For the reaction \(SO_2(g) + \frac{1}{2} O_2(g) \rightleftharpoons SO_3(g),\) if \(K_P = K_C ( RT)^x\) where the symbols have usual meaning then the value of \(x\) is (assuming ideality) :

In an estimation of sulphur by Carius method \(0.2\) g of the substance gave \(0.6\) g of BaSO\(_4\). The percentage of sulphur in the substance is _____ %.
(Given molar mass in g mol\(^{-1}\) S : \(32\), BaSO\(_4\) : \(233\))

\(0.05 \mathrm{M} \mathrm{CuSO}_4\) when treated with \(0.01 \mathrm{M} \mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7\) gives green colour solution of \(\mathrm{Cu}_2 \mathrm{Cr}_2 \mathrm{O}_7\). The [\(SPM\) : Semi Permeable Membrane] \({K}_2 \mathrm{Cr}_2 \mathrm{O}_7\)  &  \({CuSO}_4\) Side \(\mathrm{X}\) [\(SPM\)] Side \(\mathrm{Y}\) Due to osmosis :

The number of electrons involved in the reduction of permanganate to manganese dioxide in acidic medium is \(.......\).

The vapour pressures of \(A\) and \(B\) at \(25^{\circ} \mathrm{C}\) are \(90\, \mathrm{~mm}\, \mathrm{Hg}\) and \(15\, \mathrm{~mm} \,\mathrm{Hg}\) respectively. If \(\mathrm{A}\) and \(\mathrm{B}\) are mixed such that the mole fraction of \(A\) in the mixture is \(0.6\), then the mole fraction of \(B\) in the vapour phase is \(x \times 10^{-1}\). The value of \(x\) is \(.....\) (Nearest integer)

In a closed flask at \(600\) K, one mole of X\(_2\)Y\(_4\)(g) attains equilibrium as given below :
\(\text{X}_2\text{Y}_4(g) \rightleftharpoons 2\text{XY}_2(g)\)
At equilibrium, \(75\%\) X\(_2\)Y\(_4\)(g) was dissociated and the total pressure is \(1\) atm. The magnitude of \(\Delta_r G^{\ominus}\) (in kJ mol\(^{-1}\)) at this temperature is __________. (Nearest Integer) (Given : R \(= 8.3\) J mol\(^{-1}\) K\(^{-1}\); \(\ln 10 = 2.3\), \(\log 2 = 0.3\), \(\log 3 = 0.48\), \(\log 5 = 0.69\), \(\log 7 = 0.84\))

The total number of monohalogenated organic products in the following (including stereoisomers) reaction is......... \(\begin{array}{*{20}{c}} A \\ {{\text{(simplest optically active alkene)}}} \end{array}\,\xrightarrow[{(ii)\,{X_2}/\Delta }]{{(i)\,{H_2}/Ni/\Delta }}\)

Consider the following reactions \((a)\;\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CCH}(\mathrm{OH}) \mathrm{CH}_{3} \stackrel{\mathrm{conc.H}, \mathrm{SO}_{4}}{\longrightarrow}\) \((b)\;\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHCH}(\mathrm{Br}) \mathrm{CH}_{3} \stackrel{\text { alc.KOH }}{\longrightarrow}\) \((c)\;\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHCH}(\mathrm{Br}) \mathrm{CH}_{3} \xrightarrow[\text { It should be }\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CO}^{-} \mathrm{K}^{+}]{\text { given by } \mathrm{NTA}\left(\mathrm{CH}_{3}\right)_{3} \mathrm{O}^{-} \mathrm{K}^{+}}\) \((d)\;\begin{array}{*{20}{c}}
  {{{(C{H_3})}_2}C - C{H_2} - CHO} \\ 
  {|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} \\ 
  {OH\,\,\,\,\,\,\,\,\,\,\,\,\,\,} 
\end{array}\xrightarrow{\Delta }\) Which of these reaction(s) will not produce Saytzeff product ?

The elements of Group 13 with highest and lowest first ionisation enthalpies are respectively:

If three successive terms of a\(G.P.\) with common ratio \(r(r>1)\) are the lengths of the sides of a triangle and \([\mathrm{r}]\) denotes the greatest integer less than or equal to \(r\), then \(3[r]+[-r]\) is equal to :

Given below are two statements:
Statement I: An object moves from position \( r_{1} \) to position \( r_{2} \) under a conservative force field \( \vec{F} \). The work done by the force is \( W=-\int_{r_{1}}^{r_{2}}\vec{F}\cdot d\vec{r} \).
Statement II Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.
In the light of above statement, choose the correct answer from the options given below:

Let \(a, b \in R\). Let the mean and the variance of \(6\) observations \(-3,4,7,-6\), \(a,\ b\) be \(2\) and \(23\) , respectively. The mean deviation about the mean of these \(6\) observations is :

Projectiles \(A\) and \(B\) are thrown at angles of \(45^{\circ}\) and \(60^{\circ}\) with vertical respectively from top of a \(400 \mathrm{~m}\) high tower. If their ranges and times of flight are same, the ratio of their speeds of projection \(v_A: v_B\) is _______.