AIEEE 2006 | Application of Derivatives Question 194 | Mathematics

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

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

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

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

$$\pi {x^2}$$

AIEEE 2005

MCQ (Single Correct Answer)

-1

Area of the greatest rectangle that can be inscribed in the
ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$

$$2ab$$

$$ab$$

$$\sqrt {ab} $$

$${a \over b}$$

AIEEE 2005

MCQ (Single Correct Answer)

-1

Out of Syllabus

The normal to the curve
$$x = a\left( {\cos \theta + \theta \sin \theta } \right),y = a\left( {\sin \theta - \theta \cos \theta } \right)$$ at any point
$$\theta\, '$$ is such that

it passes through the origin

it makes an angle $${\pi \over 2} + \theta $$ with the $$x$$-axis

it passes through $$\left( {a{\pi \over 2}, - a} \right)$$

it is at a constant distance from the origin

AIEEE 2005

MCQ (Single Correct Answer)

-1

A spherical iron ball $$10$$ cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of $$50$$ cm$$^3$$ /min. When the thickness of ice is $$5$$ cm, then the rate at which the thickness of ice decreases is

$${1 \over {36\pi }}$$ cm/min

$${1 \over {18\pi }}$$ cm/min

$${1 \over {54\pi }}$$ cm/min

$${5 \over {6\pi }}$$ cm/min

PREVIOUS NEXT

Questions Asked from Application of Derivatives (MCQ (Single Correct Answer))

Number in Brackets after Paper Indicates No. of Questions