co ( CN )_6\right]^{3-}}\) ;
\(\underset{( IV )}{\left[ Co \left( NH _3\right)_5\left( H _2 O \right)\right]^{3+}} ; \underset{( V )}{\left[ CoF _6\right]^{3-}}\)

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 \(\tan \left(2 \tan ^{-1}\left(\frac{3}{5}\right)+\sin ^{-1}\left(\frac{5}{13}\right)\right)\) is equal to:

If the value of \(\lim _{x \rightarrow 0}(2-\cos x \sqrt{\cos 2 x})^{\left(\frac{x+2}{x^{2}}\right)}\) is equal to \(e^{a}\), then \(a\) is equal to \(.....\)

For \(z \in C\) if the minimum value of \((|z-3 \sqrt{2}|+|z-p \sqrt{2} i|)\) is \(5 \sqrt{2}\), then a value of \(P\) is \(.......\)