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JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 29 January 2024, Shift 1, Maths Q17

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

Let

\vec{a},\vec{b}

and

\vec{c}

be three non-zero vectors such that

\vec{b}

and

\vec{c}

are non-collinear. If

\vec{a}+5\vec{b}

is collinear with

\vec{c}

,

\vec{b}+6\vec{c}

is collinear with

\vec{a}

and

\vec{a}+\alpha\vec{b}+\beta\vec{c}=\vec{0}

, then

\alpha+\beta

is equal to

(1) $-25$
(2) $-30$
(3) $30$
(4) $35$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Vector Algebra
Topic: Linear Independence
Idea tested: Linear Combination Concept

Same topic in other shifts

All Linear Independence questions

28 Jul 2022, Shift 1 · Q3Let the vectors $\vec{a}=(1+t)\hat{i}+(1-t)\hat{j}+\hat{k},\ \vec{b}=(1-t)\hat{i}+(1+t)\hat{j}+2\hat{k}$ and…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 42 of the 174 JEE Main shifts held from 2017 to 2026.