1
WB JEE 2017
MCQ (Single Correct Answer)
+1
-0.25
Change Language
The value of $$\mathop {\lim }\limits_{n \to \infty } \left[ {{n \over {{n^2} + {1^2}}} + {n \over {{n^2} + {2^2}}} + ... + {1 \over {2n}}} \right]$$ is
A
$${{n\pi } \over 4}$$
B
$${\pi \over 4}$$
C
$${\pi \over {4n}}$$
D
$${\pi \over {2n}}$$
2
WB JEE 2017
MCQ (Single Correct Answer)
+1
-0.25
Change Language
The value of the integral $$\int_0^1 {{e^{{x^2}}}} dx$$
A
is less than 1
B
is greater than 1
C
is less than or equal to 1
D
lies in the closed interval [1, e]
3
WB JEE 2017
MCQ (Single Correct Answer)
+1
-0.25
Change Language
$$\int_0^{100} {{e^{x - [x]}}} dx$$ is equal to
A
$${{{e^{100}} - 1} \over {100}}$$
B
$${{{e^{100}} - 1} \over {e - 1}}$$
C
$$100(e - 1)$$
D
$${{e - 1} \over {100}}$$
4
WB JEE 2017
MCQ (Single Correct Answer)
+2
-0.5
Change Language
If $$f(x) = \int_{ - 1}^x {|t|} \,dt$$, then for any $$x \ge 0,\,f(x)$$ is equal to
A
$${1 \over 2}(1 - {x^2})$$
B
$$1 - {x^2}$$
C
$${1 \over 2}(1 + {x^2})$$
D
$$1 + {x^2}$$
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