Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 6 - Application of Derivatives>EXERCISE>Q 9

HARD

KVPY Aptitude Test - Stream SX

IMPORTANT

Earn 100

A function $y = f (x)$ has a second-order derivative $f^{''} (x) = 6 (x - 1)$ . If its graph passes through the point $(2, 1)$ and at that point tangent to the graph is $y = 3 x - 5$ , then the value of $f (0)$ is

50% studentsanswered this correctly

Important Questions on Application of Derivatives

MEDIUM

KVPY Aptitude Test - Stream SX

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 6 - Application of Derivatives>EXERCISE>Q 10

The curve represented parametrically by the equations

x = 2 lncot t + 1

and

y = \tan t + \cot t

MEDIUM

KVPY Aptitude Test - Stream SX

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 6 - Application of Derivatives>EXERCISE>Q 11

If a variable tangent to the curve

x^{2} y = c^{3}

makes intercepts

a, b

on

x

and

y

axes, respectively, then the value of

a^{2} b

is

HARD

KVPY Aptitude Test - Stream SX

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 6 - Application of Derivatives>EXERCISE>Q 12

A curve is represented by the equations

x = \sec^{2} t

and

y = \cot t,

where

t

is a parameter. If the tangent at the point

P

on the curve, where

t = \frac{π}{4}

, meets the curve again at the point

Q,

then

| P Q |

is equal to

MEDIUM

KVPY Aptitude Test - Stream SX

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 6 - Application of Derivatives>EXERCISE>Q 13

The

x

-intercept of the tangent at any arbitrary point of the curve

\frac{a}{x^{2}} + \frac{b}{y^{2}} = 1

is proportional to

MEDIUM

KVPY Aptitude Test - Stream SX

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 6 - Application of Derivatives>EXERCISE>Q 14

The number of points in the rectangle

{(x, y) - 12 \leq x \leq 12 & - 3 \leq y \leq 3}

, which lie on the curve

y = x + \sin x

and at which the tangent to the curve is parallel to the

x

-axis, is

MEDIUM

KVPY Aptitude Test - Stream SX

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 6 - Application of Derivatives>EXERCISE>Q 15

The lines tangent to the curves

y^{3} - x^{2} y + 5 y - 2 x = 0

and

x^{4} - x^{3} y^{2} + 5 x + 2 y = 0

at the origin intersect at an angle

θ

equal to

MEDIUM

KVPY Aptitude Test - Stream SX

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 6 - Application of Derivatives>EXERCISE>Q 16

The curves

4 x^{2} + 9 y^{2} = 72

and

x^{2} - y^{2} = 5

at

(3, 2)

EASY

KVPY Aptitude Test - Stream SX

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 6 - Application of Derivatives>EXERCISE>Q 17

If

f (x) = x^{3} + 7 x - 1

, then

f (x)

has a zero between

x = 0

and

x = 1 .

The theorem that best describes this is