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.

The oxidation states of transition metal atoms in \(K _{2} Cr _{2} O _{7}, KMnO _{4}\) and \(K _{2} FeO _{4},\) respectively, are \(x , y\) and \(z\). The sum of \(x , y\) and \(z\) is

Given below are two statements :- Statement \(I\) :- Methyl orange is a weak acid. Statement \(II\) :- The benzenoid form of methyl orange is more intense/deeply coloured than the quinonoid form. In the light of the above statement, choose the most appropriate answer from the options given below :-

Statement \(I\) : Sodium hydride can be used as an oxidising agent. Statement \(II :\) The lone pair of electrons on nitrogen in pyridine makes it basic. Choose the CORRECT answer from the options given below:

The standard enthalpy and standard entropy of decomposition of \(\mathrm{N}_2 \mathrm{O}_4\) to \(\mathrm{NO}_2\) are \(55.0 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and \(175.0 \mathrm{~J} / \mathrm{K} / \mathrm{mol}\) respectively. The standard free energy change for this reaction at \(25^{\circ} \mathrm{C}\) in J \(\mathrm{mol}^{-1}\) is ______. (Nearest integer)

Which of the following is the energy of a possible excited state of hydrogen ? ............ \(\mathrm{eV}\)

The ionic radii of \(O _{2}- F ^{-}, Na ^{+}\) and \(Mg ^{2+}\) are in the order :

An ideal gas, \(\overline{\mathrm{C}}_{\mathrm{V}}=\frac{5}{2} \mathrm{R}\), is expanded adiabatically against a constant pressure of \(1 \mathrm{~atm}\) untill it doubles in volume. If the initial temperature and pressure is \(298 \mathrm{~K}\) and \(5 \mathrm{~atm}\), respectively then the final temperature is _______ \(\mathrm{K}\) (nearest integer). [ \(\overline{\mathrm{C}}_{\mathrm{V}}\) is the molar heat capacity at constant volume]

If \(2x = {y^{\frac{1}{5}}} + {y^{ - \frac{1}{5}}}\) and \((x^2 -1) \frac{{{d^2}y}}{{d{x^2}}} + \lambda x\frac{{dy}}{{dx}} + ky = 0\) , then \( \lambda + k\) is equal to

Let \(\vec{a}=\hat{i}+\hat{j}+\hat{k}, \quad \vec{b}=-\hat{i}-8 \hat{j}+2 \hat{k} \quad\) and \(\overrightarrow{\mathrm{c}}=4 \hat{\mathrm{i}}+\mathrm{c}_2 \hat{\mathrm{j}}+\mathrm{c}_3 \hat{\mathrm{k}}\) be three vectors such that \(\vec{b} \times \vec{a}=\vec{c} \times \vec{a}\). If the angle between the vector \(\vec{c}\) and the vector \(3 \hat{i}+4 \hat{j}+\hat{k}\) is \(\theta\), then the greatest integer less than or equal to \(\tan ^2 \theta\) is :

Given below are two statements: Statement \(I:\) Rotation of the earth shows effect on the value of acceleration due to gravity \((g)\). Statement \(II:\) The effect of rotation of the earth on the value of \(g\) at the equator is minimum and that at the pole is maximum. In the light of the above statements, choose the correct answer from the options given below.

Two simple harmonic motion, are represented by the equations \({y}_{1}=10 \sin \left(3 \pi {t}+\frac{\pi}{3}\right)\) \(y_{2}=5(\sin 3 \pi t+\sqrt{3} \cos 3 \pi t)\) Ratio of amplitude of \({y}_{1}\) to \({y}_{2}={x}: 1\). The value of \({x}\) is ...... .

Combustion of \(1\) mole of benzene is expressed at \(\mathrm{C}_6 \mathrm{H}_6(1)+\frac{15}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2 \mathrm{O}(1) \text {. }\) The standard enthalpy of combustion of \(2 \mathrm{~mol}\) of benzene is - ' \(x\) ' \(k J\). \(\mathrm{x}=\) _______ \((1)\) standard Enthalpy of formation of \(1 \mathrm{~mol}\) of \(\mathrm{C}_6 \mathrm{H}_6(1)\), for the reaction \(6 \mathrm{C}\) (graphite) \(+3 \mathrm{H}_2(\mathrm{~g}) \rightarrow \mathrm{C}_6 \mathrm{H}_n(1)\) is \(48.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\). \((2)\) Standard Enthalpy of formation of \(1 \mathrm{~mol}\) of \(\mathrm{CO}_2(\mathrm{~g})\), for the reaction \(\mathrm{C}\) (graphite) \(+\mathrm{O}_{2(\mathrm{~g})} \rightarrow \mathrm{CO}_2(\mathrm{~g})\) is \(-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\). \((3)\) Standard and Enthalpy of formation of \(1 \mathrm{~mol}\) of \(\mathrm{H}_2 \mathrm{O}(1)\), for the reaction \(\mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(1)\) is \(-286 \mathrm{~kJ} \mathrm{~mol}^{-1}\).