GATE CY 2025 Question Paper (15-Feb-2025) (Shift-1)

The major products X and Y formed in the following reaction sequences are

Compound K displayed a strong band at $1680{\text{ cm}}^{-1}$ in its IR spectrum. Its ${}^{1}H$ -NMR spectral data are as follows: $\delta$ (ppm) 7.30 (d, J = 7.2 Hz, 2H), 6.8 (d, J = 7.2 Hz, 2H), 3.8 (septet, J = 7.0 Hz, 1H), 2.2 (s, 3H), 1.9 (d, J = 7.0 Hz, 6H). The correct structure of compound K is

The major product formed in the following reaction sequences is

In the following asymmetric transformation, the key aldol reaction involves the attack of

The correct option with regard to the following statements is
(a) Time-independent Schrödinger equation can be exactly solved for $B{e}^{2+}$.
(b) For a particle confined in a one-dimensional box of length $l$ with infinite potential barriers, the trial variation function $\varphi =(\frac{3}{l^3}{)}^{1/2}|x|$ is not an acceptable trial wavefunction for $0\le x\le l$.
(c) Wavefunctions for system of Fermions must be anti-symmetric with respect to exchange of any two Fermions in the system.
(d) Born-Oppenheimer approximation can be used to separate the vibrational and rotational motion of a molecule.