1
JEE Main 2023 (Online) 25th January Morning Shift
Numerical
+4
-1 If the area enclosed by the parabolas $$\mathrm{P_1:2y=5x^2}$$ and $$\mathrm{P_2:x^2-y+6=0}$$ is equal to the area enclosed by $$\mathrm{P_1}$$ and $$\mathrm{y=\alpha x,\alpha > 0}$$, then $$\alpha^3$$ is equal to ____________.

2
JEE Main 2023 (Online) 24th January Evening Shift
Numerical
+4
-1 Let $$f$$ be $$a$$ differentiable function defined on $$\left[ {0,{\pi \over 2}} \right]$$ such that $$f(x) > 0$$ and $$f(x) + \int_0^x {f(t)\sqrt {1 - {{({{\log }_e}f(t))}^2}} dt = e,\forall x \in \left[ {0,{\pi \over 2}} \right]}$$. Then $$\left( {6{{\log }_e}f\left( {{\pi \over 6}} \right)} \right)^2$$ is equal to __________.

3
JEE Main 2023 (Online) 24th January Evening Shift
Numerical
+4
-1 If the area of the region bounded by the curves $$y^2-2y=-x,x+y=0$$ is A, then 8 A is equal to __________

4
JEE Main 2023 (Online) 24th January Morning Shift
Numerical
+4
-1 The value of $$12\int\limits_0^3 {\left| {{x^2} - 3x + 2} \right|dx}$$ is ____________

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