Which of the following graphs are correct for a first order reaction?

For the first order reaction,k=2.303tlog [R]0[R]⇒kt2.303=log [R]0[R]              log RoR=k2.303x t+0           ↑             ↑         ↑   ↑          y =          m           x +c Correct plot of log RoR can be represented by (d)where, slope = k2.303The time taken for any fraction of the reaction to complete is independent of the initial concentration.Let, us consider it for half of the reaction to complete.              t=2303klog aa−xFor half-life (t)=t1/2 and x=a2                   t1/2=2.303klog aa−a2           t1/2=2.303klog 2    Half-life time  t1/2=0.693kt12is independent of initial concentration. Hence, correct plot of t12 and Rocan be represented by option (a).