1
WB JEE 2021
+2
-0.5
Let f(x) be continuous periodic function with period T. Let $$I = \int\limits_a^{a + T} {f(x)\,dx}$$. Then
A
I is linear function in 'a'
B
I does not depend on 'a'
C
0 < I < a2 + 1 where I depends on 'a'
D
I is quadratic function in 'a'
2
WB JEE 2021
+2
-0.5
If $$b = \int\limits_0^1 {{{{e^t}} \over {t + 1}}dt}$$, then $$\int\limits_{a - 1}^a {{{{e^{ - t}}} \over {t - a - 1}}}$$ is
A
bea
B
be$$-$$a
C
$$-$$ be$$-$$a
D
$$-$$ bea
3
WB JEE 2021
+2
-0.5
Let $$I = \int_{\pi /4}^{\pi /3} {{{\sin x} \over x}dx}$$. Then
A
$${{\sqrt 3 } \over 8} \le I \le {{\sqrt 2 } \over 6}$$
B
$${{\sqrt 3 } \over {2\pi }} \le I \le {{2\sqrt 3 } \over \pi }$$
C
$${{\sqrt 3 } \over 9} \le I \le {{\sqrt 2 } \over {16}}$$
D
$$\pi \le I \le {{4\pi } \over 3}$$
4
WB JEE 2020
+1
-0.25
The value of

$$\sum\limits_{n = 1}^{10} {} \int\limits_{ - 2n - 1}^{ - 2n} {{{\sin }^{27}}} x\,dx + \sum\limits_{n = 1}^{10} {} \int\limits_{2n}^{2n + 1} {{{\sin }^{27}}} x\,dx$$ is equal to
A
27
B
54
C
$$-$$54
D
0
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