JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 7 April 2025, Shift 2, Maths Q15

Question 15 of 75 in this shift, Maths question 15 of 25, Section A.

Let

\vec{a}

and

\vec{b}

be the vectors of the same magnitude such that

\frac{|\vec{a}+\vec{b}|+|\vec{a}-\vec{b}|}{|\vec{a}+\vec{b}|-|\vec{a}-\vec{b}|}=\sqrt{2}+1

. Then

\frac{|\vec{a}+\vec{b}|^2}{|\vec{a}|^2}

is :

(1) $2+\sqrt{2}$ Official answer
(2) $4+2\sqrt{2}$
(3) $1+\sqrt{2}$
(4) $2+4\sqrt{2}$

Official answer

Option 1

NTA final key.

Chapter: Vector Algebra
Topic: Dot Product
Idea tested: Expansion of Sum of Vectors Squared

Same idea in other shifts

Asked 3× in all

30 Jan 2024, Shift 2 · Q18Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{b}| = 1$ and $|\vec{b} \times \vec{a}| = 2$ . Then…EasySingle correct
6 Sep 2020, Shift 2 · Q74If $\vec{x}$ and $\vec{y}$ be two non-zero vectors such that $|\vec{x}+\vec{y}|=|\vec{x}|$ and $2\vec{x}+\lambda\vec{y}$ is perpendicular…EasyNumerical 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 42 of the 174 JEE Main shifts held from 2017 to 2026.