Verified Solution • 2025–26 Session moderate

QJEEM24Ma5ce7: JEE Main 2024 Mathematics - Class 12 JEEM24Ma5ce7 Solution: Let x = m n ( m , n are co-prime natural numbers) be a solution …

Let x=mn (m,n are co-prime natural numbers) be a solution of the equation cos⁡(2sin−1⁡x)=19 and let α,β(α>β) be the roots of the equation mx2−nx−m+n=0. Then the point (α,β) lies on the line

Multiple Choice Options

  • A 3x−2y=−2
  • B 3x+2y=2
  • C 5x+8y=9
  • D 5x−8y=−9

Step-by-Step Verified Solution

Assume sin−1⁡x=θ

cos⁡(2θ)=19sin⁡θ=±23

as m and n are co-prime natural numbers,

x=23

i.e. m=2,n=3

So, the quadratic equation becomes 2x2−3x+1=0 whose roots are α=1,β=12

(1,12) lies on 5x+8y=9

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