JEE Main 2026 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 4 April 2026, Shift 1, Maths Q24

Question 24 of 75 in this shift, Maths question 24 of 25, Section B.

Let

\vec{a}_k=(\tan\theta_k)\hat{i}+\hat{j}

and

\vec{b}_k=\hat{i}-(\cot\theta_k)\hat{j}

, where

\theta_k=\frac{2^{k-1}\pi}{2^n+1}

, for some

n\in\mathbb{N}

n>5

. Then the value of

\frac{\sum_{k=1}^{n}|\vec{a}_k|^2}{\sum_{k=1}^{n}|\vec{b}_k|^2}

is ______.

Official answer

NTA final key.