1. The unit’s digit in the product of (3127)174 is

2. What least number must be added to 8961 to make it exactly divisible by 84?

3. What is the remainder when [(421)221]148 is divided by 422?

4. N guavas are distributed among 10 boys. The same no. of guavas are distributed among 13 boys. The same exercise is done with 52 boys. What should be the minimum value of N required to distribute, so that no guava is left?

5. The greatest number that exactly divides 210, 2002 and 4872 is

6. Find the unit digit of the following series: 81 × 82 × 83 × ….. × 89

7. In a three digit number, the digit in the unit place is five times the digit in the hundred’s place. If the digit in the unit’s place and the ten’s place are interchanged, the new number so formed is 18 more than the original number. If the digit in the hundred’s place is one-third of the digit in the ten’s place. What is the 1/9th of the original number?

8. Find a number lying between 2000 and 3000 such that on division by 2, 3, 4, 5, 6, 7 and 8 leaves remainder 1, 2, 3, 4, 5, 6 and 7, respectively.

9. By which largest number will the difference of square of a two digit number and square of number which is formed by interchanging the digits will be always divisible?

10. The product of two numbers is 1800 and their HCF is 15. The numbers are

11. Find the remainder when 82157 is divided by 9.

12. A 4-digit number is formed by repeating a 2-digit number such as 2525, 3232, etc. Any number of this form is always exactly divisible by: -

13. How many 3 digits numbers are divisible by 9 among the numbers – 187, 648, 543, 837

14. The ratio of two numbers is 7 : 8 and their H.C.F is 5. What would be their L.C.M ?

15. The digit in the unit’s place of {(341)98 + (211)59 – (45)100 + (105)35 – 164 + 259} is

16. Find the LCM of 0.25, 16.5, 3.2, 8.20?

17. There are two natural numbers, R and S. The LCM of R and S is 200% more than R, while their HCF is 505 less than R. Find the sum of R and S.

18. The HCF of two numbers is 101 and their LCM is 1414. The numbers are

19. Find the L.C.M of \(\frac{2}{3},\frac{3}{4}\ and\ \frac{4}{5}\)

20. To make a natural number P divisible by 19, 21 and 23, the smallest number to be added is 14. If P lies between 18000 and 19000, then find the value of P.

21. A number when divided by 296 leaves 75 as remainder.When the same number is divided by 37,the remainder will be