Decomposition of \(H_2O\) follows a first order reaction. In fifty minutes the concentration of \(H_2O_2\) decreases from \(0.5\) to \(0.125\,\min\) one such decomposition. When the concentration of \(H_2O_2\) reaches \(0.05\, M,\) the rate of formation of \(O_2\) will be :

In Dumas method for estimation of nitrogen, 0.50 g of an organic compound gave 70 mL of nitrogen collected at 300 K and 715 mm pressure. The percentage of nitrogen in the organic compound is ______ \( \% \)
(Aqueous tension at 300 K is 15 mm).

The Kjeldahl method of Nitrogen estimation fails for which of the following reaction products \(?\)

Consider, \(PF _{5}, BrF _{5}, PCl _{3}, SF _{6},\left[ ICl _{4}\right]^{-}, ClF _{3}\) and \(IF _{5}\) Amongst the above molecule(s)/ion(s), the number of molecule(s)/1on(s) having \(sp ^{3} d ^{2}\) hybridisation is \(........\)

The pair of compounds having metals in their highest oxidation state is

The complex that shows Facial - Meridional isomerism is _______.

For complete combustion of ethene. \(C _2 H _4( g )+3 O _2( g ) \rightarrow 2 CO _2( g )+2 H _2 O ( l )\) the amount of heat produced as measured in bomb calorimeter is \(1406\,kJ\,mol { }^{-1}\) at \(300\,K\). The minimum value of \(T \Delta S\) needed to reach equilibrium is \((-).......\,kJ\). (Nearest integer) Given : \(R =8.3\,JK ^{-1} mol ^{-1}\)

The mean and the standard deviation \((s.d.)\)  of five observations are \(9\) and \(0,\) respectively. If one of the observations is changed such that the mean of the new set of five observations becomes \(10,\)  then their \(s.d.\)  is?

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of an uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water.
(Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is \(1 \mathrm{gm} / \mathrm{cm}^3\).) The unknown mass is ________ kg.

\(27\) identical drops are charged at \(22\, V\,\,each.\) They combine to form a bigger drop. The potential of the bigger drop will be............ \(V.\)

Let \({ }^{n} C_{r}\) denote the binomial coefficient of \(x^{r}\) in the expansion of \((1+ x )^{ n }.\) If \(\sum_{ k =0}^{10}\left(2^{2}+3 k \right){ }^{ n } C _{ k }=\alpha .3^{10}+\beta \cdot 2^{10}, \alpha, \beta \in R\) then \(\alpha+\beta\) is equal to ....... .

The equilibrium constant for decomposition of \(\mathrm{H}_2 \mathrm{O}(\mathrm{g})\) \(\mathrm{H}_2 \mathrm{O}(\mathrm{~g}) \rightleftharpoons \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g})\left(\Delta \mathrm{G}^{\circ}=92.34 \mathrm{~kJ} \mathrm{~mol}^{-1}\right)\) is \(8.0 \times 10^{-3}\) at 2300 K and total pressure at equilibrium is 1 bar. Under this condition, the degree of dissociation \((\alpha)\) of water is ________ \(\times 10^{-2}\) (nearest integer value).
[Assume \(\alpha\) is negligible with respect to 1 ]

A body of mass \(8\,kg\) and another of mass \(2\, kg\) are moving with equal kinetic energy. The ratio of their respective momenta will be.