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Questions
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1
AIEEE 2012
MCQ (Single Correct Answer)
+4
-1
If the $$\int {{{5\tan x} \over {\tan x - 2}}dx = x + a\,\ln \,\left| {\sin x - 2\cos x} \right| + k,} $$ then $$a$$ is
equal to :
A
$$-1$$
B
$$-2$$
C
$$1$$
D
$$2$$
2
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
The value of $$\sqrt 2 \int {{{\sin xdx} \over {\sin \left( {x - {\pi \over 4}} \right)}}} $$ is
A
$$\,x + \log \,\left| {\,\cos \left( {x - {\pi \over 4}} \right)\,} \right| + c$$
B
$$\,x - \log \,\left| {\,\sin \left( {x - {\pi \over 4}} \right)\,} \right| + c$$
C
$$\,x + \log \,\left| {\,\sin \left( {x - {\pi \over 4}} \right)\,} \right| + c$$
D
$$\,x - \log \,\left| {\,\cos \left( {x - {\pi \over 4}} \right)\,} \right| + c$$
3
AIEEE 2007
MCQ (Single Correct Answer)
+4
-1
$$\int {{{dx} \over {\cos x + \sqrt 3 \sin x}}} $$ equals
A
$$\log \,\tan \,\left( {{x \over 2} + {\pi \over {12}}} \right) + C$$
B
$$\log \,\tan \,\left( {{x \over 2} - {\pi \over {12}}} \right) + C$$
C
$$\,{1 \over 2}\,\log \,\tan \,\left( {{x \over 2} + {\pi \over {12}}} \right) + C$$
D
$$\,{1 \over 2}\,\log \,\tan \,\left( {{x \over 2} - {\pi \over {12}}} \right) + C$$
4
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
$$\int {{{\left\{ {{{\left( {\log x - 1} \right)} \over {1 + {{\left( {\log x} \right)}^2}}}} \right\}}^2}\,\,dx} $$ is equal to
A
$${{\log x} \over {{{\left( {\log x} \right)}^2} + 1}} + C$$
B
$${x \over {{x^2} + 1}} + C$$
C
$${{x{e^x}} \over {1 + {x^2}}} + C$$
D
$${x \over {{{\left( {\log x} \right)}^2} + 1}} + C$$
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