Root mean square \((\mathrm{rms})\) speed of \(\mathrm{O}_2\) is \(500 \mathrm{~m} / \mathrm{s}\) at a constant temperature. Calculate the rms speed and the average kinetic energy of \(\mathrm{H}_2\) at the same temperature. (Consider, \(\left.R=8.33 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)\)

Assertion (A) : The bond dissociation energy increases from ${\mathrm{F}}_2$ to ${\mathrm{Cl}}_2$ and then decreases to ${\mathrm{I}}_2$ Reason (R) : The low bond energy of fluorine is due to the repulsion between the lone pairs of electrons in two fluorine atoms.
The correct option among the following is

The heat of combustion \(\left(\mathrm{kJ} \mathrm{mol}^{-3}\right\}\) is highest for

The experimental depression in freezing point of a dilute solution is \(0.025 \mathrm{~K}\). If the van't Hoff factor (i) is 2.0 , the calculated depression in freezing point (in \(\mathrm{K}\) ) is

The mass of Haemoglobin in $\mathrm{mg}$ required to protect from coagulation of $50 \mathrm{mL}$ of a gold sol on adding $5 \mathrm{mL}$ of $10\% \mathrm{NaCl}$ solution is: (gold number of Haemoglobin $=0.03$)

The number of sigma and pi \((\pi)\) bonds present in benzene respectively are :

An aqueous solution of \(98 \%(w / w) \mathrm{H}_2 \mathrm{SO}_4\) has density of \(1.02 \mathrm{~g} / \mathrm{cc}\). The molality of the solution is

The set of values of \(x\) for which the inequalities \(x^2-3 x-10 < 0, \quad 10 x-x^2-16>0 \quad\) hold simultaneously, is

A cell of emf \(10 \mathrm{~V}\) and internal resistance \(3 \Omega\) is connected in parallel with another cell of emf \(7 \mathrm{~V}\) and internal resistance \(\frac{3}{5} \Omega\), such that their positive terminals are joined together and so their are negative terminals. Their positive terminals are joined with the negative terminal and their negative terminal is joined with the positive terminal of a third cell of emf \(20 \mathrm{~V}\) with internal resistance \(2 \Omega\). The combination can be replaced by a battery of emf \(E\) and internal resistance \(r\), then the values of \(E\) and \(R\) are respectively

From a point $A\left(0,3\right)$ on the circle ${\left(x+2\right)}^2+{\left(y-3\right)}^2=4$, a chord $AB$ is drawn and it is extended to a point $Q$ such that $AQ=2 AB$. Then the locus of $Q$ is

If \(\frac{2+3 i}{i-2}-\frac{4 i-3}{3+4 i}=x+i y\), then \(3 x+y=\)

The solution of the differential equation \(\sqrt{1-y^2} d x+x d y-\sin ^{-1} y d y=0\), is

If \(A\) is a square matrix of order 3 , then \(\left|\operatorname{Adj}\left(\operatorname{Adj} A^2\right)\right|=\)