GATE CY 2024 Question Paper (03-Feb-2024) (Shift 1)

Fischer presentation of D-(-)-fructose is given below.

The correct structure of $\alpha$ -L-(+)-fructofuranose is

The major products X and Y in the following reaction sequence are

The major products E and F in the following reaction sequence are

${\Psi }_1,{\Psi }_2,{\Psi }_3$, and ${\Psi }_4$ are four Hückel molecular orbitals of benzene with orbital energies $E_1,E_2,E_3$, and $E_4$, respectively.
${\Psi }_1=\frac{1}{2}({\Phi }_B+{\Phi }_C-{\Phi }_E-{\Phi }_F)$
${\Psi }_2=6^{-\frac{1}{2}}({\Phi }_A-{\Phi }_B+{\Phi }_C-{\Phi }_D+{\Phi }_E-{\Phi }_F)$
${\Psi }_3=6^{-\frac{1}{2}}({\Phi }_A+{\Phi }_B+{\Phi }_C+{\Phi }_D+{\Phi }_E+{\Phi }_F)$
${\Psi }_4=12^{-\frac{1}{2}}(2{\Phi }_A+{\Phi }_B-{\Phi }_C-2{\Phi }_D-{\Phi }_E+{\Phi }_F)$
The correct order of the orbital energies is
(The six carbon atoms of benzene are denoted by A to F and ${\Phi }_j$ is the $2p_z$ orbital of $J^{th}$ carbon of benzene.)

Consider the following six vibrational modes:
symmetric stretching of $C{O}_2$, O-H symmetric stretching of $H_{2}O$, stretching of HCl, stretching of $H_2$, N-H symmetric stretching of $N{H}_3$, and bending of $C{O}_2$.
Among these modes, if k number of modes are IR active but Raman inactive, l number of modes are IR inactive but Raman active, and m number of modes are both IR and Raman active.
k, l, and m, respectively, are