\(100\, \mathrm{~g}\) of propane is completely reacted with \(1000\, \mathrm{~g}\) of oxygen. The mole fraction of carbon dioxide in the resulting mixture is \(\mathrm{x} \times 10^{-2}\). The value of \(\mathrm{x}\) is ..... . (Nearest integer) [Atomic weight : \(\mathrm{H}=1.008 ; \mathrm{C}=12.00 ; \mathrm{O}=16.00\) ]

Which of the following ions is the strongest oxidizing agent? (Atomic Number of \(\mathrm{Ce}=58, \mathrm{Eu}=63, \mathrm{~Tb}=65, \mathrm{Lu}=71\) )

Match List \(I\) with List \(II\) :

LIST \(I\) (Hybridization)	LIST \(II\) (Orientation in Space)
\((A)\) \(\mathrm{sp}^3\)	\((I)\) Trigonal bipyramidal
\((B)\) \(\mathrm{dsp}^2\)	\((II)\) Octahedral
\((C)\) \(\mathrm{sp}^3 \mathrm{~d}\)	\((III)\) Tetrahedral
\((D)\) \(s p^3 d^2\)	\((IV)\) Square planar

Choose the correct answer from the options given below :

Consider the following reactions. From these reactions which reaction will give carboxylic acid
as a major product ?
(A) \(\mathrm{R}-\mathrm{C} \equiv \mathrm{N} \xrightarrow[\text { mild condition }]{\text { (i) } \mathrm{H}^{+} / \mathrm{H}_2 \mathrm{O}}\)
(B) \(\mathrm{R}-\mathrm{MgX} \xrightarrow[\text { (ii) } \mathrm{H}_3 \mathrm{O}^{+}]{\text {(i) } \mathrm{CO}_2}\)
(C) \(\mathrm{R}-\mathrm{C} \equiv \mathrm{N} \xrightarrow[\text { (ii) } \mathrm{H}_3 \mathrm{O}^{+}]{\text {(i) } \mathrm{SnCl}_2 / \mathrm{HCl}}\)
(D) \(\mathrm{R} \cdot \mathrm{CH}_2 \cdot \mathrm{OH} \xrightarrow{\mathrm{PCC}}\)
(E)

Choose the correct answer from the options given below:

In the following compounds, the decreasing order of basic strength will be

A sample of \(0.125\,g\) of an organic compound when analysed by Duma's method yields \(22.78\,mL\) of nitrogen gas collected over \(KOH\) solution at \(280\,K\) and \(759\,mm\,Hg\). The percentage of nitrogen in the given organic compound is.(Nearest integer). \((a)\) The vapour pressure of water at \(280 K\) is \(14.2\) \(mm Hg\) \((b)\) \(R =0.082 L\) atm \(K ^{-1} mol ^{-1}\)

An ' Assertion' and a 'Reason' are given below. Choose the correct answer from the following options. Assertion \((A)\) : Vinyl halides do not undergo nucleophilic substitution easily. Reason \((R)\) : Even though the intermediate carbocation is stabilized by loosely held \(p-\) electrons, the cleavage is difficult because of strong bonding.

Let \(R = \{(x, y) \in \mathbb{N} \times \mathbb{N} : \log_e(x + y) \leq 2\}\). Then the minimum number of elements, required to be added in \(R\) to make it a transitive relation, is __________.

The focal length of the objective and the eyepiece of a telescope are \(50\,cm\) and \(5\,cm\) respectively. If the telescope is focussed for distinct vision on a scale distant \(2\,m\) from its objective, then its magnifying power will be

Let \(a_1 , a_2, a_3, .... , a_n\), be in \(A.P\). If \(a_3 + a_7 + a_{11} + a_{15} = 72\) , then the sum of its first \(17\) terms is equal to

In which of the following octahedral complex species the magnitude of \({\Delta _0}\) will be maximum ?

Two open organ pipes of length \(60 \mathrm{~cm}\) and \(90 \mathrm{~cm}\) resonate at \(6^{\text {th }}\) and \(5^{\text {th }}\) harmonics respectively. The difference of frequencies for the given modes is _______ \(\mathrm{Hz}\). (Velocity of sound in air \(=333 \mathrm{~m} / \mathrm{s}\) )

The number of points where the function \(f(x)=\left\{\begin{array}{clr}\left|2 x^{2}-3 x-7\right| \, \text { if } x \leq-1 \\ {\left[4 x^{2}-1\right]} \text { if } -1 < x < 1 \\ |x+1|+|x-2| \text { if } x \geq 1\end{array}\right.\) \([t]\) denotes the greatest integer \(\leq t\), is discontinuous is