1
WB JEE 2021
MCQ (Single Correct Answer)
+2
-0.5
Change Language
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
MCQ (Single Correct Answer)
+2
-0.5
Change Language
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
MCQ (Single Correct Answer)
+2
-0.5
Change Language
The differential of $$f(x) = {\log _e}(1 + {e^{10x}}) - {\tan ^{ - 1}}({e^{5x}})$$ at x = 0 and for dx = 0.2 is
A
0.5
B
0.3
C
$$-$$ 0.2
D
$$-$$ 0.5
4
WB JEE 2021
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Given that f : S $$\to$$ R is said to have a fixed point at c of S if f(c) = c. Let f : [1, $$\infty$$) $$\to$$ R be defined by f(x) = 1 + $$\sqrt x $$. Then
A
f has no fixed point in [1, $$\infty$$)
B
f has unique fixed point in [1, $$\infty$$)
C
f has to fixed points in [1, $$\infty$$)
D
f has infinitely many fixed points in [1, $$\infty$$)
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