1
WB JEE 2020
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let f, be a continuous function in [0, 1], then $$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{j = 0}^n {{1 \over n}} f\left( {{j \over n}} \right)$$ is
A
$${1 \over 2}\int\limits_0^{{1 \over 2}} {f(x)\,} dx$$
B
$$\int\limits_{{1 \over 2}}^1 {f(x)\,} dx$$
C
$$\int\limits_0^1 {f(x)\,} dx$$
D
$$\int\limits_0^{{1 \over 2}} {f(x)\,} dx$$
2
WB JEE 2019
MCQ (Single Correct Answer)
+1
-0.25
Change Language
The value of the integration

$$\int\limits_{ - {\pi \over 4}}^{\pi /4} {\left( {\lambda |\sin x| + {{\mu \sin x} \over {1 + \cos x}} + \gamma } \right)} dx$$
A
is independent of $$\lambda$$ only
B
is independent of $$\mu$$ only
C
is independent of $$\gamma$$ only
D
depends on $$\lambda$$, $$\mu$$ and $$\gamma$$
3
WB JEE 2019
MCQ (Single Correct Answer)
+1
-0.25
Change Language
The value of $$\mathop {\lim }\limits_{x \to 0} {1 \over x}\left[ {\int\limits_y^a {{e^{{{\sin }^2}t}}dt - } \int\limits_{x + y}^a {{e^{{{\sin }^2}t}}dt} } \right]$$ is equal to
A
$${{e^{{{\sin }^2}y}}}$$
B
$${{e^{{2{\sin }}y}}}$$
C
e| sin y|
D
$${e^{\cos e{c^2}y}}$$
4
WB JEE 2019
MCQ (Single Correct Answer)
+1
-0.25
Change Language
The value of the integral $$\int\limits_{ - 1}^1 {\left\{ {{{{x^{2015}}} \over {{e^{|x|}}({x^2} + \cos x)}} + {1 \over {{e^{|x|}}}}} \right\}} dx$$ is equal to
A
0
B
1 $$-$$ e$$-$$1
C
2e$$-$$1
D
2(1 $$-$$ e$$-$$1)
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