Number System, Average & Mathematical Operations
1. A number when divided by 12 leaves remainder 7. What will be the remainder when the same number is divided by 6?
2. Find the LCM of 84, 120, and 138.
3. What is the unit digit of 7²³?
4. Find the remainder when 435 is divided by 13.
5. The average of 8 numbers is 45. If one number 17 is replaced by 23, what is the new average?
6. In a class, 3 students scored 60, 2 students scored 70, and 5 students scored 80. What is the average score?
7. What is the value of 15 + 3 × 4 - 8 ÷ 2?
8. If + means ×, - means +, × means ÷, ÷ means -, then find the value of 12 × 4 + 3 - 2 ÷ 1.
9. What is the square of 123?
10. Find the value of 97 × 103.
11. A 5-digit number 7_43_ is divisible by 11. If the sum of digits is 25, find the missing digits.
12. What is the average of first 15 natural numbers?
13. The HCF of three numbers is 12. If the numbers are in ratio 3:7:10, find the numbers.
14. What is the unit digit of 3⁴⁷?
15. A car travels 60 km/h for 2 hours and 40 km/h for 3 hours. What is the average speed?
16. Solve: 2 + 3 × (4 - 1) ÷ 3
17. Find the remainder when 234567 is divided by 9.
18. The average of 20 numbers is 45. The average of first 12 numbers is 42 and that of last 9 numbers is 48. Find the 12th number.
19. Calculate 456 × 789 using suitable method.
20. How many numbers between 100 and 200 are divisible by 12, 15, and 18?
21. If @ means +, # means -, $ means ×, % means ÷, find: 15 @ 3 $ 4 # 8 % 2
22. The average of 10 consecutive numbers is 15.5. What is the smallest number?
23. What is the unit digit of 2⁵⁰?
24. Find the smallest number greater than 200 which when divided by 144, 180, and 192 leaves the same remainder in each case.
25. The average of 15 numbers is 40. If the average of 5 of them is 35, what is the average of the remaining 10 numbers?
26. Find the square of 105.
27. Evaluate: 36 ÷ 4 × 3 + 2 - 1
28. Which of the following numbers is divisible by 8?
29. How many numbers from 1 to 100 are divisible by 6, 8, and 12?
30. What is the average of first 25 odd numbers?
31. Calculate 89 × 91.
32. What is the unit digit of 6²⁵?
33. If * means ÷, ÷ means +, + means ×, × means -, find: 20 * 4 ÷ 3 + 2 × 1
34. Three numbers are in ratio 2:3:4 and their HCF is 36. Find the largest number.
35. The average of 12 numbers is 50. If each number is increased by 5, what is the new average?
36. Solve: 5 + 2 × (8 - 3) ÷ 2
37. Find the remainder when 987654321 is divided by 9.
38. What is the square of 198?
39. Find the smallest 4-digit number divisible by 15, 20, and 25.
40. What is the average of first 20 even numbers?
41. What is the unit digit of 4³⁷?
42. Calculate 76 × 84.
43. Evaluate: 48 ÷ 6 + 4 × 3 - 2
44. Which number is divisible by 6?
45. The average of 18 numbers is 35. The average of first 10 numbers is 32 and that of last 10 numbers is 38. Find the sum of 9th and 10th numbers.
46. Find the LCM of 48, 72, and 96.
47. What is the square of 295?
48. What is the unit digit of 9²⁹?
49. If ⊕ means ×, ⊗ means +, ⊙ means ÷, ⊖ means -, find: 12 ⊕ 3 ⊗ 8 ⊙ 4 ⊖ 2
50. A person travels from A to B at 30 km/h and returns at 60 km/h. What is his average speed for the entire journey?