NIMCET 2024 — Mathematics PYQ
NIMCET | Mathematics | 2024The points (1,21) and (3,−21) are
Choose the correct answer:
- A.
In between the lines 2x+3y=6 and 2x+3y=−6
(Correct Answer) - B.
on the same side of the line 2x+3y=6
- C.
on the same side of the line 2x+3y=−6
In between the lines 2x+3y=6 and 2x+3y=−6
Explanation
L1:2x+3y−6=0
L2:2x+3y+6=0
Point (1,21):
2(1)+3(0.5)−6=2+1.5−6=−2.5
2(1)+3(0.5)+6=2+1.5+6=9.5
Product of values: (-2.5)(9.5) < 0 (Point is between lines)
Point (3,−21):
2(3)+3(−0.5)−6=6−1.5−6=−1.5
2(3)+3(−0.5)+6=6−1.5+6=10.5
Product of values: (-1.5)(10.5) < 0 (Point is between lines)
Both points lie in the region where L1 and L2 have opposite signs.
Correct Option: (A)
Explanation
L1:2x+3y−6=0
L2:2x+3y+6=0
Point (1,21):
2(1)+3(0.5)−6=2+1.5−6=−2.5
2(1)+3(0.5)+6=2+1.5+6=9.5
Product of values: (-2.5)(9.5) < 0 (Point is between lines)
Point (3,−21):
2(3)+3(−0.5)−6=6−1.5−6=−1.5
2(3)+3(−0.5)+6=6−1.5+6=10.5
Product of values: (-1.5)(10.5) < 0 (Point is between lines)
Both points lie in the region where L1 and L2 have opposite signs.
Correct Option: (A)