JEE Main 2022 · 27 Jul · Shift 2 · Mathematics Q6

MathematicsSingle correct+4 / -1Question 6 of 90

Let $f(x)=2+|x|-|x-1|+|x+1|$ , $x\in\mathbf R$ .

Consider

(S1) : $f'\left(-\dfrac32\right)+f'\left(-\dfrac12\right)+f'\left(\dfrac12\right)+f'\left(\dfrac32\right)=2$

(S2) : $\displaystyle\int_{-2}^2f(x)\,dx=12$

Then,

both (S1) and (S2) are correct

both (S1) and (S2) are wrong

only (S1) is correct

only (S2) is correct

Answer and worked solution

Official answer: D

Pieces. f is $-x$ , $2+x$ , $2+3x$ , $4+x$ on $(-\infty,-1)$ , $(-1,0)$ , $(0,1)$ , $(1,\infty)$ .

(S1). $-1+1+3+1=4\ne2$ , so it is wrong.

(S2). $1.5+1.5+3.5+5.5=12$ , so it is correct.

(D)

Topics:Properties of definite integrals Differentiability

JEE Main 2022 · 27 Jul · Shift 2, Mathematics question 6