CUET UG Mathematics Applied Maxima and Minima Previous Year Question Paper and Solution with PDF

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CUET UG Mathematics Applied
Previous Year Questions

CUET UG Mathematics Applied
Previous Year Questions
CUET UG Mathematics Applied

CUET UG Mathematics Applied Previous Year Questions (PYQs)

CUET UG Mathematics Applied Maxima And Minima PYQ

Qus : 1 CUET UG Mathematics Applied PYQ

For the function $f(x)=2x^{3}-9x^{2}+12x-5$, $x\in[0,3]$, match List-I with List-II:

List-I

List-II

(A) Absolute maximum value

(B) Absolute minimum value

(D) Point of minima

(I) 3

(II) 0

(III) −5

(IV) 4

Choose the correct answer from the options given below:

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CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2024 Mathematics PYQ

Solution

Qus : 2 CUET UG Mathematics Applied PYQ

If $x$ is a real, then minimum value of $x^2-8x+17$ is:

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CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2022 Applied Mathematics PYQ

Solution

Given

$f(x)=x^2-8x+17$

Complete the square:

$x^2-8x+17=(x^2-8x+16)+1$

$=(x-4)^2+1$

Since $(x-4)^2 \ge 0$

Minimum value occurs when $(x-4)^2=0$

So minimum value = $1$

Qus : 3 CUET UG Mathematics Applied PYQ

A cable network provider in a small town has $500$ subscribers and he used to collect Rs. $300$ per month from each subscriber. He proposes to increase the monthly charges and it is believed that for every increase of Rs. $1$, one subscriber will discontinue the service. If Rs. $x$ is the monthly increase in subscription amount, then the number of subscribers are:

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CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2022 Applied Mathematics PYQ

Solution

Initially subscribers = $500$

For every Rs. $1$ increase → 1 subscriber leaves.

So for increase of Rs. $x$ → $x$ subscribers leave.

Remaining subscribers

$=500-x$

Qus : 4 CUET UG Mathematics Applied PYQ

A cable network provider in a small town has $500$ subscribers and he used to collect Rs. $300$ per month from each subscriber. He proposes to increase the monthly charges and it is believed that for every increase of Rs. $1$, one subscriber will discontinue the service. The number of subscribers which gives the maximum revenue is:

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Go to Discussion

CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2022 Applied Mathematics PYQ

Solution

From previous question,

Revenue:

$R=(300+x)(500-x)$

Expand:

$R=150000+200x-x^2$

This is a quadratic function:

$R=-x^2+200x+150000$

Maximum occurs at

$x=\frac{-b}{2a}$

Here,

$a=-1,; b=200$

$x=\frac{-200}{2(-1)}$

$x=100$

So number of subscribers:

$500-x=500-100=400$

Qus : 5 CUET UG Mathematics Applied PYQ

What is increase in charges per subscriber that yields maximum revenue?

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CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2022 Applied Mathematics PYQ

Solution

From previous calculation,

Maximum occurs at

$x=100$

So increase in charges per subscriber = Rs. $100$

Qus : 6 CUET UG Mathematics Applied PYQ

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CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2022 Applied Mathematics PYQ

Solution

Revenue function:

$R=(300+x)(500-x)$

Expand:

$R=150000+200x-x^2$

This quadratic is maximum at

$x=100$

Now substitute:

$R=(300+100)(500-100)$

$R=400\times 400$

$R=160000$

Qus : 7 CUET UG Mathematics Applied PYQ

In a school, an auditorium was used for its cultural activities. The shape of the floor of the auditorium is rectangular with dimensions $x$ and $y$ $(x>y)$ and has fixed parameter $p$. Based on the above information answer the following questions. If $x$ and $y$ represent the length and breadth of the rectangular region, then:

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CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2022 Applied Mathematics PYQ

Solution

For a rectangle,

Perimeter $P=2(\text{length}+\text{breadth})$

Here

length $=x$

breadth $=y$

Given fixed parameter $p$ represents the perimeter.

$p=2(x+y)$

Qus : 8 CUET UG Mathematics Applied PYQ

In a school, an auditorium was used for its cultural activities. The shape of the floor of the auditorium is rectangular with dimensions $x$ and $y$ $(x>y)$ and has fixed parameter $p$. Based on the above information answer the following questions. The area $A$ of the floor, as a function of $x$ can be expressed as:

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CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2022 Applied Mathematics PYQ

Solution

From previous result

$p=2(x+y)$

$x+y=\frac{p}{2}$

Hence

$y=\frac{p}{2}-x$

Area of rectangle

$A=xy$

Substitute $y$

$A=x\left(\frac{p}{2}-x\right)$

$A=\frac{px}{2}-x^2$

$A=\frac{px-2x^2}{2}$

Qus : 9 CUET UG Mathematics Applied PYQ

In a school, an auditorium was used for its cultural activities.

The shape of the floor of the auditorium is rectangular with dimensions $x$ and $y$ $(x>y)$ and has fixed parameter $p$.

Based on the above information answer the following questions.

The value of $x$, for which area of floor of auditorium is maximum is:

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Go to Discussion

CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2022 Applied Mathematics PYQ

Solution

$p = 2(x+y)$

$x+y=\frac{p}{2}$

Hence

$y=\frac{p}{2}-x$

Area of rectangle

$A=xy$

$A=x\left(\frac{p}{2}-x\right)$

$A=\frac{px}{2}-x^2$

To maximize area

$\frac{dA}{dx}=\frac{p}{2}-2x$

Set derivative equal to zero

$\frac{p}{2}-2x=0$

$2x=\frac{p}{2}$

$x=\frac{p}{4}$

Qus : 10 CUET UG Mathematics Applied PYQ

In a school, an auditorium was used for its cultural activities.

The shape of the floor of the auditorium is rectangular with dimensions $x$ and $y$ $(x>y)$ and has fixed parameter $p$.

Based on the above information answer the following questions.

The value of $y$, for which the area of the floor of auditorium is maximum is:

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3
4
Go to Discussion

CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2022 Applied Mathematics PYQ

Solution

From earlier relation

$x+y=\frac{p}{2}$

From maximum area condition

$x=\frac{p}{4}$

$y=\frac{p}{2}-\frac{p}{4}$

$y=\frac{p}{4}$

Qus : 11 CUET UG Mathematics Applied PYQ

In a school, an auditorium was used for its cultural activities.

The shape of the floor of the auditorium is rectangular with dimensions $x$ and $y$ $(x>y)$ and has fixed parameter $p$.

Based on the above information answer the following questions.

Maximum area of floor is:

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4
Go to Discussion

CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2022 Applied Mathematics PYQ

Solution

From the given condition

$p=2(x+y)$

$x+y=\frac{p}{2}$

Area of rectangle

$A=xy$

Put

$y=\frac{p}{2}-x$

$A=x\left(\frac{p}{2}-x\right)$

$A=\frac{px}{2}-x^2$

To maximize area

$\frac{dA}{dx}=\frac{p}{2}-2x=0$

Hence

$x=\frac{p}{4}$

Then

$y=\frac{p}{2}-\frac{p}{4}=\frac{p}{4}$

Maximum area

$A=xy$

$=\frac{p}{4}\times\frac{p}{4}$

$=\frac{p^2}{16}$

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