1
JEE Main 2021 (Online) 25th February Morning Shift
+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 Shift
+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
$$- \sqrt 2 - \sqrt 3 - 1$$
3
JEE Main 2021 (Online) 24th February Evening Shift
+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)
4
JEE Main 2021 (Online) 24th February Evening Shift
+4
-1
Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f'(x) $$\ne$$ 0 for all x $$\in$$ R. If $$\left| {\matrix{ {f(x)} & {f'(x)} \cr {f'(x)} & {f''(x)} \cr } } \right|$$ = 0, for all x$$\in$$R, then the value of f(1) lies in the interval :
A
(0, 3)
B
(9, 12)
C
(3, 6)
D
(6, 9)
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