WB JEE 2008 | Differentiation Question 2 | Mathematics

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

WB JEE 2009

MCQ (Single Correct Answer)

-0.25

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

$${1 \over {12a}}$$

$${{4\sqrt 2 } \over {3a}}$$

$${{3a} \over {4\sqrt 2 }}$$

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