JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 10 April 2023, Shift 1, Maths Q17

Question 17 of 90 in this shift, Maths question 17 of 30, Section A.

An arc PQ of a circle subtends a right angle at its centre O. The mid point of the arc PQ is R. If

\overrightarrow{OP}=\vec{u}

\overrightarrow{OR}=\vec{v}

and

\overrightarrow{OQ}=\alpha\vec{u}+\beta\vec{v}

, then

\alpha,\beta^2

are the roots of the equation

(1) $3x^2-2x-1=0$
(2) $3x^2+2x-1=0$
(3) $x^2-x-2=0$ Official answer
(4) $x^2+x-2=0$

Official answer

Option 3

NTA final key.

Chapter: Vector Algebra
Topic: Linear Independence
Idea tested: Unique Linear Combinations

Same topic in other shifts

All Linear Independence questions

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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.