Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 13

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Let $A$ be the maximum area of the incircle of the right-angled triangle with hypotenuse of length $(\sqrt{2} + 1)$ units and $B$ be the minimum area of the circumcircle of the right-angled triangle with area $4$ square units. Then, which of the following option(s) is/are correct?

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Important Questions on Application of Derivatives

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 14

The length of the portion of a tangent line to the curve

x^{2 / 3} + y^{2 / 3} = 4

at the point

P

, cut off by the coordinate axes, is

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 15

Which of the following statement(s) is/are correct?

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 16

Which of the following statement(s) is/are correct for the function

f (x) = \frac{x^{2} - 2}{3 x^{2} - 9}

?

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 4

The least natural number

a

for which

x + a x^{- 2} > 2 \forall x \in (0, \infty)

is:

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 5

Any tangent at a point

P (x, y)

to the ellipse

\frac{x^{2}}{8} + \frac{y^{2}}{18} = 1

meets the positive co-ordinate axes in the points

A

and

B

such that the area of the

∆ O A B

is least, then the point

P

is of the form

(m, n)

where

m + n + 10

is

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 6

If the tangent at

P (1, 1)

on the curve

y^{2} = x {(2 - x)}^{2}

meets the curve again at

Q

, then the point

Q

is of the form

(\frac{3 a}{b}, \frac{a}{2 b})

, where minimum integral value of

a^{2} + b^{2}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 7

The curve

y = a x^{3} + b x^{2} + c x

is inclined at

45 °

to

x

-axis at

(0, 0)

but it touches

x

-axis at

(1, 0)

, then

a + b + c + 10

is

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 13

If

f (x) = x^{3} + 4 x^{2} + λ x + 1

is a monotonically decreasing function of

x

in the largest possible interval

(- 2, - \frac{2}{3}) .

Then