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In a regular triangular prism the distance from the centre of one base to one of the vertices of the other base is $l .$ The altitude of the prism for which the volume is greatest, is

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Important Questions on Application of Derivatives

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 23

The maximum area of the rectangle whose sides pass through the angular points of a given the rectangle is of sides

a

and

b

is -

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 28

A light shines from the top of a pole

50 ft

. high. A ball is dropped from the same height from a point

30 ft .

away from the light. If the shadow of the ball moving at the rate of

100 λ ft / \sec

along the ground

1 / 2 \sec .

later [ Assume the ball falls a distance

s = 16 t^{2} ft .

' t'

sec.], then

|λ|

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 29

A variable

Δ A B C

in the

x y

plane has its orthocentre at vertex

' B'

, a fixed vertex

' A'

at the origin and the third vertex

' C'

restricted to lie on the parabola

y = 1 + \frac{7 x^{2}}{36}

. The point

B

starts at the point

(0, 1)

at time

t = 0

and moves upward along the

y

-axis at a constant velocity of

2 cm / \sec

. If the area of the triangle increasing at the rate of

p {cm}^{2} / sec

when

t = \frac{7}{2} \sec

, then

7 p

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 32

If the set of all values of the parameter

a

for which the function

f (x) = \sin 2 x - 8 (a + 1) \sin x + (4 a^{2} + 8 a - 14) x

increases for all

x \in R

and has no critical points for all

x \in R

, is

(- \infty, - m - \sqrt{n}) \cup (\sqrt{n}, \infty)

then

(m^{2} + n^{2})

is (where

m and n

are prime numbers):

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 38

f (x)

is a polynomial of degree

6

, which satisfies

\lim_{x \to 0} {(1 + \frac{f (x)}{x^{3}})}^{\frac{1}{x}} = e^{2}

and has local maximum at

x = 1

and local minimum at

x = 0

and

x = 2

, then the value of

{(\frac{5}{9})}^{4} f (\frac{18}{5})

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 39

The three sides-of a trapezium are equal each being

6 cms

long. Let

Δ {cm}^{2}

be the maximum area of the trapezium. The value of

\sqrt{3} Δ

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 40

A sheet of poster has its area

18 m^{2}

. The margin at the top & bottom are

75 cms

and at the sides

50 cms

. Let

l and n

are the dimensions of the poster in meters when the area of the printed space is maximum. The value of

l^{2} + n^{2}

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 41

The fuel charges for running a train are proportional to the square of the speed generated in miles per hour and costs

Rs . 48

per hour at

16

miles per hour. The most economical speed if the fixed charges i.e., salaries etc., amount to

Rs . 300

per hour -

In a regular triangular prism the distance from the centre of one base to one of the vertices of the other base is l. The altitude of the prism for which the volume is greatest, is

Important Questions on Application of Derivatives

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In a regular triangular prism the distance from the centre of one base to one of the vertices of the other base is $l .$ The altitude of the prism for which the volume is greatest, is