1
JEE Main 2021 (Online) 25th February Morning Slot
+4
-1
The value of $$\int\limits_{ - 1}^1 {{x^2}{e^{[{x^3}]}}} dx$$, where [ t ] denotes the greatest integer $$\le$$ t, is :
A
$${{e + 1} \over 3}$$
B
$${{e - 1} \over {3e}}$$
C
$${1 \over {3e}}$$
D
$${{e + 1} \over {3e}}$$
2
JEE Main 2021 (Online) 24th February Evening Slot
+4
-1
If a curve y = f(x) passes through the point (1, 2) and satisfies $$x {{dy} \over {dx}} + y = b{x^4}$$, then for what value of b, $$\int\limits_1^2 {f(x)dx = {{62} \over 5}}$$?
A
$${{31} \over 5}$$
B
10
C
5
D
$${{62} \over 5}$$
3
JEE Main 2021 (Online) 24th February Evening Slot
+4
-1
The value of the integral, $$\int\limits_1^3 {[{x^2} - 2x - 2]dx}$$, where [x] denotes the greatest integer less than or equal to x, is :
A
$$-$$ 5
B
$$- \sqrt 2 - \sqrt 3 + 1$$
C
$$-$$ 4
D
$$- \sqrt 2 - \sqrt 3 - 1$$
4
JEE Main 2021 (Online) 24th February Evening Slot
+4
-1
Let f(x) be a differentiable function defined on [0, 2] such that f'(x) = f'(2 $$-$$ x) for all x$$\in$$ (0, 2), f(0) = 1 and f(2) = e2. Then the value of $$\int\limits_0^2 {f(x)} dx$$ is :
A
1 + e2
B
2(1 + e2)
C
1 $$-$$ e2
D
2(1 $$-$$ e2)
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