Mathematics

Problem

Match Column I with Column II.

Column I	Column II
(a) If $\lim_{x\to\infty}(\sqrt{x^2-x-1})-ax-b=0$ , where $a>0$ , then there exists at least one $a$ and $b$ for which point $(a,2b)$ lies on the line.	(p) $y=-3$
(b) If $\lim_{x\to 0}\frac{(1+a^3)+8e^{1/x}}{1+(1-b^3)e^{1/x}}=2$ , then there exists at least one $a$ and $b$ for which point $(a,b^3)$ lies on the line.	(q) $3x-2y-5=0$
(c) If $\lim_{x\to\infty}(\sqrt{x^4-x^2+1})-ax^2-b=0$ , then there exists at least one $a$ and $b$ for which point $(a,-4b)$ lies on the line.	(r) $15x-2y-11=0$
(d) If $\lim_{x\to a}\frac{x^7+a^7}{x+a}=7$ where $a<0$ , then there exists at least one $a$ for which point $(-a,2)$ lies on the line.	(s) $y=2$