GATE CY 2023 Question Paper (05-Feb-2023) (Shift 2)

The major product obtained by the treatment of (η⁵ -C₅H₅)₂Ni with Na/Hg in ethanol is

The number of shared corners of the constituent SiO₄ units in orthosilicate, pyrosilicate, cyclic silicate and sheet silicate, respectively, are

Concentration of Q in a consecutive reaction $\mathrm{P}\stackrel{{\mathrm{k}}_1}{\to }\mathrm{Q}\stackrel{{\mathrm{k}}_2}{\to }\mathrm{R}$ is given by $[\mathrm{Q}]=\frac{{\mathrm{k}}_1]\mathrm{p}{]}_0}{{\mathrm{k}}_2-{\mathrm{k}}_1}[{\mathrm{e}}^{-{\mathrm{k}}_1\mathrm{t}}-{\mathrm{e}}^{-{\mathrm{k}}_2\mathrm{t}}]$, where [𝑃]₀ is the initial concentration of P. If the value of 𝑘₂ = 25 s⁻¹ , the value of 𝑘₁ that leads to the longest waiting time for Q to reach its maximum is

The wave function for Be³⁺ in a certain state is given by $\psi =\mathrm{N}{\mathrm{e}}^{-\left(\frac{4}{{\mathrm{a}}_0}\mathrm{r}\right)}$, where 𝑁 is the normalization constant, 𝑟 is the distance of the electron from the nucleus and 𝑎₀ is the Bohr radius. The most probable distance of the electron from the nucleus in this state is

Match the following