A hydrocarbon containing C and H has \(92.3 \% \mathrm{C}\). When 39 g of hydrocarbon was completely burnt in \(\mathrm{O}_2, x\) moles of water and y moles of \(\mathrm{CO}_2\) were formed. \(x\) moles of water is sufficient to liberate 0.75 moles of \(\mathrm{H}_2\) with Na metal. What is the weight (in g ) of oxygen consumed?
\((\mathrm{C}=12 \mathrm{u} ; \mathrm{H}=1 \mathrm{u})\)

Find the observed EMF of the cell \(\mathrm{Cd}\left|\mathrm{Cd}^{2+}(0.01 \mathrm{M}) \| \mathrm{Cd}^{2+}(0.01 \mathrm{M})\right| \mathrm{Cd}\) under conditions, internal resistance of \(4 \Omega\) and producing a current of \(0.15 \mathrm{~A}\).
(Given, \(E^{\circ} \mathrm{Cu}^{2+} / \mathrm{Cu}=0.35 \mathrm{~V}\)
and \(\quad E_{\mathrm{Cd}^{2+} / \mathrm{Cd}}^{\circ}=-0.4 \mathrm{~V}\) )

The initial rates of decrease of \(\mathrm{I}_2\) in acetone - iodine reaction catalysed by \(\mathrm{H}^{+}\) are given in the table.
\(\begin{array}{|c|c|c|c|c|}
\hline \begin{array}{c}
\text { Experiment } \\
\end{array} & \begin{array}{c}
\text { Initial } \\
{\left[\mathrm{I}_2\right]} \\
\left(\mathrm{mol} \mathrm{L}^{-1}\right)
\end{array} & \begin{array}{c}
\text { Initial } \\
{\left[\mathrm{H}^{+}\right]} \\
\left(\mathrm{mol} \mathrm{L}^{-1}\right)
\end{array} & \begin{array}{c}
\text { Initial } \\
{\left[\mathrm{CH}_3 \mathrm{COCH}_3\right]} \\
\left(\mathrm{mol} \mathrm{L}^{-1}\right)
\end{array} & \begin{array}{c}
\text { Initial rate of decrease of } \mathrm{I}_2 \\
\left(\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}\right)
\end{array} \\
\hline 1 & 0.01 & 0.1 & 0.1 & 0.096 \\
2 & 0.01 & 0.2 & 0.1 & 0.192 \\
3 & 0.02 & 0.2 & 0.1 & 0.192 \\
4 & 0.01 & 0.2 & 0.2 & 0.384 \\
\hline
\end{array}\)
The order with respect to \(\mathrm{I}_2, \mathrm{H}^{+}\), acetone and total order of the reaction respectively are:

Consider the sets I, II and III. Identify the set(s) which is (are) correctly matched.
I. Staggered ethane > eclipsed ethane ......... torsional strain.
II. 2, 2-Dimethylbutane > 2-methylpentane ......... boiling point
III. cis-But-2-ene > trans-But-2-ene ......... dipole moment

One litre of \(0.15 \mathrm{M} \mathrm{Na}_2 \mathrm{SO}_3\) aqueous solution is mixed with \(500 \mathrm{~mL}\) of \(0.2 \mathrm{M} \mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7\) aqueous solution in acid medium. What is the number of moles of \(\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7\) remaining in the solution after the reaction?

The bond angle between \(\mathrm{C}-\mathrm{O}\) and \(\mathrm{O}-\mathrm{H}\) bonds in alcohols is close to

Which among the following isoelectronic species has the smallest size?
\[
\mathrm{O}^{2-}, \mathrm{F}^{-}, \mathrm{Ne}, \mathrm{Na}^{+}, \mathrm{Mg}^{2+}, \mathrm{Al}^{3+}, \mathrm{Si}^{4+}
\]

Let \(\overrightarrow{\mathrm{OA}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{OB}}=-2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}+6 \hat{\mathrm{k}}\) be the position vectors of two points \(A\) and \(B\). If \(C\) is a point on the bisector \(\angle \mathrm{AOB}\) and \(\mathrm{OC}=\sqrt{42}\), then \(\overrightarrow{\mathrm{OC}}=\)

The length of the chord intercepted by the circle \(x^2+y^2-8 x-2 y-8=0\) on the line \(x+y+1=0\) is units.

A plane electromagnetic wave of frequency \(25 \mathrm{MHz}\) travels in free space along the X-direction. At a particular point in space and time the electric field is \(\vec{E}=6.3 \hat{\mathrm{j} ~ V m}{ }^{-1}\). Then the magnetic field at that point is

If the point of intersection of the pair of the transverse common tangents and that of the pair of direct common tangents drawn to the circles \(x^2+y^2-14 x+6 y+33=0\) and \(x^2+y^2+30 x-2 y+1=0\) are \(T\) and \(D\) respectively, then the centre of the circle having TD as diameter is

A hydrogen atom falls from \(\mathrm{n}^{\text {th }}\) higher energy orbit to first energy orbit ( \(\mathrm{n}=1\) ). The energy released is equal to 12.75 ev . The \(n^{\text {th }}\) orbit is

A circle passes through the centre of another circle \(x^2+y^2-3 x-4 y-1=0\) and whose centre is \((5,2)\). Then the equation of this circle is.........