1
JEE Main 2021 (Online) 26th February Evening Shift
MCQ (Single Correct Answer)
+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
2
JEE Main 2021 (Online) 26th February Morning Shift
MCQ (Single Correct Answer)
+4
-1
The value of $$\int\limits_{ - \pi /2}^{\pi /2} {{{{{\cos }^2}x} \over {1 + {3^x}}}} dx$$ is :
A
$$2\pi$$
B
$${\pi \over 2}$$
C
$$4\pi$$
D
$${\pi \over 4}$$
3
JEE Main 2021 (Online) 26th February Morning Shift
MCQ (Single Correct Answer)
+4
-1
The value of $$\sum\limits_{n = 1}^{100} {\int\limits_{n - 1}^n {{e^{x - [x]}}dx} }$$, where [ x ] is the greatest integer $$\le$$ x, is :
A
100e
B
100(e $$-$$ 1)
C
100(1 + e)
D
100(1 $$-$$ e)
4
JEE Main 2021 (Online) 25th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
If $${I_n} = \int\limits_{{\pi \over 4}}^{{\pi \over 2}} {{{\cot }^n}x\,dx}$$, then :
A
$${1 \over {{I_2} + {I_4}}},{1 \over {{I_3} + {I_5}}},{1 \over {{I_4} + {I_6}}}$$ are in A.P.
B
I2 + I4, I3 + I5, I4 + I6 are in A.P.
C
$${1 \over {{I_2} + {I_4}}},{1 \over {{I_3} + {I_5}}},{1 \over {{I_4} + {I_6}}}$$ are in G.P.
D
I2 + I4, (I3 + I5)2, I4 + I6 are in G.P.
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