Q.1 Which of the following numbers is a prime number?
21
29
35
49
Explanation - A prime number has only two distinct positive divisors: 1 and itself. 29 is divisible only by 1 and 29.
Correct answer is: 29
Q.2 What is the least common multiple (LCM) of 12 and 18?
36
54
72
24
Explanation - LCM of 12 and 18 is the smallest number divisible by both 12 and 18, which is 36.
Correct answer is: 36
Q.3 Find the greatest common divisor (GCD) of 48 and 180.
12
24
36
18
Explanation - GCD is the largest number that divides both numbers exactly. Factors: 48: 2^4*3, 180: 2^2*3^2*5; common factors: 2^2*3=12.
Correct answer is: 12
Q.4 Which of the following is a perfect square?
50
64
70
81
Explanation - 64 = 8^2. Perfect squares are numbers obtained by squaring an integer.
Correct answer is: 64
Q.5 Which of the following is divisible by 11?
121
132
143
All of the above
Explanation - All numbers follow the rule of divisibility by 11 (difference of sum of alternate digits is divisible by 11).
Correct answer is: All of the above
Q.6 If a number is divisible by both 4 and 6, it must also be divisible by:
12
18
24
6
Explanation - A number divisible by 4 and 6 must be divisible by their LCM, which is 12.
Correct answer is: 12
Q.7 Which of the following numbers is a perfect cube?
27
45
81
100
Explanation - 27 = 3^3. Perfect cubes are numbers obtained by cubing an integer.
Correct answer is: 27
Q.8 Find the remainder when 2^10 is divided by 7.
2
4
5
1
Explanation - 2^10 = 1024. 1024 ÷ 7 gives remainder 2.
Correct answer is: 2
Q.9 Which of the following numbers is a composite number?
17
23
29
35
Explanation - Composite numbers have more than two factors. 35 = 5*7.
Correct answer is: 35
Q.10 The sum of all divisors of 12 is:
16
28
24
36
Explanation - Divisors of 12: 1,2,3,4,6,12. Sum = 1+2+3+4+6+12=28.
Correct answer is: 28
Q.11 The difference between the LCM and GCD of 12 and 18 is:
24
20
12
36
Explanation - LCM(12,18)=36, GCD(12,18)=12. Difference = 36-12=24.
Correct answer is: 24
Q.12 Which of the following numbers is divisible by 9?
243
287
315
All except 287
Explanation - A number divisible by 9 has digit sum divisible by 9. 243: 2+4+3=9, 315: 3+1+5=9, 287: 2+8+7=17.
Correct answer is: All except 287
Q.13 Find the smallest prime number greater than 50.
51
53
55
57
Explanation - 53 is the first prime number greater than 50.
Correct answer is: 53
Q.14 Which of the following is not a prime number?
2
3
9
5
Explanation - 9 is divisible by 3, so it is not prime.
Correct answer is: 9
Q.15 If a number is divisible by both 2 and 5, it must end with:
0
2
5
Any digit
Explanation - For divisibility by 2, number ends in 0,2,4,6,8. For 5, ends in 0 or 5. Both conditions together => ends in 0.
Correct answer is: 0
Q.16 The number of positive divisors of 28 is:
4
5
6
8
Explanation - 28 = 2^2 * 7^1. Number of positive divisors = (2+1)*(1+1)=3*2=6.
Correct answer is: 6
Q.17 Which of the following numbers is a multiple of 7?
84
91
99
All except 99
Explanation - 84 ÷7=12, 91 ÷7=13, 99 ÷7=14.142.. So 99 is not a multiple of 7.
Correct answer is: All except 99
Q.18 Find the GCD of 56 and 98.
7
14
28
49
Explanation - Factors: 56=2^3*7, 98=2*7^2. Common factors: 2*7=14.
Correct answer is: 14
Q.19 Which of the following numbers is odd?
102
203
408
600
Explanation - Odd numbers end with 1,3,5,7,9. 203 ends with 3, so it's odd.
Correct answer is: 203
Q.20 The sum of first 10 natural numbers is:
45
50
55
60
Explanation - Sum of first n natural numbers = n(n+1)/2 = 10*11/2 = 55.
Correct answer is: 55
Q.21 Which of the following numbers is divisible by 6?
54
55
56
57
Explanation - Number divisible by 6 must be divisible by both 2 and 3. 54 meets both conditions.
Correct answer is: 54
Q.22 The smallest positive integer divisible by 2, 3, and 5 is:
10
15
30
60
Explanation - LCM of 2,3,5 is 2*3*5=30.
Correct answer is: 30
Q.23 Which of the following is a two-digit prime number?
21
37
51
63
Explanation - 37 is prime; the others are divisible by numbers other than 1 and themselves.
Correct answer is: 37
Q.24 The number of even divisors of 36 is:
4
6
8
9
Explanation - 36=2^2*3^2. Number of divisors = (2+1)*(2+1)=9. Even divisors must include 2: 2*1,2*3,2*9,4*1,4*3,4*9 => 6 divisors.
Correct answer is: 6