MHTCET 20 Apr 2026 Shift 1 Paper

Concept:The two curves form a symmetric diamond-shaped region, so its area is half the product of the diagonals.Explanation:The curves are $y=|x|-1$ and $y=-|x|+1$.At their intersection, $|x|-1 = -|x|+1$.This gives $2|x| = 2$, so $|x|=1$, hence $x=\pm 1$.At $x=\pm 1$, $y=0$, so the intersection points are $(-1,0)$ and $(1,0)$.The curve $y=|x|-1$ is a V-shape with vertex at $(0,-1)$.The curve $y=-|x|+1$ is an inverted V-shape with vertex at $(0,1)$.Together, they enclose a diamond with vertices $(-1,0)$, $(0,1)$, $(1,0)$, and $(0,-1)$.The horizontal diagonal has length $2$, and the vertical diagonal also has length $2$.Area $= \frac{1}{2} \times 2 \times 2 = 2$ square units.Answer:The area bounded by the curves is $2$ sq. units, which is Option B.