MyGoalPrep LogoMyGoalPrep.com

Jee Main 2025Medium JEE math MCQ

Let the lines $3x - 4y - \alpha = 0$, $8x - 11y - 33 = 0$, and $2x - 3y + \lambda = 0$ be concurrent. If the image of the point $(1, 2)$ in the line $2x - 3y + \lambda = 0$ is $\left(\frac{57}{13}, \frac{-40}{13}\right)$, then $|\alpha\lambda|$ is equal to
  1. A. $84$
  2. B. $113$
  3. C. $91$
  4. D. $101$

Solution

The correct option is **C**. (C. $91$)

MATH

mediumPYQ Reworded
Question
Read carefully, then pick the best option.
Let the lines 3x4yα=03x - 4y - \alpha = 0, 8x11y33=08x - 11y - 33 = 0, and 2x3y+λ=02x - 3y + \lambda = 0 be concurrent. If the image of the point (1,2)(1, 2) in the line 2x3y+λ=02x - 3y + \lambda = 0 is (5713,4013)\left(\frac{57}{13}, \frac{-40}{13}\right), then αλ|\alpha\lambda| is equal to
AI hints
Ask for a nudge. Keep it specific.
Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep