1
WB JEE 2008
MCQ (Single Correct Answer)
+1
-0.25

If $$x = {e^t}\sin t$$, $$y = {e^t}\cos t$$ then $${{{d^2}y} \over {d{x^2}}}$$ at x = $$\pi$$ is

A
$$2{e^x}$$
B
$${1 \over 2}{e^x}$$
C
$${1 \over {2{e^x}}}$$
D
$${2 \over {{e^x}}}$$
2
WB JEE 2008
MCQ (Single Correct Answer)
+1
-0.25

The value of $${{dy} \over {dx}}$$ at $$x = {\pi \over 2}$$, where y is given by $$y = {x^{\sin x}} + \sqrt x $$ is

A
$$1 + {1 \over {\sqrt {2\pi } }}$$
B
1
C
$${1 \over {\sqrt {2\pi } }}$$
D
$$1 - {1 \over {\sqrt {2\pi } }}$$
3
WB JEE 2009
MCQ (Single Correct Answer)
+1
-0.25

The second order derivative of a sin3t with respect to a cos3t at $$t = {\pi \over 4}$$ is

A
2
B
$${1 \over {12a}}$$
C
$${{4\sqrt 2 } \over {3a}}$$
D
$${{3a} \over {4\sqrt 2 }}$$
4
WB JEE 2009
MCQ (Single Correct Answer)
+1
-0.25

If $$y = {\tan ^{ - 1}}\sqrt {{{1 - \sin x} \over {1 + \sin x}}} $$, then the value of $${{dy} \over {dx}}$$ at $$x = {\pi \over 6}$$ is

A
$$-$$ 1/2
B
1/2
C
1
D
$$-$$1
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Graduate Aptitude Test in Engineering
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Class 12