MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Competitive Thinking>Q 124

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IMPORTANT

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Let $f_{n} (x)$ be the $n^{th}$ derivative of $f (x)$ . The least value of $n$ so that $f_{n} = f_{n + 1}$ where $f (x) = x^{2} + e^{x}$ is

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Important Questions on Applications of Derivatives

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IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Competitive Thinking>Q 125

If from a wire of length

36

metre a rectangle of greatest area is made, then its two adjacent sides in metre are

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Competitive Thinking>Q 126

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in

sq . m

) of the flower-bed, is

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Competitive Thinking>Q 127

The sum of two non-zero numbers is

4

. The minimum value of the sum of their reciprocals is

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Competitive Thinking>Q 128

The area of a rectangle will be maximum for the given perimeter, when rectangle is a

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Competitive Thinking>Q 129

A population

p (t)

of

1000

bacteria introduced into nutrient medium grows according to the relation

p (t) = 1000 + \frac{1000 t}{100 + t^{2}}

. The maximum size of this bacterial population is

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Competitive Thinking>Q 130

The least value of the sum of any positive real number and its reciprocal is

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Competitive Thinking>Q 131

The function

f (x) = x + \sin x

has

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IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Competitive Thinking>Q 132

The value of

a

, so that the sum of the squares of the roots of the equation

x^{2} - (a - 2) x - a + 1 = 0

, assume the least value, is