Numbers
Q1. The HCF of 36 and 48 is
Correct Answer: C. 12
Explanation: $36 = 2^2 \times 3^2$ and $48 = 2^4 \times 3$. The highest common factor is $2^2 \times 3 = 12$.
Explanation: $36 = 2^2 \times 3^2$ and $48 = 2^4 \times 3$. The highest common factor is $2^2 \times 3 = 12$.
Q2. The LCM of 12 and 18 is
Correct Answer: B. 36
Explanation: $12 = 2^2 \times 3$ and $18 = 2 \times 3^2$. The least common multiple is $2^2 \times 3^2 = 36$.
Explanation: $12 = 2^2 \times 3$ and $18 = 2 \times 3^2$. The least common multiple is $2^2 \times 3^2 = 36$.
Q3. Which of the following is a prime number?
Correct Answer: C. 29
Explanation: 29 has only two factors, 1 and 29, hence it is a prime number.
Explanation: 29 has only two factors, 1 and 29, hence it is a prime number.
Q4. The smallest prime number is
Correct Answer: C. 2
Explanation: 2 is the only even prime and the smallest prime number.
Explanation: 2 is the only even prime and the smallest prime number.
Q5. The place value of 7 in 85,43,706 is
Correct Answer: C. 700
Explanation: 7 is in the hundreds place, so its place value is 700.
Explanation: 7 is in the hundreds place, so its place value is 700.
Q6. Which number is divisible by 9?
Correct Answer: A. 4581
Explanation: The sum of the digits is $4 + 5 + 8 + 1 = 18$, which is divisible by 9.
Explanation: The sum of the digits is $4 + 5 + 8 + 1 = 18$, which is divisible by 9.
Q7. A number is divisible by 5 if its last digit is
Correct Answer: A. 0 or 5
Explanation: A number is divisible by 5 if and only if its last digit is 0 or 5.
Explanation: A number is divisible by 5 if and only if its last digit is 0 or 5.
Q8. The HCF of two numbers is 12 and their LCM is 144. If one number is 36, the other is
Correct Answer: B. 48
Explanation: Since $\text{HCF} \times \text{LCM} = \text{Product of numbers}$, the other number is $(12 \times 144) / 36 = 48$.
Explanation: Since $\text{HCF} \times \text{LCM} = \text{Product of numbers}$, the other number is $(12 \times 144) / 36 = 48$.
Q9. Which of the following is a composite number?
Correct Answer: C. 21
Explanation: $21 = 3 \times 7$, meaning it has more than two factors and is therefore composite.
Explanation: $21 = 3 \times 7$, meaning it has more than two factors and is therefore composite.
Q10. How many prime numbers are there between 1 and 20?
Correct Answer: C. 8
Explanation: The prime numbers between 1 and 20 are 2, 3, 5, 7, 11, 13, 17, and 19, making a total of 8.
Explanation: The prime numbers between 1 and 20 are 2, 3, 5, 7, 11, 13, 17, and 19, making a total of 8.
Q11. The face value of 6 in 36,427 is
Correct Answer: A. 6
Explanation: The face value of any digit is always equal to the digit itself, which is 6.
Explanation: The face value of any digit is always equal to the digit itself, which is 6.
Q12. The smallest 4-digit number divisible by 6 is
Correct Answer: B. 1002
Explanation: The smallest 4-digit number is 1000. $1000 \div 6 = 166$ with a remainder of 4. Adding 2 gives 1002, which is perfectly divisible by 6.
Explanation: The smallest 4-digit number is 1000. $1000 \div 6 = 166$ with a remainder of 4. Adding 2 gives 1002, which is perfectly divisible by 6.
Q13. The greatest number that divides 60 and 75 exactly is
Correct Answer: C. 15
Explanation: The greatest number that divides both exactly is their Highest Common Factor, $\text{HCF}(60, 75) = 15$.
Explanation: The greatest number that divides both exactly is their Highest Common Factor, $\text{HCF}(60, 75) = 15$.
Q14. The product of two numbers is 240 and their HCF is 4. Their LCM is
Correct Answer: B. 60
Explanation: Since $\text{LCM} = \text{Product} / \text{HCF}$, the calculation is $240 / 4 = 60$.
Explanation: Since $\text{LCM} = \text{Product} / \text{HCF}$, the calculation is $240 / 4 = 60$.
Q15. Sum of two odd numbers is always
Correct Answer: B. even
Explanation: An odd number plus an odd number always equals an even number (e.g., $3 + 5 = 8$).
Explanation: An odd number plus an odd number always equals an even number (e.g., $3 + 5 = 8$).
Q16. The number of factors of 24 is
Correct Answer: B. 8
Explanation: The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, giving a total of 8 factors.
Explanation: The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, giving a total of 8 factors.
Q17. The LCM of 8, 12 and 16 is
Correct Answer: C. 48
Explanation: Breaking them down: $8 = 2^3$, $12 = 2^2 \times 3$, and $16 = 2^4$. The $\text{LCM} = 2^4 \times 3 = 48$.
Explanation: Breaking them down: $8 = 2^3$, $12 = 2^2 \times 3$, and $16 = 2^4$. The $\text{LCM} = 2^4 \times 3 = 48$.
Q18. A number divisible by both 2 and 3 is also divisible by
Correct Answer: C. 6
Explanation: If a number is divisible by two coprime numbers like 2 and 3, it must also be divisible by their product ($2 \times 3 = 6$).
Explanation: If a number is divisible by two coprime numbers like 2 and 3, it must also be divisible by their product ($2 \times 3 = 6$).
Q19. The sum of place values of 5 in 5,053 is
Correct Answer: C. 5050
Explanation: The 5 in the thousands place equals 5000, and the 5 in the tens place equals 50. Their sum is $5000 + 50 = 5050$.
Explanation: The 5 in the thousands place equals 5000, and the 5 in the tens place equals 50. Their sum is $5000 + 50 = 5050$.
Q20. The successor of the greatest 4-digit number is
Correct Answer: B. 10000
Explanation: The greatest 4-digit number is 9999. Its successor is $9999 + 1 = 10000$.
Explanation: The greatest 4-digit number is 9999. Its successor is $9999 + 1 = 10000$.