JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 28 June 2022, Shift 1, Maths Q25

Question 25 of 90 in this shift, Maths question 25 of 30, Section B.

A ray of light passing through the point P(2, 3) reflects on the

x

-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ratio 2:1. Let the co-ordinates of the foot of the perpendicular M from R on the bisector of the angle PAQ be

(\alpha, \beta)

. Then, the value of

7\alpha+3\beta

is equal to __________.

Official answer

NTA final key.

Chapter: Straight Lines
Topic: Straight Line Distance
Idea tested: Image of a point in a line

Same idea in other shifts

Asked 7× in all

8 Apr 2024, Shift 2 · Q15If the image of the point $(-4, 5)$ in the line $x + 2y = 2$ lies on the circle $(x+4)^2 + (y-3)^2 = r^2$ , then r is equal to :EasySingle correct
8 Apr 2024, Shift 2 · Q22Let a ray of light passing through the point $(3, 10)$ reflects on the line $2x + y = 6$ and the reflected ray passes through the point…MediumNumerical value
9 Apr 2024, Shift 1 · Q14A ray of light coming from the point $P(1,2)$ gets reflected from the point Q on the $x$ -axis and then passes through the point $R(4,3)$ .…MediumSingle correct
29 Jan 2024, Shift 1 · Q15In a $\Delta ABC$ , suppose $y=x$ is the equation of the bisector of the angle $B$ and the equation of the side $AC$ is $2x-y=2$ . If…HardSingle correct
25 Feb 2021, Shift 1 · Q70The image of the point (3, 5) in the line $x - y + 1 = 0$ , lies on :EasySingle correct
6 Sep 2020, Shift 2 · Q64Let L denote the line in the $xy$ -plane with $x$ and $y$ intercepts as 3 and 1 respectively. Then the image of the point $(-1,-4)$ in this…EasySingle correct

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.