Question

If the point $(a,2)$ lies between the lines $x-y-1=0$ and $2(x-y)-5=0$, then the set of values of $a$ is -

• A. $(-\infty ,3)\cup (\frac{9}{2},\infty )$
• B. $(3,\frac{9}{2})$
• C. $(-\infty ,3)$
• D. $(\frac{9}{2},\infty )$

Answer 1

The correct option is B $(3,\frac{9}{2})$

$x-y=1$ and $x-y=\frac{5}{2}$

if point $(a,2)$ lies between these two lines.

then

$1<(a-2)<\frac{5}{2}$

$\Rightarrow 3<a<\frac{9}{2}$

$\therefore B$