MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 10

MEDIUM

12th CBSE

IMPORTANT

Earn 100

A man $160 cm$ tall, walks away from a source of light situated at the top of a pole $6 m$ high, at the rate of $1.1 m / \sec$ . How fast is the length of his shadow increasing when he is $1 m$ away from the pole?

Important Questions on Derivative as a Rate Measurer

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 11

A man

180 cm

tall walks at a rate of

2 m / \sec

. away, from a source of light that is

9 m

above the ground. How fast is the length of his shadow increasing when he is

3 m

away from the base of light?

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 12

A ladder

13 m

long leans against a wall. The foot of the ladder is pulled along the ground away from the wall, at the rate of

1.5 m / \sec

. How fast is the angle

θ

between the ladder and the ground is changing when the foot of the ladder is

12 m

away from the wall.

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 13

A particle moves along the curve

y = x^{2} + 2 x

. At what point(s) on the curve are the

x

and

y

coordinates of the particle changing at the same rate?

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12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 14

If

y = 7 x - x^{3}

and

x

increases at the rate of

4

units per second, how fast is the slope of the curve changing when

x = 2

?

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 15

A particle moves along the curve

y = x^{3}

. Find the points on the curve at which the

y

-coordinate changes three times more rapidly than the

x

-coordinate.

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 16

Find an angle

θ

which increases twice as fast as its cosine.

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 16

Find an angle $θ$ whose rate of increase is twice the rate of decrease of its cosine.

HARD

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 17

The top of a ladder $6$ metres long is resting against a vertical wall on a level pavement, when the ladder begins to slide outwards. At the moment when the foot of the ladder is $4$ metres from the wall, it is sliding away from the wall at the rate of $0.5 m / \sec$ . How fast is the top-sliding downwards at this instance?

How far is the foot from the wall when it and the top are moving at the same rate?