| Column I | Statement | Column II | Interval | |---|---|---|---| |

MATHEMATICS · Subjective · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

Column I	Statement	Column II	Interval
(a)	If $\log_{1/x}\left\{\frac{2(x-2)}{(x+1)(x-5)}\right\}\ge1$ , then $x$ can belong to	(p)	$\left(0,\frac{1}{3}\right]$
(b)	If $\log_3x-(\log_3x)^2\le\frac{3}{2}\log_{\frac{\sqrt2}{2}}4$ , then $x$ can belong to	(q)	$[1,2]$
(c)	If $\log_{1/2}(4-x)\ge\log_{1/2}2-\log_{1/2}(x-1)$ , then $x$ can belong to	(r)	$[3,4]$
(d)	Let $\alpha$ and $\beta$ be the roots of $(\lambda^2-3\lambda+4)x^2-4(2\lambda-1)x+16=0$ . If $\beta>1>\alpha$ , then $\lambda$ can lie in	(s)	$(3,8)$