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CBSE Class 9  >  Class 9 Test  >  : Additional Practice  >  Test: Polynomials- Case Based Type Questions - Class 9 MCQ

Polynomials- Case Based Type Questions - Free with solutions Class 9


MCQ Practice Test & Solutions: Test: Polynomials- Case Based Type Questions (10 Questions)

You can prepare effectively for Class 9 Class 9: Additional Practice with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Polynomials- Case Based Type Questions". These 10 questions have been designed by the experts with the latest curriculum of Class 9 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 20 minutes
  • - Number of Questions: 10

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Test: Polynomials- Case Based Type Questions - Question 1
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Beti Bachao, Beti Padhao (BBBP) is a personal campaign of the Government of India that aims to generate awareness and improve the efficiency of welfare services intended for girls.

In a school, a group of (x + y) teachers, (x2 + y2) girls and (x3 + y3) boys organised a campaign on Beti Bachao, Beti Padhao.

Q. If in the group, there are 10 teachers and 58 girls, then what is the number of boys?

Detailed Solution: Question 1

No. of teachers = x + y = 10

⇒ (x + y)2 = (10)2

⇒ x2 + y2 + 2xy = 100

[Since (a + b)2 = a2 + b2 + 2ab]

No. of students = (x2 + y2) = 58

⇒ 58 + 2xy = 100

⇒ 2xy = 100 – 58

⇒ 2xy = 42

⇒ xy = 42/2

⇒ xy = 21

Now, since (x + y)3 = [x3 + y3 + 3xy(x + y)]

⇒ (10)3 = [x3 + y3 + 3 × 21(10)]

⇒ 1000 = (x3 + y3 + 630)

⇒ 1000 – 630 = (x3 + y3)

⇒ (x3 + y3) = 370

Test: Polynomials- Case Based Type Questions - Question 2
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Beti Bachao, Beti Padhao (BBBP) is a personal campaign of the Government of India that aims to generate awareness and improve the efficiency of welfare services intended for girls.

In a school, a group of (x + y) teachers, (x2 + y2) girls and (x3 + y3) boys organised a campaign on Beti Bachao, Beti Padhao.

Q. Which is the correct identity?

Detailed Solution: Question 2

Here, Correct identity is (a + b)2 = a2 + b2 + 2ab.

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Test: Polynomials- Case Based Type Questions - Question 3
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Beti Bachao, Beti Padhao (BBBP) is a personal campaign of the Government of India that aims to generate awareness and improve the efficiency of welfare services intended for girls.

In a school, a group of (x + y) teachers, (x2 + y2) girls and (x3 + y3) boys organised a campaign on Beti Bachao, Beti Padhao.

Q. Which mathematical concept is used here?

Detailed Solution: Question 3

Here, we used Polynomials Concept.

In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Test: Polynomials- Case Based Type Questions - Question 4
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Beti Bachao, Beti Padhao (BBBP) is a personal campaign of the Government of India that aims to generate awareness and improve the efficiency of welfare services intended for girls.

In a school, a group of (x + y) teachers, (x2 + y2) girls and (x3 + y3) boys organised a campaign on Beti Bachao, Beti Padhao.

Q. (x – y)3 =

Detailed Solution: Question 4

We know that (x - y)3 can be written as

(x - y)(x - y)(x - y)

We know that (x - y)(x - y) can be multiplied and written as

= x2 - xy - yx + y2 (x - y)

= x2 - 2xy + y2 (x - y)

= x3 - 2x2y + xy2 - yx2 + 2xy2 - y3

= x3 – y3 – 2xy(x – y)

Test: Polynomials- Case Based Type Questions - Question 5
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Beti Bachao, Beti Padhao (BBBP) is a personal campaign of the Government of India that aims to generate awareness and improve the efficiency of welfare services intended for girls. In a school, a group of (x + y) teachers, (x2 + y2) girls and (x3 + y3) boys organised a campaign on Beti Bachao, Beti Padhao.

Q. Using the identity (x2 – y2) = (x + y)(x – y), find (x2 – y2) if x – y = 23 and x + y = 10.

Detailed Solution: Question 5

To find (x2 - y2), we can use the identity:

  • (x2 - y2) = (x + y)(x - y)

We know:

  • x - y = 23
  • x + y = 10

Let's denote x + y as A. Therefore, we have:

  • A = 10
  • x - y = 23

Next, we can find xy:

  • xy = (x+y)(x-y)/2 = (10)(23)/2 = 115

Now, we can calculate:

  • (x2 - y2) = (x + y)(x - y) = 10 * 23 = 230

Thus, the value of (x2 - y2) is 230.

Test: Polynomials- Case Based Type Questions - Question 6
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National Association For The Blind (NAB) aimed to empower and well-inform visually challenged population of our country, thus enabling them to lead a life of dignity and productivity.

Ravi donated to NAB. When his cousin asks to tell the amount donated by him, he just gave the below hint.

Q. Find the amount donated by Ravi.

Detailed Solution: Question 6

Test: Polynomials- Case Based Type Questions - Question 7
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National Association For The Blind (NAB) aimed to empower and well-inform visually challenged population of our country, thus enabling them to lead a life of dignity and productivity.

Ravi donated to NAB. When his cousin asks to tell the amount donated by him, he just gave the below hint.

Q. (x – y)3 =

Detailed Solution: Question 7

We know that (x - y)3 can be written as

(x - y)(x - y)(x - y)

We know that (x - y)(x - y) can be multiplied and written as

x2 - xy - yx + y2 (x - y)

= x2 - 2xy + y2 (x - y)

= x3 - 2x2y + xy2 - yx2 + 2xy2 - y3

= x3 – y3 – 3xy(x – y)

Test: Polynomials- Case Based Type Questions - Question 8
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National Association For The Blind (NAB) aimed to empower and well-inform visually challenged population of our country, thus enabling them to lead a life of dignity and productivity.

Ravi donated to NAB. When his cousin asks to tell the amount donated by him, he just gave the below hint.

Q. (x + a)(x + b) = x2 + ................ x + ab

Detailed Solution: Question 8

(x + a)(x + b) = x2 + (a + b)x + ab

Test: Polynomials- Case Based Type Questions - Question 9
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National Association For The Blind (NAB) aimed to empower and well-inform visually challenged population of our country, thus enabling them to lead a life of dignity and productivity.

Ravi donated to NAB. When his cousin asks to tell the amount donated by him, he just gave the below hint.

Q. Which mathematical concept is involved in the above situation?

Detailed Solution: Question 9

Here, we used Polynomials Concept.

In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Test: Polynomials- Case Based Type Questions - Question 10
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National Association For The Blind (NAB) aimed to empower and well-inform visually challenged population of our country, thus enabling them to lead a life of dignity and productivity.

Ravi donated to NAB. When his cousin asks to tell the amount donated by him, he just gave the below hint.

Q. Find the amount donated by Ravi if

Detailed Solution: Question 10

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This test contains 10 MCQs on Polynomials- Case Based Type Questions with detailed solutions for each question. It is part of the Class 9: Additional Practice course on EduRev, designed to align with the current Class 9 syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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