1
JEE Main 2023 (Online) 1st February Evening Shift
+4
-1 The area of the region given by $$\{ (x,y):xy \le 8,1 \le y \le {x^2}\}$$ is :

A
$$16{\log _e}2 - {{14} \over 3}$$
B
$$8{\log _e}2 - {{13} \over 3}$$
C
$$16{\log _e}2 + {7 \over 3}$$
D
$$8{\log _e}2 + {7 \over 6}$$
2
JEE Main 2023 (Online) 30th January Evening Shift
+4
-1 Let $q$ be the maximum integral value of $p$ in $[0,10]$ for which the roots of the equation $x^2-p x+\frac{5}{4} p=0$ are rational. Then the area of the region $\left\{(x, y): 0 \leq y \leq(x-q)^2, 0 \leq x \leq q\right\}$ is :
A
$\frac{125}{3}$
B
243
C
164
D
25
3
JEE Main 2023 (Online) 29th January Evening Shift
+4
-1 The area of the region $$A = \left\{ {(x,y):\left| {\cos x - \sin x} \right| \le y \le \sin x,0 \le x \le {\pi \over 2}} \right\}$$ is

A
$$\sqrt 5 + 2\sqrt 2 - 4.5$$
B
$$1 - {3 \over {\sqrt 2 }} + {4 \over {\sqrt 5 }}$$
C
$$\sqrt 5 - 2\sqrt 2 + 1$$
D
$${3 \over {\sqrt 5 }} - {3 \over {\sqrt 2 }} + 1$$
4
JEE Main 2023 (Online) 29th January Morning Shift
+4
-1

Let $$\Delta$$ be the area of the region $$\left\{ {(x,y) \in {R^2}:{x^2} + {y^2} \le 21,{y^2} \le 4x,x \ge 1} \right\}$$. Then $${1 \over 2}\left( {\Delta - 21{{\sin }^{ - 1}}{2 \over {\sqrt 7 }}} \right)$$ is equal to

A
$$2\sqrt 3 - {1 \over 3}$$
B
$$2\sqrt 3 - {2 \over 3}$$
C
$$\sqrt 3 - {4 \over 3}$$
D
$$\sqrt 3 - {2 \over 3}$$
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