Which one of the following is formed (mainly) when red phosphorus is heated in a sealed tube at \(803 \,\mathrm{~K} ?\)

Given below are two statements: Statement \((I)\) : A \(\pi\) bonding \(MO\)has lower electron density above and below the inter-nuclear axis. Statement \((II)\) : The \(\pi^*\) antibonding \(MO\) has a node between the nucles.
In the light of the above statements, choose the most appropriate answer from the options given below:

The lanthanoide that would show colour is

\(9.3 \mathrm{~g}\) of pure aniline upon diazotisation followed by coupling with phenol gives an orange dye. The mass of orange dye produced (assume \(100\)% yield/ conversion) is _______ \(g\). (nearest integer)

If the radius of the \(3^{\text {rd }}\) Bohr's orbit of hydrogen atom is \(r_{3}\) and the radius of \(4^{\text {th }}\) Bohr's orbit is \(r_{4}\). Then ....

For the reaction \(2 \mathrm{H}_{2}(\mathrm{g})+2 \mathrm{NO}(\mathrm{g}) \rightarrow \mathrm{N}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) the observed rate expression is, rate \(=\mathrm{k}_{\mathrm{f}}[\mathrm{NO}]^{2}\left[\mathrm{H}_{2}\right] .\) The rate expression of the reverse reaction is

The correct order of spin only magnetic moments for the following complex ions is

The magnetic field in a travelling electromagnetic wave has a peak value of \(20\ n T\). The peak value of electric field strength is......\(Vm^{-1}\)

The reaction rate for the reaction \(\left[\mathrm{PtCl}_{4}\right]^{2-}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons\left[\mathrm{Pt}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}_{3}\right]^{-}+\mathrm{Cl}^{-}\) was measured as a function of concentrations of different species. It was observed that \(\frac{-\mathrm{d}\left[\left[\mathrm{PtCl}_{4}\right]^{2-}\right]}{\mathrm{dt}}=4.8 \times 10^{-5}\left[\left[\mathrm{PtCl}_{4}\right]^{2-}\right]-2.4 \times10^{-3}\)
\(\left[\left[\mathrm{Pt}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}_{3}\right]^{-}\right]\left[\mathrm{Cl}^{-}\right]\) where square brackets are used to denote molar concentrations. The equilibrium constant \(\mathrm{K}_{\mathrm{c}}=....\). (Nearest integer)

If the circles \(x^2 + y^2 + 5Kx + 2y + K = 0\) and \(2(x^2 + y^2) + 2Kx + 3y -1 = 0 \), \((K \in R)\), intersect at the points \(P\) and \(Q\),then the line \(4x + 5y -K = 0 \) passes through \(P\) and \(Q\) for

Let \(S=\left\{\theta \in(0,2 \pi): 7 \cos ^{2} \theta-3 \sin ^{2} \theta-2\right.\) \(\left.\cos ^{2} 2 \theta=2\right\}\). Then, the sum of roots of all the equations \(x ^{2}-2\left(\tan ^{2} \theta+\cot ^{2} \theta\right) x +6 \sin ^{2} \theta=0\) \(\theta \in S\), is\(...\)

A solid ball of radius \(R\) has a charge density \(\rho \) given by \(\rho  = {\rho _0}\left( {1 - \frac{r}{R}} \right)\) for \(0 \leq r \leq R\). The electric field outside the ball is

A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is \(\frac{7}{\mathrm{x}}\) where \(\mathrm{x}\) is___________.