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1
JEE Main 2021 (Online) 16th March Evening Shift
+4
-1
Consider the integral
$$I = \int_0^{10} {{{[x]{e^{[x]}}} \over {{e^{x - 1}}}}dx}$$,
where [x] denotes the greatest integer less than or equal to x. Then the value of I is equal to :
A
45 (e $$-$$ 1)
B
45 (e + 1)
C
9 (e + 1)
D
9 (e $$-$$ 1)
2
JEE Main 2021 (Online) 16th March Evening Shift
+4
-1
Let P(x) = x2 + bx + c be a quadratic polynomial with real coefficients such that $$\int_0^1 {P(x)dx}$$ = 1 and P(x) leaves remainder 5 when it is divided by (x $$-$$ 2). Then the value of 9(b + c) is equal to :
A
9
B
11
C
7
D
15
3
JEE Main 2021 (Online) 26th February Evening Shift
+4
-1
For x > 0, if $$f(x) = \int\limits_1^x {{{{{\log }_e}t} \over {(1 + t)}}dt}$$, then $$f(e) + f\left( {{1 \over e}} \right)$$ is equal to :
A
$${1 \over 2}$$
B
$$-$$1
C
0
D
1
4
JEE Main 2021 (Online) 26th February Morning Shift
The value of $$\int\limits_{ - \pi /2}^{\pi /2} {{{{{\cos }^2}x} \over {1 + {3^x}}}} dx$$ is :
$$2\pi$$
$${\pi \over 2}$$
$$4\pi$$
$${\pi \over 4}$$