AIEEE 2007 | Application of Derivatives Question 190 | Mathematics

A value of $$c$$ for which conclusion of Mean Value Theorem holds for the function $$f\left( x \right) = {\log _e}x$$ on the interval $$\left[ {1,3} \right]$$ is

$${\log _3}e$$

$${\log _e}3$$

$$2\,\,{\log _3}e$$

$${1 \over 2}{\log _3}e$$

AIEEE 2007

MCQ (Single Correct Answer)

-1

If $$p$$ and $$q$$ are positive real numbers such that $${p^2} + {q^2} = 1$$, then the maximum value of $$(p+q)$$ is

$${1 \over 2}$$

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

$${\sqrt 2 }$$

$$2$$

AIEEE 2006

MCQ (Single Correct Answer)

-1

The function $$f\left( x \right) = {x \over 2} + {2 \over x}$$ has a local minimum at

$$x=2$$

$$x=-2$$

$$x=0$$

$$x=1$$

AIEEE 2006

MCQ (Single Correct Answer)

-1

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length $$x$$. The maximum area enclosed by the park is

$${3 \over 2}{x^2}$$

$$\sqrt {{{{x^3}} \over 8}} $$

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

$$\pi {x^2}$$

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