Match the columns

MATHEMATICS · Subjective · ISC · Mathematics · Calculus · Calculus

Problem

Match the columns.

Column I	Column II
(a) $\lim_{n\to\infty}\cos^2\!\left(\pi\sqrt[3]{n^3+n^2+2n-n}\right)$ , where $n$ is an integer	(p) $\frac{1}{2}$
(b) $\lim_{n\to\infty}n\sin\!\left(2\pi\sqrt{1+n^2}\right)$ , where $n\in\mathbb{N}$	(q) $\frac{1}{4}$
(c) $\lim_{n\to\infty}(-1)^n\sin\!\left(\pi\sqrt{n^2+0.5n+1}\right)\sin\!\left(\frac{(n+1)\pi}{4n}\right)$ , where $n\in\mathbb{N}$	(r) $\pi$
(d) If $\lim_{x\to\infty}\left(\frac{x+a}{x-a}\right)^x=e$ , where $a$ is a real constant, find $a$ .	(s) non-existent