Thermal decomposition of ${\mathrm{AgNO}}_3$ produces two paramagnetic gases. The total number of electrons present in the antibonding molecular orbitals of the gas that has the higher number of unpaired electrons is _____ .

The complex showing a spin-only magnetic moment of \(2.82\) B.M. is

The $1^{\mathrm{st}}$, $2^{\mathrm{nd}}$ and the $3^{\mathrm{rd}}$ ionization enthalpies, ${\mathrm{I}}_1, {\mathrm{I}}_2$ and ${\mathrm{I}}_3$, of four atoms with atomic numbers $\mathrm{n}, \mathrm{n}+1, \mathrm{n}+2,$ and $\mathrm{n}+3,$ where $\mathrm{n}<10,$ are tabulated below. What is the value of $\mathrm{n}$?

Atomic number	Ionization Enthalpy (kJ/mol)
	${\mathrm{I}}_1$	${\mathrm{I}}_2$	${\mathrm{I}}_3$
$\mathrm{n}$	$1681$	$3374$	$6050$
$\mathrm{n}+1$	$2081$	$3952$	$6122$
$\mathrm{n}+2$	$496$	$4562$	$6910$
$\mathrm{n}+3$	$738$	$1451$	$7733$

The work function ( \(\Phi\) ) of some metals is listed below. The number of metals which will show photoelectric effect when light of \(300 \mathrm{~nm}\) wavelength falls on the metal is

Not considering the electronic spin, the degeneracy of the second excited state (n = $3$) of H atom is $9$, while the degeneracy of the second excited state of ${\mathrm{H}}^{-}$ is :

Upon heating with $\mathrm{C}{\mathrm{u}}_2\mathrm{S}$ , the reagent(s) that give copper metal is/are

A monoatomic ideal gas undergoes a process in which the ratio of \(P\) to \(V\) at any instant is constant and equals to 1 . What is the molar heat capacity of the gas?

The slope of the tangent to the curve ${\left(y-x^5\right)}^2=\text{x}{\left(1+{\text{x}}^2\right)}^2$ at the point (1, 3) is ________.

A thin ring of mass \(2 \mathrm{~kg}\) and radius \(0.5 \mathrm{~m}\) is rolling without slipping on a horizontal plane with velocity 1 \(\mathrm{m} / \mathrm{s}\). A small ball of mass \(0.1 \mathrm{~kg}\), moving with velocity \(20 \mathrm{~m} / \mathrm{s}\) in the opposite directions, hits the ring at a height of \(0.75 \mathrm{~m}\) and goes vertically up with velocity 10 \(\mathrm{m} / \mathrm{s}\). Immediately after the collision

The boiling point of water in a \(0.1\) molal silver nitrate solution (solution \(\mathbf{A}\) ) is \(\mathbf{x}^{\circ} \mathrm{C}\). To this solution \(\mathbf{A}\), an equal volume of \(0.1\) molal aqueous barium chloride solution is added to make a new solution B. The difference in the boiling points of water in the two solutions \(\mathbf{A}\) and \(\mathbf{B}\) is \(\mathbf{y} \times 10^{-2}{ }^{\circ} \mathrm{C}\).
(Assume: Densities of the solutions \(\mathbf{A}\) and \(\mathbf{B}\) are the same as that of water and the soluble salts dissociate completely.
Use: Molal elevation constant (Ebullioscopic Constant), \(K_{b}=0.5 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\); Boiling point of pure water as \(100^{\circ} \mathrm{C}\).)
The value of $\mathrm{x}$ is ___.

\(\mathrm{MgSO}_4\) on reaction with \(\mathrm{NH}_4 \mathrm{OH}\) and \(\mathrm{Na}_2 \mathrm{HPO}_4\) forms a white crystalline precipitate. What is its formula?

The maximum number of possible isomers (including stereoisomers) which may be formed on mono-bromination of $1$-methylcyclohex- $1$-ene using ${\mathrm{Br}}_2$ and $\mathrm{UV}$ light is ___.

Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Indicate your answer by darkening the appropriate bubbles of the \(4 \times 4\) matrix given in the ORS.