Class 10 Mathematics (NCERT)

1. The exponent of 2 in the prime factorisation of 144 is:

• A. 2
• B. 4
• C. 1
• D. 6

2. The HCF of two numbers a and b is 5 and their LCM is 200. What is the product of a and b?

• A. 205
• B. 1000
• C. 40
• D. 100

3. The total number of prime factors of a prime number is:

• A. 1
• B. 2
• C. 0
• D. Infinite

4. Which of the following is an irrational number?

• A. √4
• B. √9
• C. √7
• D. 22/7

5. The LCM of two co-prime numbers x and y is always equal to:

• A. 1
• B. x + y
• C. x / y
• D. x × y

6. If two positive integers p and q can be expressed as p = a²b³ and q = a³b, where a and b are prime numbers, then HCF(p, q) is:

• A. ab
• B. a²b
• C. a³b³
• D. a²b²

7. Referring to Question 6, what is LCM(p, q)?

• A. a²b
• B. a³b³
• C. a³b
• D. a²b³

8. The smallest composite number and the smallest prime number have an HCF of:

• A. 1
• B. 2
• C. 4
• D. 0

9. What is the LCM of the smallest prime number and the smallest composite number?

• A. 2
• B. 4
• C. 8
• D. 6

10. The fundamental theorem of arithmetic states that every composite number can be uniquely factorized as a product of:

• A. Odd numbers
• B. Even numbers
• C. Prime numbers
• D. Rational numbers

11. If HCF(306, 657) = 9, then LCM(306, 657) is equal to:

• A. 22338
• B. 22383
• C. 22833
• D. 306 × 657

12. The product of a non-zero rational number and an irrational number is always:

• A. Always rational
• B. Always irrational
• C. Rational or irrational
• D. Zero

13. The sum or difference of a rational number and an irrational number is:

• A. An integer
• B. A rational number
• C. An irrational number
• D. A whole number

14. If p is a prime number and p divides a² (where a is a positive integer), then p also divides:

• A. a/2
• B. a
• C. 2a
• D. a³

15. What is the value of x in the factor tree: 2 × (3 × x) = 42?

• A. 5
• B. 7
• C. 9
• D. 14

16. Express 140 as a product of its prime factors:

• A. 2² × 5 × 7
• B. 2 × 5² × 7
• C. 2³ × 5
• D. 2 × 3 × 5 × 7

17. Express 156 as a product of prime factors:

• A. 2² × 3 × 13
• B. 2 × 3² × 13
• C. 2² × 3² × 13
• D. 2 × 3 × 17

18. Three bells toll together at intervals of 9, 12, and 15 minutes respectively. If they toll together now, after how much time will they toll together next?

• A. 60 minutes
• B. 90 minutes
• C. 180 minutes
• D. 360 minutes

19. If n is a natural number, then 6ⁿ always ends with the digit:

• A. 0
• B. 2
• C. 6
• D. 4

20. Can the number 4ⁿ, where n is a natural number, end with the digit zero?

• A. Yes, for n = 0
• B. Yes, for all even n
• C. No, because prime factorisation of 4ⁿ does not contain 5
• D. Yes, for n = 5

21. The set of real numbers consists of:

• A. Only rational numbers
• B. Only irrational numbers
• C. Both rational and irrational numbers
• D. Only integers

22. What is the greatest number that divides 70 and 125, leaving remainders 5 and 8 respectively?

• A. 13
• B. 65
• C. 875
• D. 1750

23. Which of the following is NOT a prime factor of 3825?

• A. 3
• B. 5
• C. 17
• D. 7

24. Given that HCF(a, b) × LCM(a, b) = 1200 and a = 30, what is the value of b?

• A. 30
• B. 40
• C. 60
• D. 120

25. If (3 + √5) is a root, then (3 - √5) is also a root and their sum is:

• A. Irrational
• B. Rational (6)
• C. Zero
• D. 2√5

26. The product of (2 + √3) and (2 - √3) is:

• A. An irrational number
• B. A rational number equal to 1
• C. A rational number equal to 7
• D. 4

27. How many prime factors does the number 5005 have?

• A. 2
• B. 3
• C. 4
• D. 5

28. HCF of any two consecutive even natural numbers is always:

• A. 1
• B. 2
• C. 4
• D. 0

29. HCF of any two consecutive natural numbers is always:

• A. 1
• B. 2
• C. 0
• D. Depends on the numbers

30. Is π (Pi) a rational or an irrational number?

• A. Rational number
• B. Irrational number
• C. Integer
• D. Natural number