First slide

Equation of line in Straight lines

Question

The point $(a^{2}, a)$ lies between the straight lines $x + y = 6 and x + y = 2$ for

Moderate

A

all values of $a$
B

no value of $a$
C

$| 2 a - 3 | < 1$
D

$| 2 a + 5 | > 1$

Solution

$(a^{2}, a)$ lies between the given lines
if $a^{2} + a - 6 > 0 and a^{2} + a - 2 < 0$ ..(1)
or $a^{2} + a - 6 < 0 and a^{2} + a - 2 > 0$ ..(2)
(1) does not hold for any value of $a$
From $(2) - 3 < a < 2 and [a < - 2 or a > 1]$
$\begin{array}{l} \Rightarrow - 3 < a < - 2 or 1 ∣< a < 2 \\ \Rightarrow | 2 a + 5 | < 1 or | 2 a - 3 | < 1 \end{array}$

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