1
JEE Advanced 2024 Paper 2 Online
+3
-1
Let $S=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: x \geq 0, y \geq 0, y^2 \leq 4 x, y^2 \leq 12-2 x\right.$ and $\left.3 y+\sqrt{8} x \leq 5 \sqrt{8}\right\}$. If the area of the region $S$ is $\alpha \sqrt{2}$, then $\alpha$ is equal to
A
$\frac{17}{2}$
B
$\frac{17}{3}$
C
$\frac{17}{4}$
D
$\frac{17}{5}$
2
JEE Advanced 2021 Paper 1 Online
+3
-1
The area of the region

$$\left\{ {\matrix{ {(x,y):0 \le x \le {9 \over 4},} & {0 \le y \le 1,} & {x \ge 3y,} & {x + y \ge 2} \cr } } \right\}$$ is
A
$${{11} \over {32}}$$
B
$${{35} \over {96}}$$
C
$${{37} \over {96}}$$
D
$${{13} \over {32}}$$
3
JEE Advanced 2020 Paper 1 Offline
+3
-1
Let the functions f : R $$\to$$ R and g : R $$\to$$ R be defined by

f(x) = ex $$-$$ 1 $$-$$ e$$-$$|x $$-$$ 1|

and g(x) = $${1 \over 2}$$(ex $$-$$ 1 + e1 $$-$$ x).

The the area of the region in the first quadrant bounded by the curves y = f(x), y = g(x) and x = 0 is
A
$$(2 - \sqrt 3 ) + {1 \over 2}(e - {e^{ - 1}})$$
B
$$(2 + \sqrt 3 ) + {1 \over 2}(e - {e^{ - 1}})$$
C
$$(2 - \sqrt 3 ) + {1 \over 2}(e + {e^{ - 1}})$$
D
$$(2 + \sqrt 3 ) + {1 \over 2}(e + {e^{ - 1}})$$
4
JEE Advanced 2019 Paper 1 Offline
+3
-1
The area of the region

{(x, y) : xy $$\le$$ 8, 1 $$\le$$ y $$\le$$ x2} is
A
$$8{\log _e}2 - {{14} \over 3}$$
B
$$8{\log _e}2 - {{7} \over 3}$$
C
$$16{\log _e}2 - {{14} \over 3}$$
D
$$16{\log _e}2 - 6$$
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