1
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 __________.
2
JEE Main 2021 (Online) 26th February Evening Shift
Numerical
+4
-1
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 ___________.
3
JEE Main 2021 (Online) 26th February Morning Shift
Numerical
+4
-1
The value of the integral $$\int\limits_0^\pi {|{{\sin }\,}2x|dx}$$ is ___________.
4
JEE Main 2021 (Online) 26th February Morning Shift
Numerical
+4
-1
The area bounded by the lines y = || x $$-$$ 1 | $$-$$ 2 | is ___________.
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