1
JEE Main 2021 (Online) 16th March Morning Shift
Numerical
+4
-1
Out of Syllabus
Let f : (0, 2) $$\to$$ R be defined as f(x) = log2$$\left( {1 + \tan \left( {{{\pi x} \over 4}} \right)} \right)$$. Then, $$\mathop {\lim }\limits_{n \to \infty } {2 \over n}\left( {f\left( {{1 \over n}} \right) + f\left( {{2 \over n}} \right) + ... + f(1)} \right)$$ is equal to ___________.
2
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 ___________.
3
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 ___________.
4
JEE Main 2021 (Online) 26th February Morning Shift
Numerical
+4
-1
The value of the integral $$\int\limits_0^\pi {|{{\sin }\,}2x|dx}$$ is ___________.