Match List -I with List-II

Choose the correct answer from the options given below :

(A)-(IV), (B)-(III),(C)-(I),(D)-(II)

The correct answer is Option (2) → (A)-(IV), (B)-(III),(C)-(I),(D)-(II)

(A) $\lim\limits_{x→0}\frac{1-\cos 2x}{x}=\lim\limits_{x→0}\frac{2\sin^2x}{x}$

$=2×1×0=0$ (IV)

(B) $\lim\limits_{x→0}\frac{\sin 2x×2}{(x×2)}=1×2=2$ (III)

(C) $\lim\limits_{x→1}\frac{x^5-1}{x^2-1}=\frac{0}{0}form$

Using L'hopital's rule

$\lim\limits_{x→1}\frac{5x^4}{2x}=\frac{5}{2}$ (I)

(D) $\lim\limits_{x→0}\frac{(x+1)^5-1}{x}=\frac{0}{0}form$

Using L'hopital's rule

$\lim\limits_{x→0}\frac{5(x+1)^4}{1}=5$ (II)