Question

If (a, a²) falls inside the angle made by the lines
y = x/2, x > 0 and y = 3x, x > 0, then 'a' belongs to :

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

Answer 1

Answer: (B)

$\left( \frac { 1 } { 2 } , 3 \right)$

Answer 2

$\frac { 3 a - a ^ { 2 } } { - 1 }$ < 0

a(a – 3) < 0 .......(i)

> 0

2a² – a > 0

2a > 0.......(ii)

Solving (i) and (ii)

$\frac { 1 } { 2 }$ < a < 3