The half-life of a first order reaction: (A) depends on the reactant…

The correct answer is Option (2) → B, C

For a first order reaction, ln([R]₀/[R]) = kt. At t = t_1/2, [R] = [R]₀/2:

    t_1/2 = 2.303 log 2 / k = 0.693/k

(A) depends on the reactant concentration raised to the first power — False. [R]₀ does not appear in t_1/2 = 0.693/k (that is true of a zero order reaction).
(B) depends on rate constant — True. t_1/2 is inversely proportional to k.
(C) is independent of the reactant concentration — True. The half-life is the same whatever the starting concentration.
(D) is independent of rate constant — False. It contradicts t_1/2 = 0.693/k.

NCERT (2026-27 edition):
Half-Life of a Reaction – “… t_1/2 = 0.693/k (3.17)
It can be seen that for a first order reaction, half-life period is constant, i.e., it is independent of initial concentration of the reacting species. The half-life of a first order equation is readily calculated from the rate constant and vice versa.”