Please refer to **Case Study Chapter 1 Real Numbers Mathematics** with answers provided below. These case study based questions are expected to come in the upcoming Class 10 Mathematics examinations. We have provided case study questions class 10 maths for all chapters on our website as per the latest examination pattern issued by CBSE, NCERT, and KVS.

## Chapter 1 Real Numbers Case study Questions Class 10 Maths

**I. To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections — section A and section B of grade X. There are 32 students in section A and 36 students in section B.**

**Question. 36 can be expressed as a product of its primes as: **

(a) 2^{2} × 3^{2}

(b) 2^{1} × 3^{3}

(c) 2^{3} × 3^{1}

(d) 2^{0} × 3^{0}

**Answer**

A

**Question. 7 × 11 × 13 × 15 + 15 is a: **

(a) Prime number

(b) Composite number

(c) Neither prime nor composite

(d) None of the above

**Answer**

B

**Question. What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of section A or section B? **

(a) 144

(b) 128

(c) 288

(d) 272

**Answer**

C

**Question. If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32 , 36) is: **

(a) 2

(b) 4

(c) 6

(d) 8

**Answer**

B

**Question. If p and q are positive integers such that p = ab ^{2} and q = a^{2}b, where a, b are prime numbers, then the LCM (p, q) is **

(a) ab

(b) a

^{2}b

^{2}

(c) a

^{3}b

^{2}

(d) a

^{3}b

^{3}

**Answer**

B

**II. Traffic Lights (or traffic signals) are lights used to control movement of traffics. They are installed on roads at intersections and crossings. The different colours of light tell drivers what to do. The traffic lights at different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively.**

**Question. 108 can be expressed as a product of its primes as **

(a) 2^{3} × 3^{2}

(b) 2^{3} × 3^{3}

(c) 2^{2} × 3^{2}

(d) 2^{2} × 3^{3}

**Answer**

D

**Question. The HCF of 48, 72, 108 is **

(a) 18

(b) 16

(c) 12

(d) 10

**Answer**

C

**Question. If all the traffic lights change simultaneously at 8:20:00 hrs, they will again change simultaneously at **

(a) 8:27:12 hrs

(b) 8:32:24 hrs

(c) 8:40:08 hrs

(d) 8:24:24 hrs

**Answer**

A

**Question. The [HCF × LCM] for the numbers 48, 72, 108 is **

(a) 2472

(b) 3680

(c) 4090

(d) 5184

**Answer**

D

**Question. The LCM of 48, 72, 108 is **

(a) 520

(b) 432

(c) 396

(d) 420

**Answer**

B

**III. The Army Day is celebrated on 15th January every year in India. The day is celebrated in the form of parades and other military shows in the national capital New Delhi as well as in all headquarters of army.Parade I: An Army contingent of 616 members is to march behind an army band of 32 members in parade. The two groups are to march in the same number of columns.Parade II: An Army contingent of 1000 members is to march behind an army band of 56 members in parade. The two groups are to march in the same number of columns.**

**Question. What is the maximum number of columns in which they can march? **

(a) 6

(b) 8

(c) 10

(d) 12

**Answer**

B

**Question. The HCF of numbers 1000 and 56 is **

(a) 2

(b) 4

(c) 6

(d) 8

**Answer**

D

**Question. Which of the following is the correct expression of the number 1000 as a product of its prime numbers? **

(a) 2^{3} × 5^{3}

(b) 10^{3}

(c) 8 × 125

(d) 8

**Answer**

A

**Question. The expression of 616 as a product of its prime numbers is **

(a) 2^{2} × 14^{1} × 11^{1}

(b) 2^{3} × 7^{1} × 11^{1}

(c) 2^{4} × 7^{1} × 11^{1}

(d) None of these.

