In Duma's method of estimation of nitrogen, \(0.1840 \,g\) of an organic compound gave \(30 \,mL\) of nitrogen collected at \(287\, K\) and \(758\, mm\) of \(Hg\) pressure. The percentage composition of nitrogen in the compound is ...... . (Round off to the Nearest Integer). [Given : Aqueous tension at \(287\, K =14 \,mm\) of \(Hg\) ]

For the reaction at \(298 \mathrm{~K}, 2 \mathrm{~A}+\mathrm{B} \rightarrow \mathrm{C} . \Delta \mathrm{H}\) \(=400 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and \(\Delta \mathrm{S}=0.2 \mathrm{~kJ} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\). The reaction will become spontaneous above _______ \(\mathrm{K}\).

Evaluate the following statements related to group \(14\) elements for their correctness. \((A)\)Covalent radius decreases down the group from \(\mathrm{C}\) to \(\mathrm{Pb}\) in a regular manner. \((B)\) Electronegativity decreases from \(\mathrm{C}\) to \(\mathrm{Pb}\) down the group gradually. \((C)\) Maximum covalence of \(\mathrm{C}\) is \(4\) whereas other elements can expand their covalence due to presence of \(d\) orbitals. \((D)\) Heavier elements do not form \(\mathrm{p} \pi-p \pi\) bonds. \((E)\) Carbon can exhibit negative oxidation states. Choose the correct answer from the options given below:

The order of stability of the following carbocations is : \((I)\,\,C{H_2} = CH - \mathop C\limits^ \oplus  {H_2}\) \((II)\,\,C{H_3} - CH_2 - \mathop C\limits^ \oplus  {H_2}\)

For reaction : \(SO _2( g )+\frac{1}{2} O _2( g ) \rightleftharpoons SO _3( g )\) \(K _{ P }=2 \times 10^{12}\) at \(27^{\circ}\,C\) and 1 atm pressure. The \(K _{ c }\) for the same reaction is \(.........\times 10^{13}\). (Nearest integer) (Given \(R =0.082\,L\,atm\,K ^{-1}\,mol ^{-1}\) )

Which of the following acts as a strong reducing agent? (Atomic number : \(\mathrm{Ce}=58, \mathrm{Eu}=63\), \(\mathrm{Gd}=64, \mathrm{Lu}=71)\)

The equation that is incorrect is

Let the locus of the mid points of the chords of circle \(x^2+(y-1)^2=1\) drawn from the origin intersect the line \(x+y=1\) at \(P\) and \(Q\). Then, the length of \(P Q\) is :

A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height \(h\) as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height \(h = \alpha R\). The value of \(\alpha\) is _______.

A soft drink was bottled with a partial pressure bf \(CO _{2}\) of \(3\) bar over the liquid at room temperature. The partial pressure of \(CO _{2}\) over the solution approaches a value of 30 bar when \(44\, g\) of \(CO _{2}\) is dissolved in \(1\, kg\) of water at room temperature. The approximate \(pH\) of the soft drink is............... \(\times 10^{-1}\) (First dissociation constant of \(H _{2} CO _{3}=4.0 \times 10^{-7}\)\(\log 2=0.3 ;\) density of the soft \(\left.\operatorname{drink}=1\, g\, mL ^{-1}\right)\)

A stone is projected at angle \(30^{\circ}\) to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be :

Let \(A\, = \,\left( {\begin{array}{*{20}{c}}
0&{2q}&r\\
p&q&{ - r}\\
p&{ - q}&r
\end{array}} \right)\). If \(A{A^T}\, = \,{I_3},\,\left| p \right|\) then \(\left| p \right|\) is

The number of \(4-\)letter words, with or without meaning, each consisting of \(2\) vowels and \(2\) consonants, which can be formed from the letters of the word \(UNIVERSE\) without repetition is \(.........\).