The locus of the centre of a circle which touches externally the circle $x^2 + y^2 - 6x - 6y + 14 = 0$ and also touches the $y$-axis is given by the equation:

Which one of the following orders is correct for the first ionisation energies of the elements?

The complete hydrolysis of $ICl , ClF _3$ and $BrF _5$, respectively, gives

An air column in a tube $32 ~cm$ long,closed at one end,is in resonance with a tuning fork. The air column in another tube,open at both ends,of length $66 ~cm$ is in resonance with another tuning fork. When these two tuning forks are sounded together,they produce $8$ beats per second. Then the frequencies of the two tuning forks are (Consider fundamental frequencies only):

Calculate the $pOH$ of a solution at $25\,^{\circ}C$ that contains $1 \times 10^{-10} \, M$ of hydronium ions,i.e.,$H_3O^{+}$.

Three perfect gases at absolute temperatures $T_1, T_2$ and $T_3$ are mixed. The masses of molecules are $m_1, m_2$ and $m_3$ and the number of molecules are $n_1, n_2$ and $n_3$ respectively. Assuming no loss of energy,the final temperature of the mixture is