CAT 2020 Quant Question [Slot 1] with Solution 11

Question

The area of the region satisfying the inequalities \(|x| - y \le 1,y \ge 0\) and \(y \le 1\) is

Option: 3
Solution:

The graph of \(|x| - y \le 1;y \ge 0\) and \(y \le 1\) is as follows:

Area of \(ABCD = \) Area of EFCD - Area of EAD - Area of BFC

\( = EF \times FC - \frac{1}{2} \times EA \times ED - \frac{1}{2} \times BF \times FC\)

\( = 4 \times 1 - \frac{1}{2} \times 1 \times 1 - \frac{1}{2} \times 1 \times 1\)

\( = 4 - 1 = 3\) Square units.

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