Question

If the point $(1, a)$ lies between the straight lines $x + y = 1$ and $2(x+y) = 3$ then a lies in interval

• A. $\left(\frac{3}{2},\infty\right)$
• B. $\left(1,\frac{3}{2}\right)$
• C. $\left(-\infty, 0\right)$
• D. $\left(0,\frac{1}{2}\right)$

Answer 1

Answer: (D)

Since, $(1, a)$ lies between $x + y = 1$
and $2(x+y) = 3$
$\therefore $ Put $x = 1$ in $2\left(x+y\right) = 3$.
We get the range of y. Thus,
$2\left(1+y\right) = 3 \Rightarrow y = \frac{3}{2}-1 = \frac{1}{2}$
Thus ‘a’lies in $\left(0, \frac{1}{2}\right)$