Mathematics Exercise – Mixed Bag

1. (1² - 2² + 3² - 4² + 5² - 6² +…+ 9² - 10²)=?

2. Which of the following fractions is less than 7/8 and greater than 1/3?

3. If n is a natural number, then the largest number dividing (n³-n) is?

4. The sum of two rational numbers is -1/3. If one of the numbers is 7/8, find the other.

5. In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is?

6. The largest four digit number exactly divisible by each of 12, 15, 18, 27 is?

7. The numbers 2272 and 875 are divided by a three digit number N, giving the same remainder. The sum of the digits of N is?

8. The number (6n²+ 6n) for natural number n is always divisible by?

9. Evaluate 0.54x 0.54 – 0.46x0.46.

10. A common factor of (47⁴³ + 43⁴³) and (47⁴⁷ + 43⁴⁷) is?

11. 11. 9 men went to a hotel. 8 of them spent Rs 3 each over their meals and the ninth spent Rs 2 more than the average expenditure of all nine. Find the total money spent by all of them.

12. A group of 6 students has an average weight of 55 kg and if one of them is removed, the average of the remaining goes up by 4. What is the weight of the student who was removed?

13. Three years ago, the average age of A, B and C was 27 years and that of B and C five years ago 20 years. What is A’s present age?

14. Three years ago, the average age of five family members was 17 years. A baby having been born, the average age of the family is the same today. What is the age of the baby?

15. A certain number of trucks were required to transport 60 tons of steel wire from the TISCO factory in Jamshedpur. However, it was found that since each truck could take 0.5 tons of cargo less, another 4 trucks were needed. How many trucks were initially planned to be used?

16. In a certain exam, the average was found to be x marks. After deducting computational error, the average marks of 94 candidates got reduced from 84 to 64. The average thus came down by 18.8 marks. The number of candidates who took the exam was?

17. An investor in shares makes a profit of Rs. 920 in his fifth investment, by increasing his average of profit of first four investments by Rs. 14. His average profit over the first four investments is

18. The average number of printing errors per page in a book of 512 pages is 4. If the total number of printing errors in the first 302 pages is 1208, the average number of printing errors in the remaining pages in the book is?

19. In a factory, the average salary of the employees is Rs. 70. If the average salary of 12 officers is Rs. 400 and that of the remaining employees is Rs. 60, then the number of employees is?

20. The average marks of a student in 8 subjects are 87. Of these, the highest marks are 2 more than the one next in value. If these two subjects are eliminated then the average marks of the eliminated subjects is 85. What are the highest marks obtained by her?