**Case study Questions in the Class 10 Mathematics Chapter 1 **are very important to solve for your exam. Class 10 Maths Chapter 1 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving Class 10 Maths Case Study Questions Chapter 1 **Real Numbers**

In CBSE Class 10 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

# Real Numbers Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Maths **Chapter 1 Real Numbers**

**Case Study/Passage-Based Questions**

**Case Study 1:** Srikanth has made a project on real numbers, where he finely explained the applicability of exponential laws and divisibility conditions on real numbers. He also included some assessment questions at the end of his project as listed below. **(i) For what value of n, 4 ^{n }ends in 0?**

(a) 10 | (b) when n is even |

(c) when n is odd | (d) no value of n |

Answer: (d) no value of n

**(ii) If a is a positive rational number and n is a positive integer greater than 1, then for what value of n, a ^{n} is a rational number?**

(a) when n is any even integer | (b) when n is any odd integer |

(c) for all n > 1 | (d) only when n = 0 |

Answer: (c) for all n > 1

**(iii) If x and yare two odd positive integers, then which of the following is true?**

(a) x^{2} + y^{2} is even | (b) x^{2} + y^{2} is not divisible by 4 |

(c) x^{2} + y^{2} is odd | (d) both (a) and (b) |

Answer: (d) both (a) and (b)

**(iv) The statement ‘One of every three consecutive positive integers is divisible by 3’ is**

(a) always true | (b) always false |

(c) sometimes true | (d) None of these |

Answer: (a) always true

**(v) If n is any odd integer, then n2 – 1 is divisible by**

(a) 22 | (b) 55 | (c) 88 | (d) 8 |

Answer: (d) 8

**Case Study 2:** HCF and LCM are widely used in number system especially in real numbers in finding relationship between different numbers and their general forms. Also, product of two positive integers is equal to the product of their HCF and LCM

Based on the above information answer the following questions.

**(i) If two positive integers x and y are expressible in terms of primes as x =p ^{2}q^{3} and y=p^{3}q, then which of the following is true?**(a) HCF = pq

^{2}x LCM

(b) LCM = pq

^{2}x HCF

(c) LCM = p

^{2}q x HCF

(d) HCF = p

^{2}q x LCM

Answer: (b) LCM = pq2 x HCF

**ii) A boy with collection of marbles realizes that if he makes a group of 5 or 6 marbles, there are always two marbles left, then which of the following is correct if the number of marbles is p?**(a) p is odd

(b) p is even

(c) p is not prime

(d) both (b) and (c)

Answer: (d) both (b) and (c)

**(iii) Find the largest possible positive integer that will divide 398, 436 and 542 leaving remainder 7, 11, 15 respectively.**(a) 3

(b) 1

(c) 34

(d) 17

Answer: (d) 17

**(iv) Find the least positive integer that on adding 1 is exactly divisible by 126 and 600.**(a) 12600

(b) 12599

(C) 12601

(d) 12500

Answer: (b) 12599

**(v) If A, B and C are three rational numbers such that 85C – 340A = 109, 425A + 85B = 146, then the sum of A, B and C is divisible by**(a) 3

(b) 6

(c) 7

(d) 9

Answer: (a) 3

**Case Study 3:**Real numbers are an essential concept in mathematics that encompasses both rational and irrational numbers. Rational numbers are those that can be expressed as fractions, where the numerator and denominator are integers and the denominator is not zero. Examples of rational numbers include integers, decimals, and fractions. On the other hand, irrational numbers are those that cannot be expressed as fractions and have non-terminating and non-repeating decimal expansions. Examples of irrational numbers include √2, π (pi), and e. Real numbers are represented on the number line, which extends infinitely in both positive and negative directions. The set of real numbers is closed under addition, subtraction, multiplication, and division, making it a fundamental number system used in various mathematical operations and calculations.

**Which numbers can be classified as rational numbers?**a) Fractions

b) Integers

c) Decimals

d) All of the above

Answer: d) All of the above

**What are rational numbers?**a) Numbers that can be expressed as fractions

b) Numbers that have non-terminating decimal expansions

c) Numbers that extend infinitely in both positive and negative directions

d) Numbers that cannot be expressed as fractions

Answer: a) Numbers that can be expressed as fractions

**What are examples of irrational numbers?**a) √2, π (pi), e

b) Integers, decimals, fractions

c) Numbers with terminating decimal expansions

d) Numbers that can be expressed as fractions

Answer: a) √2, π (pi), e

**How are real numbers represented?**a) On the number line

b) In complex mathematical formulas

c) In algebraic equations

d) In geometric figures

Answer: a) On the number line

**What operations are closed under the set of real numbers?**a) Addition, subtraction, multiplication

b) Subtraction, multiplication, division

c) Addition, multiplication, division

d) Addition, subtraction, multiplication, division

Answer: d) Addition, subtraction, multiplication, division

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