**Answer**

B

**Question. The LCM of 32 and 616 is **

(a) 1248

(b) 1836

(c) 2464

(d) 3016

**Answer**

C

**IV. A Mathematics Exhibition is being conducted in your school and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience. Observe the given factor tree and answer the following questions:**

**Question. What will be the value of z? **

(a) 22

(b) 23

(c) 17

(d) 19

**Answer**

B

**Question. The prime factorisation of 13915 is **

(a) 5 × 11^{2} × 13^{2}

(b) 5 × 11^{3} × 23^{2}

(c) 5 × 11^{2} × 23

(d) 5 × 112 × 13^{2}

**Answer**

C

**Question. According to Fundamental Theorem of Arithmetic, 13915 is a **

(a) Composite number

(b) Prime number

(c) Neither prime nor composite

(d) Even number

**Answer**

A

**Question. What will be the value of y? **

(a) 23

(b) 22

(c) 11

(d) 19

**Answer**

C

**Question. What will be the value of x? **

(a) 15005

(b) 13915

(c) 56920

(d) 17429

**Answer**

B

**I. Richard Paul and Linda Elder state that “Thinking is not driven by answers but by questions”. Keeping this idea in mind, mathematics teacher of class X of Blue Marble School decided to develop interest and motivate students to become actively involved in the concept he asked some questions. The teacher drew a flow chart for real numbers family on the board as shown below. The chart for the set of real numerals includes all the types of numbers. Observe the chart carefully.**

**Question. Which of the following is not irrational ? **

(a) (3+ √7)

(b) (3 −√7)

(c) (3+ √7)(3 − √7)

(d) 3 √7

**Answer**

C

**Question. The decimal expansion of the number 144/ 2 ^{2} Χ 5^{3} Χ 7 **

(a) Terminating

(b) non-terminating

(c) non-terminating non-repeating

(d) non-terminating repeating

**Answer**

D

**Question. The decimal expansion of the rational number 14587 1250 will terminate after: **

(a) one decimal place

(b) two decimal places

(c) three decimal places

(d) four decimal places

**Answer**

B

**Question. The sum of a rational and irrational number is **

(a) Rational

(b) Irrational

(c) both of the above

(d) none of the above

**Answer**

B

**Question. A rational number in its decimal expansion is 327.7081. What would be the prime factors of q when the number is expressed in the p/q form? **

(a) 2 and 3

(b) 3 and 5

(c) 2, 3 and 5

(d) 2 and 5

**Answer**

D

**II. An object when thrown upwards reaches a certain height and then falls downwards. Whenever an object falls towards the earth, acceleration is involved. This acceleration is due to the earth’s gravitational force. Therefore, this acceleration is called the acceleration due to the gravitational force of the earth (or acceleration due to gravity). It is denoted by g. The unit of g is the same as that of acceleration, that is, m/s2. Its value is 9.8 m/s2 on Earth. When discussing the acceleration of gravity, it was mentioned that the value of g is dependent upon location. There are slight variations in the value of g on earth’s surface. The following acceleration of gravity values can be calculated for the various planets.**

**Question. An irrational number lying between 8.83 and 11.2 is C**

(a) 8.8010203040…

(b) 8.9010203040…

(c) 11.10203040…

(d) None of these

**Answer**

C

**Question. The 2 ^{n} × 5^{m} form of denominator 21/2 and its decimal expansion respectively are **

(a) 2

^{0}× 5

^{1}

(b) 2

^{1}× 5

^{1}

(c) 2

^{0}× 5

^{0}

(d) None of these

**Answer**

B

**Question. Which of the following is the decimal expansion of a rational number? **

(a) 26.0

(b) 8.83

(c) 3.75

(d) All of these

**Answer**

D

**Question. The decimal expansion of the rational number 56/5 will has **

(a) One decimal place

(b) Two decimal places

(c) Three decimal places

(d) Four decimal places

**Answer**

A

**Question. The p/q form of the number 3.75 will be **

(a) 11/4

(b) 17/2

(c) 15/4

(d) None of these

**Answer**

C

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