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1
JEE Main 2021 (Online) 26th August Morning Shift
Numerical
+4
-1
The area of the region $$S = \{ (x,y):3{x^2} \le 4y \le 6x + 24\} $$ is ____________.
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2
JEE Main 2021 (Online) 27th July Evening Shift
Numerical
+4
-1
If $$\int_0^\pi {({{\sin }^3}x){e^{ - {{\sin }^2}x}}dx = \alpha - {\beta \over e}\int_0^1 {\sqrt t {e^t}dt} } $$, then $$\alpha$$ + $$\beta$$ is equal to ____________.
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3
JEE Main 2021 (Online) 27th July Morning Shift
Numerical
+4
-1
Let the domain of the function

$$f(x) = {\log _4}\left( {{{\log }_5}\left( {{{\log }_3}(18x - {x^2} - 77)} \right)} \right)$$ be (a, b). Then the value of the integral $$\int\limits_a^b {{{{{\sin }^3}x} \over {({{\sin }^3}x + {{\sin }^3}(a + b - x)}}} dx$$ is equal to _____________.
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4
JEE Main 2021 (Online) 25th July Evening Shift
Numerical
+4
-1
Let a curve y = f(x) pass through the point (2, (loge2)2) and have slope $${{2y} \over {x{{\log }_e}x}}$$ for all positive real value of x. Then the value of f(e) is equal to ______________.
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