If $f(x)=\sin\left(\cos^{-1}\left(\frac{1-2^{2x}}{1+2^{2x}}\right)\right)$ and its first derivative with respect to $x$ is $-\frac{b}{a}\log_{e}2$ when $x=1$, where a and b are integers, then the minimum value of $|a^{2}-b^{2}|$ is __________.

JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 17 March 2021, Shift 1, Maths Q89

Question 89 of 90 in this shift, Maths question 29 of 30, Section B.

f(x)=\sin\left(\cos^{-1}\left(\frac{1-2^{2x}}{1+2^{2x}}\right)\right)

and its first derivative with respect to

x

-\frac{b}{a}\log_{e}2

when

x=1

, where a and b are integers, then the minimum value of

|a^{2}-b^{2}|

is __________.

Official answer

481

NTA final key.