Class 10 Maths Real Number Important Questions DPP PDF | Board 2025

SECTION – A
Questions 1 to 20 carry 1 mark each.

MCQs

1. Which one of the following is not a rational number?
   (a) √2
   (b) 0
   (c) √4
   (d) √-16
2. Which one of the following is an irrational number?
   (a) √4
   (b) 3√8
   (c) √100
   (d) -√0.64
3. What is the decimal form of $3\frac{3}{8}$
   (a) 3.35
   (b) 3.375
   (c) 33.75
   (d) 337.5
4. What is the decimal form of $\frac{5}{6}$?
   (a) 0.83
   (b) 0.833
   (c) 0.63
   (d) 0.633
5. What is the decimal representation of the rational number $\frac{8}{27}$?
   (a) 0.296
   (b) 0.296
   (c) 0.296
   (d) 0.296
6. 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) $\frac{1}{66}$
7. What is the value of (√5 + √2)(√5 – √2)?
   (a) 10
   (b) 7
   (c) 3
   (d) None of these
8. Express 0.36 in $\frac{p}{q}$ form.
   (a) $\frac{9}{25}$
   (b) $\frac{18}{50}$
   (c) $\frac{36}{99}$
   (d) $\frac{3}{8}$
9. 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.
10. 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
11. 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) $\frac{19}{30}$
12. 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) $\frac{13}{29}$
13. 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
14. For some integer nm, every even integer is of the form
    (a) m
    (b) m+1
    (c) 2m
    (d) 2m+1
15. L.C.M. of two co-prime numbers is always
    (a) product of numbers
    (c) difference of numbers
    (b) sum of numbers
    (d)none
16. What is the H.C.F. of two consecutive even numbers
    (a) 1
    (b)2
    (c) 4
    (d) 8
17. For some integer q, every odd integer is of the form
    (a) q
    (b) q+1
    (c) 2q
    (d) 2q+1
18. $(n^2 – 1)$ 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?