Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 121

HARD

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IMPORTANT

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If $f (x)$ is a non-zero polynomial of degree four, having local extreme points at $x = - 1, 0, 1;$ then the set $S = {x \in R : f (x) = f (0)}$ contains exactly

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Important Questions on Application of Derivatives

EASY

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 1

The rate of change of area of a circle with respect to its radius

R

at

R = 6 cm

is

EASY

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 2

The total revenue in Rupees received from the sale of $x$ units of a product is given by $R (x) = 13 x^{2} + 26 x + 15$ . Find the marginal revenue when $x = 15$ .

EASY

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 3

The position of a particle moving along a horizontal line of any time

t

is given by

s (t) = 3 t^{2} - 2 t - 8 .

The time at which the particle is at rest is

EASY

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 4

If each side of a square plate increases at the rate of

3 cm / \min,

then the rate of increase of the area, when its side is

10 cm

is

EASY

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 5

Length of each side of an equilateral triangle increases at the rate of

2 cm

in every second. The rate of increase of the area of the triangle, when its side is of length

10 cm

is

EASY

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 6

The abscissa of a point moving along the curve

y^{2} = 12 x

increases at the rate of

2 cm / \sec .

Then, the co-ordinates of the point, rates of increase of whose abscissa and ordinate are the same are

EASY

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 7

If the volume of a bubble increases at the rate of

10

cubic

cm / \min,

then the rate of increase of the surface area when its radius is

1 cm

is

MEDIUM

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 8

The total revenue in

₹

received from the sale of

x

units of an article is given by the equation

R (x) = 3 x^{2} + 36 x + 5

. The marginal revenue when

x = 15

is