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JEE Main 202524 JanuaryEvening Shift
Exam
JEE Main
Year
2025
Date
24 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2025 · 24 January · Evening Shift · Mathematics · Straight Lines

Let the points ((11)/(2), α) lie on or inside the triangle with...

Let the points (112,α)\left(\frac{11}{2}, \alpha\right) lie on or inside the triangle with sides x+y=11,x+2y=16and2x+3y=29x+y=11, x+2 y=16 and 2 x+3 y=29. Then the product of the smallest and the largest values of α\alpha is equal to :Let the points ((11)/(2), α) lie on or inside the triangle with sides x+y=11, x+2 y=16 and 2 x+3 y=29 . Then the

Options

  1. A44
  2. B22
  3. C33
  4. D55

Correct answer

C. 33

Step-by-step solution

Let the points ((11)/(2), α) lie on or inside the triangle with sides x+y=11, x+2 y=16 and 2 x+3 y=29 . Then the
Clearly, x=112x=\frac{11}{2} intersect x+y−11=0x+y-11=0 at \left(\frac{11}{2}, \frac{11}{2}\right)and2x+3y−29=0at(112,6)⇒α=[112,6]αmin⁡⋅αmax⁡=112⋅6=33and 2 x+3 y-29=0 at \left(\frac{11}{2}, 6\right) \Rightarrow \alpha=\left[\frac{11}{2}, 6\right] \alpha_{\min } \cdot \alpha_{\max }=\frac{11}{2} \cdot 6=33
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