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Saturday, 31 October

JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 3 April 2025, Shift 1, Maths Q13

Question 13 of 75 in this shift, Maths question 13 of 25, Section A.

A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines L1:2x+y+6=0\mathrm{L}_1 : 2x + y + 6 = 0 and L2:4x+2y−p=0, p>0\mathrm{L}_2 : 4x + 2y - p = 0,\ p > 0, at the points A and B, respectively. If AB=92\mathrm{AB} = \frac{9}{\sqrt{2}} and the foot of the perpendicular from the point A on the line L2\mathrm{L}_2 is M, then AMBM\frac{\mathrm{AM}}{\mathrm{BM}} is equal to
  1. (1)2
  2. (2)3Official answer
  3. (3)4
  4. (4)5

Official answer

Option 2

NTA final key.

Chapter
Straight Lines
Topic
Straight Line Distance
Idea tested
Distance between parallel lines

Same idea in other shifts

Asked 4× in all
  1. 4 Apr 2024, Shift 1 · Q16The vertices of a triangle are A(−1,3)(-1, 3), B(−2,2)(-2, 2) and C(3,−1)(3, -1). A new triangle is formed by shifting the sides of the triangle by…MediumSingle correct
  2. 3 Aug 2021, Shift 1 · Q72The sum of the values of 'a' for which circles of radius 53\frac{\sqrt{5}}{3}, touch the straight lines, x−2y−a=0x - 2y - a = 0 and…MediumSingle correct
  3. 5 Sep 2020, Shift 1 · Q74If the line, 2x−y+3=02x-y+3=0 is at a distance 15\frac{1}{\sqrt{5}} and 25\frac{2}{\sqrt{5}} from the lines 4x−2y+α=04x-2y+\alpha=0 and…MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.