WB JEE 2008 | Differentiation Question 1 | Mathematics

WB JEE 2008

MCQ (Single Correct Answer)

-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

$$2{e^x}$$

$${1 \over 2}{e^x}$$

$${1 \over {2{e^x}}}$$

$${2 \over {{e^x}}}$$

WB JEE 2008

MCQ (Single Correct Answer)

-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

$$1 + {1 \over {\sqrt {2\pi } }}$$

$${1 \over {\sqrt {2\pi } }}$$

$$1 - {1 \over {\sqrt {2\pi } }}$$

WB JEE 2008

MCQ (Single Correct Answer)

-0.25

Select the correct statement from (a), (b), (c), (d). The function $$f(x) = x{e^{1 - x}}$$

strictly increases in the interval (1/2, 2)

increases in the interval (0, $$\infty$$)

decreases in the interval (0, 2)

strictly decreases in the interval (1, $$\infty$$)

WB JEE 2008

MCQ (Single Correct Answer)

-0.25

The function $$f(x) = {e^{ax}} + {e^{ - ax}},a > 0$$ is monotonically increasing for

$$-$$1 < x < 1

x < $$-$$1

x > $$-$$1

x > 0

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