Among the statements (a)-(d), the correct ones are:

a) Lithium has the highest hydration enthalpy among the alkali metals.

b) Lithium chloride is insoluble in pyridine.

c) Lithium cannot form ethynide upon its reaction with ethyne.

d) Both lithium and magnesium react slowly with${\mathrm{H}}_2\mathrm{O}$.

The correct option is C

$\left(\mathrm{a}\right),\left(\mathrm{c}\right)$ and $\left(\mathrm{d}\right)$ only

Explanation for correct option:

(C) $\left(a\right)\mathbf{,}\mathbf{}\left(c\right)$ and $\left(d\right)$ only

1. Lithium has the highest hydration enthalpy among alkali metals because it has smallest size and highest charge density.
2. Hence, statement $\left(\mathrm{a}\right)$ is correct.
3. Lithium cannot form ethynide upon its reaction with ethyne because it has a small size and high ionization energy which makes it difficult to remove the outermost electron.
4. Hence, statement $\left(\mathrm{c}\right)$ is also correct.
5. Both lithium and magnesium react slowly with ${\mathrm{H}}_2\mathrm{O}$ because Lithium and Magnesium have less density than water, so first these elements float on water then ultimately vanishes forming hydroxides. The reactions between Lithium and water can be given as follows:
6. $2\mathrm{Li}+2{\mathrm{H}}_2\mathrm{O}\to 2\mathrm{LiOH}+{\mathrm{H}}_2$
7. In the case of Magnesium, the reaction is so slow that it is not visible to human eye. But it reacts with steam to liberate hydrogen. The reactions are given as follows:
8. $\mathrm{Mg}+{\mathrm{H}}_2\mathrm{O}\to$No reaction
9. $\mathrm{Mg}+{\mathrm{H}}_2\mathrm{O}\stackrel{100°\mathrm{C}}{\to }\mathrm{MgO}+{\mathrm{H}}_2$
10. Hence, statement $\left(\mathrm{d}\right)$ is also correct.

Explanation for incorrect option:

(A) $\left(a\right)\mathbf{,}\mathbf{}\left(b\right)$ and $\left(d\right)$ only

1. From the above it can be observed that statement $\left(\mathrm{a}\right)$ and $\left(\mathrm{d}\right)$ are correct.
2. The statement lithium chloride is insoluble in pyridine is incorrect.
3. This is so because lithium chloride is a covalent compound, so it is soluble in organic solvents like pyridine.
4. Hence statement $\left(\mathrm{b}\right)$ is incorrect.

(B) $\left(b\right)$ and $\left(c\right)$ only

From the above discussion, it can be observed that statement $\left(\mathrm{b}\right)$ is incorrect but statement $\left(\mathrm{c}\right)$ is correct.

(D) $\left(a\right)$ and $\left(d\right)$ only

From the above discussion it can be observed that statement $\left(\mathrm{a}\right)$ and $\left(\mathrm{d}\right)$ are correct but also statement $\left(\mathrm{c}\right)$ is correct, which is not mentioned here.

Hence option C is correct, as statements $\left(\mathrm{a}\right),\left(\mathrm{c}\right)$ and $\left(\mathrm{d}\right)$ are correct.