Javascript is required
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JEE Main 2021 (Online) 16th March Morning Shift
Numerical  +4  -1
If the normal to the curve y(x) = $$\int\limits_0^x {(2{t^2} - 15t + 10)dt}$$ at a point (a, b) is parallel to the line x + 3y = $$-$$5, a > 1, then the value of | a + 6b | is equal to ___________.
2
JEE Main 2021 (Online) 26th February Evening Shift
Numerical  +4  -1
Let the normals at all the points on a given curve pass through a fixed point (a, b). If the curve passes through (3, $$-$$3) and (4, $$-$$2$$\sqrt 2$$), and given that a $$-$$ 2$$\sqrt 2$$ b = 3,
then (a2 + b2 + ab) is equal to __________.
If $${I_{m,n}} = \int\limits_0^1 {{x^{m - 1}}{{(1 - x)}^{n - 1}}dx}$$, for m, $$n \ge 1$$, and
$$\int\limits_0^1 {{{{x^{m - 1}} + {x^{n - 1}}} \over {{{(1 + x)}^{m + 1}}}}} dx = \alpha {I_{m,n}}\alpha \in R$$, then $$\alpha$$ equals ___________.
The value of the integral $$\int\limits_0^\pi {|{{\sin }^2}2x|dx}$$ is ___________.