1
WB JEE 2019
MCQ (Single Correct Answer)
+1
-0.25
Change Language
If $$\int {{2^{{2^x}}}.\,{2^x}dx} = A\,.\,{2^{{2^x}}} + C$$, then A is equal to
A
$${1 \over {\log 2}}$$
B
log 2
C
$${{{(\log 2)}^2}}$$
D
$${1 \over {{{(\log 2)}^2}}}$$
2
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)
3
WB JEE 2019
MCQ (Single Correct Answer)
+1
-0.25
Change Language
$$\mathop {\lim }\limits_{n \to \infty } {3 \over n}\left[ {1 + \sqrt {{n \over {n + 3}}} + \sqrt {{n \over {n + 6}}} + \sqrt {{n \over {n + 9}}} + ... + \sqrt {{n \over {n + 3(n - 1)}}} } \right]$$
A
does not exist
B
is 1
C
is 2
D
is 3
4
WB JEE 2019
MCQ (Single Correct Answer)
+1
-0.25
Change Language
The general solution of the differential equation $$\left( {1 + {e^{{x \over y}}}} \right)dx + \left( {1 - {x \over y}} \right){e^{x/y}}dy = 0$$ is (C is an arbitrary constant)
A
$$x - y{e^{{x \over y}}} = C$$
B
$$y - x{e^{{x \over y}}} = C$$
C
$$x + y{e^{{x \over y}}} = C$$
D
$$y + x{e^{{x \over y}}} = C$$
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