Q.1 Which of the following numbers is divisible by 3?
12345
12346
12347
12348
Explanation - A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of digits in 12348 is 18, which is divisible by 3.
Correct answer is: 12348
Q.2 What is the least number that must be added to 796 so that it becomes divisible by 9?
2
3
4
5
Explanation - Sum of digits of 796 = 22. The next multiple of 9 is 27, so 27 - 22 = 5 should be added.
Correct answer is: 2
Q.3 What is the HCF of 72 and 120?
6
12
24
18
Explanation - The prime factors of 72 = 2³×3², and 120 = 2³×3×5. Common factors = 2³×3 = 24.
Correct answer is: 24
Q.4 What is the LCM of 15, 20, and 25?
150
200
300
400
Explanation - Prime factors: 15=3×5, 20=2²×5, 25=5². LCM = 2²×3×5²=300.
Correct answer is: 300
Q.5 Which of the following is a prime number?
91
93
97
99
Explanation - 97 has no divisors other than 1 and itself.
Correct answer is: 97
Q.6 Find the remainder when 23 is divided by 5.
3
4
2
1
Explanation - 23 ÷ 5 = 4 remainder 3.
Correct answer is: 3
Q.7 Which of these numbers is a perfect cube?
27
16
64
125
Explanation - 27 = 3³, hence a perfect cube.
Correct answer is: 27
Q.8 The unit digit of 7⁴ is:
1
3
9
7
Explanation - The unit digit pattern of powers of 7 repeats every 4 terms (7,9,3,1). For 7⁴, it is 1.
Correct answer is: 1
Q.9 The number 0.121212... is:
Terminating decimal
Recurring decimal
Irrational number
Whole number
Explanation - 0.121212... repeats the digits '12' indefinitely, making it a recurring decimal.
Correct answer is: Recurring decimal
Q.10 If a number leaves remainder 2 when divided by 5, what will be the remainder when twice the number is divided by 5?
0
1
2
4
Explanation - If n ≡ 2 (mod 5), then 2n ≡ 4 (mod 5).
Correct answer is: 4
Q.11 Which of the following is not an integer?
√4
√9
√7
√16
Explanation - √7 is an irrational number, not an integer.
Correct answer is: √7
Q.12 What is the smallest prime number?
0
1
2
3
Explanation - 2 is the smallest and only even prime number.
Correct answer is: 2
Q.13 How many even numbers are there between 1 and 100?
49
50
51
52
Explanation - Even numbers are 2, 4, ..., 100 → total = 100/2 = 50, but between 1 and 100 excludes 100 → 49.
Correct answer is: 49
Q.14 Find the sum of first 10 natural numbers.
45
50
55
60
Explanation - Sum = n(n+1)/2 = 10×11/2 = 55.
Correct answer is: 55
Q.15 Which number is both a square and a cube?
36
64
125
216
Explanation - 64 = 8² = 4³, so it is both a perfect square and cube.
Correct answer is: 64
Q.16 What is the sum of digits of 9999?
36
27
45
24
Explanation - Sum of digits = 9+9+9+9 = 36.
Correct answer is: 36
Q.17 If 2x = 64, then x equals:
4
5
6
7
Explanation - 2⁶ = 64, hence x = 6.
Correct answer is: 6
Q.18 What is the digital root of 9876?
3
6
9
4
Explanation - Sum of digits = 30 → 3+0 = 3 is the digital root.
Correct answer is: 3
Q.19 Which of the following numbers is divisible by both 2 and 5?
35
45
50
75
Explanation - A number divisible by both 2 and 5 must end with 0. Only 50 does.
Correct answer is: 50
Q.20 The number 0 is:
Natural number
Whole number
Prime number
Composite number
Explanation - 0 is the smallest whole number but not a natural number.
Correct answer is: Whole number
Q.21 If a number ends with 25, it is always divisible by:
5
10
25
50
Explanation - Any number ending with 25 is divisible by 25.
Correct answer is: 25
Q.22 Which of the following is not a rational number?
1/2
3/4
√2
0.25
Explanation - √2 cannot be expressed as p/q, hence irrational.
Correct answer is: √2
Q.23 What is 7 × 11 × 13 equal to?
999
1001
1003
1011
Explanation - 7×11×13 = 1001 = 1000 + 1.
Correct answer is: 1001
Q.24 The number 45 is divisible by which of the following?
2 and 3
3 and 5
2 and 5
4 and 5
Explanation - 45 is divisible by 3 (sum of digits=9) and by 5 (ends with 5).
Correct answer is: 3 and 5
Q.25 How many zeros are there in 10⁶?
5
6
7
8
Explanation - 10⁶ = 1 followed by 6 zeros.
Correct answer is: 6