GATE CY 2018 Question Paper (04-Feb-2018) (Shift 2)

The major product of the following reaction sequence is

The major product formed in the following retro-aldol reaction is

The elimination product of the following reaction is

A one-dimensional anharmonic oscillator is treated by perturbation theory. The harmonic oscillator is used as the unperturbed system and the perturbation is $\frac{1}{6}\gamma x^3$ ($\gamma$ is a constant). Using only the first order correction, the total ground state energy of the anharmonic oscillator is
(Note: For a one-dimensional harmonic oscillator ${\psi }_0(x)=(\frac{\alpha }{\pi }{)}^{1/4}{e}^{-\alpha x^2};\alpha =(\frac{k\mu }{{\hslash }^2}{)}^{1/2}$)

The $O_2$ coordinated to metal ion centres in oxy-myoglobin and oxy-hemocyanin exists,respectively, as