A wheel of radius R and mass M is placed at the bottom of a fixed...

(i) is incorrect.

If force is applied normal to surface at point $X$

$τ = {F}_{y}Rsin \theta$

Thus $τ$ depends on $\theta$ and it is not constant

(ii) is incorrect

If force applied tangentially at S

$τ = F \times R \ne 0$

But it will climb as mentioned in question.

If force is applied normal to surface at P then line of action of force will pass from Q and thus $τ = 0$

(iv) is incorrect.

If force is applied at P tangentially the $τ = F \times 2R = constant$