Question 1

1. If LCM(x, y) = 36 and HCF(x, y) = 2, find the product of the numbers x and y.

A) 18B) 38C) 72D) 34

Answer

✓ Correct Answer: Option C

Question 2

2. Which of the following rational numbers has a terminating decimal expansion?

A) $\frac{15}{1600}$B) $\frac{17}{210}$C) $\frac{29}{343}$D) $\frac{77}{210}$

Answer

✓ Correct Answer: Option A

Question 3

Question 4

4. Given that $a = x^3 y^2$ and $b = xy^3$ (where x and y are prime numbers), what is the HCF of a and b?

A) $x^3 y^3$B) $x y^2$C) $x^2 y^2$D) x y

Answer

✓ Correct Answer: Option B

Question 5

5. The decimal expansion of $\frac{43}{2^4 \times 5^3}$ will terminate after how many decimal places?

A) 2 placesB) 3 placesC) 4 placesD) 5 places

Answer

✓ Correct Answer: Option C

Question 6

6. What is the least number that is divisible by all numbers from 1 to 10 (both inclusive)?

A) 100B) 504C) 1260D) 2520

Answer

✓ Correct Answer: Option D

Question 7

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

A) Always rationalB) Always irrationalC) Sometimes rational, sometimes irrationalD) 1

Answer

✓ Correct Answer: Option B

Question 8

8. If p is a prime number, then $\sqrt{p}$ is always a/an:

A) Irrational numberB) Rational numberC) IntegerD) Even number

Answer

✓ Correct Answer: Option A

Question 9

9. Two positive integers p and q can be expressed as $p = ab^2$ and $q = a^3b$, where a and b are prime numbers. What is their LCM?

A) abB) $a^2b^2$C) $a^3b^2$D) $a^3b^3$

Answer

✓ Correct Answer: Option C

Question 10

10. What is the sum of the exponents of prime factors in the prime factorization of 196?

A) 2B) 3C) 4D) 5

Answer

✓ Correct Answer: Option C

Question 11

11. If the HCF of 65 and 117 is expressible in the form 65m - 117, find the value of m.

A) 1B) 2C) 3D) 4

Answer

✓ Correct Answer: Option B

Question 12

12. Find the largest number that divides 70 and 125, leaving remainders 5 and 8 respectively.

A) 11B) 13C) 17D) 65

Answer

✓ Correct Answer: Option B

Question 13

13. The number 3.272727... (or 3.\overline{27}) is a/an:

A) IntegerB) Rational numberC) Irrational numberD) None of the above

Answer

✓ Correct Answer: Option B

Question 14

14. The value of $\pi - \frac{22}{7}$ is:

A) ZeroB) A rational numberC) An irrational numberD) An integer

Answer

✓ Correct Answer: Option C

Question 15

15. The decimal expansion of $\frac{14587}{1250}$ will terminate after:

A) 1 decimal placeB) 2 decimal placesC) 3 decimal placesD) 4 decimal places

Answer

✓ Correct Answer: Option D

Question 16

16. If n is any natural number, then the number $6^n - 5^n$ always ends with the digit:

A) 1B) 3C) 5D) 7

Answer

✓ Correct Answer: Option A

Question 17

17. What is the ratio of LCM and HCF of the least composite number and the least prime number?

A) 1 : 2B) 2 : 3C) 1 : 1D) 2 : 1

Answer

✓ Correct Answer: Option D

Question 18

18. For some integer m, every even integer is of the form:

A) mB) 2mC) m + 1D) 2m + 1

Answer

✓ Correct Answer: Option B

Question 19

19. For some integer q, every odd integer is of the form:

A) qB) q + 1C) 2qD) 2q + 1

Answer

✓ Correct Answer: Option D

Question 20

20. Which of the following is NOT an irrational number?

A) $2 + \sqrt{3}$B) $\sqrt{2}$C) $5 - \sqrt{7}$D) $\sqrt{16}$

Answer

✓ Correct Answer: Option D

Accepted Answer

✓ Correct Answer: Option B

Interactive Grade 10 Math Quiz: Real Numbers

1. If LCM(x, y) = 36 and HCF(x, y) = 2, find the product of the numbers x and y.

2. Which of the following rational numbers has a terminating decimal expansion?

3. Find the HCF of 96 and 404 using the prime factorization method.

4. Given that $a = x^3 y^2$ and $b = xy^3$ (where x and y are prime numbers), what is the HCF of a and b?

5. The decimal expansion of $\frac{43}{2^4 \times 5^3}$ will terminate after how many decimal places?

6. What is the least number that is divisible by all numbers from 1 to 10 (both inclusive)?

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

8. If p is a prime number, then $\sqrt{p}$ is always a/an:

9. Two positive integers p and q can be expressed as $p = ab^2$ and $q = a^3b$, where a and b are prime numbers. What is their LCM?

10. What is the sum of the exponents of prime factors in the prime factorization of 196?

11. If the HCF of 65 and 117 is expressible in the form 65m - 117, find the value of m.

12. Find the largest number that divides 70 and 125, leaving remainders 5 and 8 respectively.

13. The number 3.272727... (or 3.\overline{27}) is a/an:

14. The value of $\pi - \frac{22}{7}$ is:

15. The decimal expansion of $\frac{14587}{1250}$ will terminate after:

16. If n is any natural number, then the number $6^n - 5^n$ always ends with the digit:

17. What is the ratio of LCM and HCF of the least composite number and the least prime number?

18. For some integer m, every even integer is of the form:

19. For some integer q, every odd integer is of the form:

20. Which of the following is NOT an irrational number?