Straight Lines
Straight Lines
nta_pyq_2025_jan
Grade 11
Question:
Let the points ( 11 , \alpha) lie on or inside the triangle with sides x + y = 11, x + 2y = 16 and 2x + 3y = 29. Then 2 the product of the smallest and the largest values of \alpha is equal to :
Step-by-Step Solution
Key Concept: Apply the core result for lines, slopes and distances and simplify using the given constraints.
(3) Clearly, x = 11 2 intersect x + y - 11 = 0 at ( 11 2 , 11 2 ) and 2x + 3y - 29 = 0 at ( 11 2 , 6) \Rightarrow \alpha = [ 11 2 , 6] 11 \alphamin ⋅ \alphamax = ⋅ 6 = 33 2
Correct Answer: 3