I have provided the **Class 10 Maths Real Number Worksheet DPP 2024**. This DPP has 80 Marks. Also the worksheet contains the 1 to 35.

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## Best Class 10 Maths Real Number DPP 2025

**Multiple Choice Type Questions**

What is the greatest possible speed at which a girl can walk 95 m and 171 m in an exact number of minutes ?

(a) 17 m/min

(b) 19 m/min

(c) 23 m/min

(d) 13 m/min

Three alarm clocks ring their alarms at regular intervals of 20 min, 25min and 30 min respectively. If they first beep together at 12 noon, at what time will they beep again for the first time?

(a) 4:00 pm

(b) 4:30 pm

(c) 5:00 pm

(d) 5:30 pm

The greatest number which when divided by 1251, 9377 and 15628 leaves remainder 1, 2 and 3 respectively is

(a) 575

(b) 450

(c) 750

(d) 625

The LCM of two numbers is 2400. Which of the following CANNOT be their HCF ?

(a) 300

(b) 400

(c) 500

(d) 600

The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is:

(a) 13

(b) 65

(c) 875

(d) 1,750

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

(a) 10

(b) 100

(c) 504

(d) 2520

### Assertion and Reason Questions

Assertion (A): For no value of n, where n is a natural number, the number 6n ends with the digit zero.

Reason (R): For a number to end with digit zero, its prime factors should have 2 and 5.

(a) Both A and R are true and R is the correct explanation of A.

(b) Both A and R are true but R is not the correct explanation of A.

(c) A is true but R is false.

(d) A is false but R is true.

Assertion (A): If LCM of two numbers is 2475 and their product is 12375, then their HCF is 5.

Reason (R): HCF (a, b) × LCM (a, b) = a × b.

(a) Both A and R are true and R is the correct explanation of A.

(b) Both A and R are true but R is not the correct explanation of A.

(c) A is true but R is false.

(d) A is false but R is true.

Assertion (A): If product of two numbers is 5730 and their HCF is 17.then their LCM is 340.

Reason (R): HCF is always a factor of LCM.

(a) Both A and R are true and R is the correct explanation of A.

(b) Both A and R are true and R is not the correct explanation of A.

(c) A is true but R is false.

(d) A is false but R is true.

Assertion (A): Every rational number is a real number.

Reason (R): Real numbers include both rational and irrational numbers.

(a) Both A and R are true, and R is the correct explanation of A.

(b) Both A and R are true, but R is NOT the correct explanation of A.

(c) A is true, but R is false.

(d) A is false, but R is true.

### 1 and 3 marks Questions

Find the least number which when divided by 12, 16 and 24 leaves remainder 7 in each case.

Two numbers are in the ratio 2 : 3 and their LCM is 180. What is the HCF of these numbers?

Prove that √3 is an irrational number.

Explain why 2 x 3 x 5 + 5 and 5 x 7 x 11 + 7 x 5 are composite numbers.

The LCM of two numbers is 182 and their HCF is 13. If one of the numbers is 26. find the other.

Show that 5 + 2 √7 is an irrational number, where √7 is given to be an irrational number.

The LCM of two numbers is 9 times their HCF. The sum of LCM and HCF is 500. Find the HCF of the two numbers.

1f HCF of 65 and 117 is expressible in the form 65n-117, then find the value of n..

Prove that √2 is an irrational number.

Show that 11 x 19 x 23 + 3 x 11 is not a prime number.

Prove that √5 is an irrational number.

Prove that 2 + 5√3 is an irrational number. It is given that √3 is an irrational number.

Prove that 5 − 2√3 is an irrational number. It is given that √3 is an irrational number.

Prove that 6-4√5 is an irrational number, given that √5 is an irrational number.

