JEE Main 2022 · 26 Jun · Shift 1 · Mathematics Q19

MathematicsSingle correct+4 / -1Question 19 of 90

Let $f(x)=2\cos^{-1}x+4\cot^{-1}x-3x^2-2x+10$ , $x\in[-1,1]$ . If $[a,b]$ is the range of the function $f$ , then $4a-b$ is equal to :

11-\pi

11+\pi

15-\pi

Answer and worked solution

Official answer: B

Monotonic. $f'(x)=-\dfrac2{\sqrt{1-x^2}}-\dfrac4{1+x^2}-6x-2\le-2-2+4=0$ on $[-1,1]$ , so $f$ decreases.

Ends. $f(1)=0+\pi-3-2+10=\pi+5=a$ and $f(-1)=2\pi+3\pi-3+2+10=5\pi+9=b$ .

Value. $4a-b=11-\pi$ .

(B)

JEE Main 2022 · 26 Jun · Shift 1, Mathematics question 19