Phrases Maxima and Minima Previous Year Question Paper and Solution with PDF

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Phrases Previous Year Questions (PYQs)

Phrases Maxima And Minima PYQ

Qus : 1

Suppose that the temperature at a point (x,y), on a metal plate is

$T(x,y)=4x^2-4xy+y^2$ , An ant, walking on the plate, traverses a circle of radius 5 centered at the origin. What is the highest temperature encountered by the ant?

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Qus : 2

A particle is at rest at the origin. It moves along the x −axis with an acceleration

$x-x^2$ , where x is the distance of the particle at time t. The particle next comes to rest after it has covered a distance

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Qus : 3

Consider the function

$f(x)=\begin{cases}{-{x}^3+3{x}^2+1,} & {if\, x\leq2} \\ {\cos x,} & {if\, 2{\lt}x\leq4} \\ {{e}^{-x},} & {if\, x{\gt}4}\end{cases}$ Which of the following statements about f(x) is true:

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Qus : 4

The curve

$y=\frac{x}{1+x\tan x}$ attains maxima

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Qus : 5

The function

$f(x)=\frac{x}{1+x\tan x}$ ,

$0\leq x\leq\frac{\pi}{2}$ is maximum when

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Qus : 6

The maximum value of 4 sin²x + 3 cos²x + sin(x/2) + cos(x/2) is

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Qus : 7

The critical point and nature for the function f(x, y) = x² –2x + 2y² + 4y – 2 is

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Qus : 8

A condition that

$x^{3} + ax^{2} + bx + c$ may have no extremum is

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Qus : 9

$f(x)=\begin{cases}{{x}^2} & {,\leq0} \\ {2\sin x} & {,0}\end{cases}$ , then x = 0 is

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Qus : 10

Two non-negative numbers whose sum is 9 and the product of the one number and square of the other number is maximum, are

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Solution

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