**Real Number Unit Exam Worksheet 2024:**

### SECTION – A

**Questions 1 to 20 carry 1 mark each.**

MCQs

**Which one of the following is not a rational number?**(a) √2

(b) 0

(c) √4

(d) √-16**Which one of the following is an irrational number?**(a) √4

(b) 3√8

(c) √100

(d) -√0.64**What is the decimal form of**(a) 3.35**$3\frac{3}{8}$**

(b) 3.375

(c) 33.75

(d) 337.5**What is the decimal form of $\frac{5}{6}$?**(a) 0.83

(b) 0.833

(c) 0.63

(d) 0.633**What is the decimal representation of the rational number $\frac{8}{27}$?**(a) 0.296

(b) 0.296

(c) 0.296

(d) 0.296**If 0.6666… is represented as p/q, what is the value of $\frac{p}{q}$?**(a) $\frac{2}{3}$

(b) $\frac{6}{99}$

(c) $\frac{3}{5}$

(d) $\frac{1}{66}$**What is the value of (√5 + √2)(√5 – √2)?**(a) 10

(b) 7

(c) 3

(d) None of these**Express 0.36 in $\frac{p}{q}$ form.**(a) $\frac{9}{25}$

(b) $\frac{18}{50}$

(c) $\frac{36}{99}$

(d) $\frac{3}{8}$**The decimal expansion of π**

(a) is terminating

(b) is non-terminating and recurring

(c) is non-terminating and non-recurring

(d) does not exist.**If a and b are positive integers, then HCF(a, b) x LCM(a,b)=**(a) a × b

(b) a + b

(c) a – b

(d) a/b**The number $0.57\overline{7}$ in the form $\frac{p}{q}$ is:**(a) $\frac{19}{35}$

(b) $\frac{57}{99}$

(c) $\frac{57}{95}$

(d) $\frac{19}{30}$**The number $0.57\overline{57}$ in the form $\frac{p}{q}$ is:**(a) $\frac{26}{45}$

(b) $\frac{13}{27}$

(c) $\frac{57}{99}$

(d) $\frac{13}{29}$**The product of L.C.M and H.C.F. of two numbers is equal to**(a) Sum of numbers

(b) Difference of numbers

(c) Product of numbers

(d) Quotients of numbers**For some integer nm, every even integer is of the form**(a) m

(b) m+1

(c) 2m

(d) 2m+1**L.C.M. of two co-prime numbers is always**(a) product of numbers

(c) difference of numbers

(b) sum of numbers

(d)none**What is the H.C.F. of two consecutive even numbers**(a) 1

(b)2

(c) 4

(d) 8**For some integer q, every odd integer is of the form**(a) q

(b) q+1

(c) 2q

(d) 2q+1**$(n^2 – 1)$ is divisible by 8, if n is –**(a) an integer

(b) a natural number

(c) an odd integer

(d) an even integer

Assertion and Reason

DIRECTION: In the question number 19 and 20, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct option

**19.**

**Assertion (A):** The sum of a rational number and an irrational number is always irrational.

**Reason (R):** The sum of a rational number and an irrational number results in a number that cannot be expressed as a fraction.

**Options:**

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Both Assertion and Reason are false.

**20.**

**Assertion:** The product of two irrational numbers is always irrational.

**Reason:** The multiplication of two irrational numbers results in a number that cannot be expressed as a fraction.

**Options:**

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Both Assertion and Reason are false.

### SECTION B

Questions 21 to 25 carry 2M each

21. If LCM (480, 672) 3360, find HCF (480,672).

22. Express 0.69 as a rational number in $\frac{p}{q}$ form.

23. Show that the number of the form $7^n$ cannot have unit digit zero.

24. State the Fundamental theorem of Arithmetic.

25. Find the missing numbers in the following factorization:

### SECTION C

Questions 26 to 31 carry 3 marks each

26. Find the HCF and LCM of 144, 180 and 192 by using prime factorization method.

27. Given that HCF (306, 657) = 9, find the LCM(306, 657).

28. Find the HCF and LCM of 17, 23 and 37 by using prime factorization method.

29. If HCF(6, a) = 2 and LCM(6, a) = 60 then find the value of a.

30. Prove that √3 is an irrational number.

### SECTION-D

Questions 32 to 35 carry 5M each

32. Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case.

32. Find the smallest 4-digit number which is divisible by 18, 24 and 32.

33. Renu purchases two bags of fertiliser of weights 75 kg and 69 kg. Find the maximum value of weight which can measure the weight of the fertiliser exact number of times.

34. In a seminar, the number, the number of participants in Hindi, English and Mathematics are 60, 84 and 108, respectively. Find the minimum number of rooms required if in each room the same number of participants are to be seated and all of them being in the same subject.

35. 144 cartons of Coke cans and 90 cartons of Pepsi cans are to be stacked in a canteen. If each stack is of the same height and is to contain cartons of the same drink, what would be the greatest number of cartons each stack would have?

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