NCERT Exemplar Mathematics - Class 12>Chapter 6 - Application of Derivatives>EXERCISE>Q 36

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A ladder, $5$ meter long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of $10 cm / \sec,$ then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is $2$ meters from the wall is:

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Important Questions on Application of Derivatives

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12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 6 - Application of Derivatives>EXERCISE>Q 37

The curve

y = x^{\frac{1}{5}}

has at

(0, 0)

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NCERT Exemplar Mathematics - Class 12>Chapter 6 - Application of Derivatives>EXERCISE>Q 38

The equation of normal to the curve

3 x^{2} - y^{2} = 8

which is parallel to the line

x + 3 y = 8

is

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IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 6 - Application of Derivatives>EXERCISE>Q 39

If the curve

a y + x^{2} = 7

and

x^{3} = y,

cut orthogonally at

(1, 1),

then the value of

a

is:

EASY

12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 6 - Application of Derivatives>EXERCISE>Q 40

If

y = x^{4} - 10

and if

x

changes from

2

to

1.99,

what is the change in

y

?

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NCERT Exemplar Mathematics - Class 12>Chapter 6 - Application of Derivatives>EXERCISE>Q 41

The equation of tangent to the curve

y (1 + x^{2}) = 2 - x,

where it crosses

x -

axis is

x + 5 y = k

, then find the value of

k

.

EASY

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IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 6 - Application of Derivatives>EXERCISE>Q 42

The points at which the tangents to the curve

y = x^{3} - 12 x + 18

are parallel to

x -

axis are:

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IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 6 - Application of Derivatives>EXERCISE>Q 43

The tangent to the curve $y = e^{2 x}$ at the point $(0, 1)$ meets $x -$ axis at:

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NCERT Exemplar Mathematics - Class 12>Chapter 6 - Application of Derivatives>EXERCISE>Q 44

The slope of tangent to the curve

x = t^{2} + 3 t - 8, y = 2 t^{2} - 2 t - 5

at the point

(2, - 1)

is