AIEEE 2006 | Application of Derivatives Question 208 | 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

A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?

Interval	Function
(- $$\infty $$, $$\infty $$)	x³ - 3x² + 3x + 3

Interval	Function
[2, $$\infty $$)	2x³ - 3x² - 12x + 6

Interval	Function
$$\left( { - \infty ,{1 \over 3}} \right]$$	3x² - 2x + 1

Interval	Function
($$ - \infty $$, - 4 )	x³ + 6x² + 6

AIEEE 2005

MCQ (Single Correct Answer)

-1

Out of Syllabus

If the equation $${a_n}{x^n} + {a_{n - 1}}{x^{n - 1}} + ........... + {a_1}x = 0$$
$${a_1} \ne 0,n \ge 2,$$ has a positive root $$x = \alpha $$, then the equation
$$n{a_n}{x^{n - 1}} + \left( {n - 1} \right){a_{n - 1}}{x^{n - 2}} + ........... + {a_1} = 0$$ has a positive root, which is

greater than $$\alpha $$

smaller than $$\alpha $$

greater than or equal to smaller than $$\alpha $$

equal to smaller than $$\alpha $$

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

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