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

The major product formed in the following reaction sequence is

The spherical harmonic function, $Y_{l,m}(\theta ,\varphi )$, with appropriate values of $l$ and $m$, is an eigen function of ${\hat{L}}_x^2+{\hat{L}}_y^2$ operator. The corresponding eigenvalue is

Consider the operators, ${\hat{a}}_{+}=\frac{1}{\sqrt{2}}(\hat{x}+i{\hat{p}}_x)$ and ${\hat{a}}_{-}=\frac{1}{\sqrt{2}}(\hat{x}-i{\hat{p}}_x)$, where $\hat{x}$ and ${\hat{p}}_x$ are the position and linear momentum operators, respectively. The commutator, $[{\hat{a}}_{+},{\hat{a}}_{-}]$ is equal to

The temperature derivative of electrochemical cell potential E at constant pressure, ${\left(\frac{\partial E}{\partial T}\right)}_P$,is given by

For an ionic micelle-forming surfactant near its critical micelle concentration (CMC), the dependence of molar conductivity and surface tension on surfactant concentration is best represented by