Verified Solution • 2025–26 Session moderate

QJEEM24Mae7a0: JEE Main 2024 Mathematics - Class 11 JEEM24Mae7a0 Solution: The portion of the line in the first quadrant is trisected by…

The portion of the line 4x+5y=204 x+5 y=20 in the first quadrant is trisected by the lines L1\mathrm{L}_1 and L2\mathrm{L}_2 passing through the origin. The tangent of an angle between the lines L1\mathrm{L}_1 and L2\mathrm{L}_2 is :

Multiple Choice Options

  • A 3041\frac{30}{41}
  • B 85\frac{8}{5}
  • C 25\frac{2}{5}
  • D 2541\frac{25}{41}

Step-by-Step Verified Solution

Co-ordinates of A=(53,83)\mathrm{A}=\left(\frac{5}{3}, \frac{8}{3}\right)

Co-ordinates of B=(103,43)\mathrm{B}=\left(\frac{10}{3}, \frac{4}{3}\right)

Slope of OA=m1=85\mathrm{OA}=\mathrm{m}_1=\frac{8}{5}

Slope of OB=m2=25\mathrm{OB}=\mathrm{m}_2=\frac{2}{5}

JEE Main 2024 (Online) 27th January Morning Shift Mathematics - Straight Lines and Pair of Straight Lines Question 31 English Explanation

amp;tan⁡θ=∣m1−m21+m1m2∣amp;tan⁡θ=651+1625=3041amp;tan⁡θ=3041\begin{aligned}& \tan \theta=\left|\frac{m_1-m_2}{1+m_1 m_2}\right| \\& \tan \theta=\frac{\frac{6}{5}}{1+\frac{16}{25}}=\frac{30}{41} \\& \tan \theta=\frac{30}{41}\end{aligned}

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