Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The point (a 2 , a + 1) lies in the angle between the lines 3x – y + 1 = 0 and x + 2y – 5 = 0 containing the origin, if-
A
a ∈ (–3, 0) ∪ 
B
a ∈ (– ∞ , 3) ∪ 
C
a ∈ 
D
a ∈ 
Text Solution
Verified by ExpertsThe correct answer is:
A
Since origin and the point (a 2 , a + 1) lie on the same side of both the lines, therefore we have
3a 2 – (a + 1) + 1 > 0
i.e. a(3a – 1) > 0
gives a ∈ (– ∞ , 0) ∪ 
and a 2 + 2(a + 1) – 5 < 0
i.e. a 2 + 2a – 3 < 0
i.e. (a – 1) (a + 3) < 0
gives a ∈ (–3, 1)
Intersection of the above inequalities gives
a ∈ (–3, 0) ∪ 
.
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