1
JEE Main 2022 (Online) 27th June Evening Shift
Numerical
+4
-1
Change Language

If the area of the region $$\left\{ {(x,y):{x^{{2 \over 3}}} + {y^{{2 \over 3}}} \le 1,\,x + y \ge 0,\,y \ge 0} \right\}$$ is A, then $${{256A} \over \pi }$$ is equal to __________.

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2
JEE Main 2022 (Online) 27th June Morning Shift
Numerical
+4
-1
Change Language
Let

$${A_1} = \left\{ {(x,y):|x| \le {y^2},|x| + 2y \le 8} \right\}$$ and

$${A_2} = \left\{ {(x,y):|x| + |y| \le k} \right\}$$. If 27 (Area A1) = 5 (Area A2), then k is equal to :

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3
JEE Main 2022 (Online) 26th June Evening Shift
Numerical
+4
-1
Change Language

The integral $${{24} \over \pi }\int_0^{\sqrt 2 } {{{(2 - {x^2})dx} \over {(2 + {x^2})\sqrt {4 + {x^4}} }}} $$ is equal to ____________.

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4
JEE Main 2022 (Online) 26th June Morning Shift
Numerical
+4
-1
Change Language

Let f(x) = max {|x + 1|, |x + 2|, ....., |x + 5|}. Then $$\int\limits_{ - 6}^0 {f(x)dx} $$ is equal to __________.

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