1) Find the remainder when 73 *75 *78 *57 *197 *37 is divided by 34.

2) Find the remainder when 67⁹⁹ is divided by 7.

3) Let N = 1421*1423*1425. What is the remainder when N is divided by 12?

4) Three numbers are in ratio 1:2:3 and HCF is 12. The numbers are:

5) What is the least number of soldiers that can be drawn up in troops of 12, 15, 18 and 20 soldiers and also in form of a solid square? What is the least number of soldiers that can be drawn up in troops of 12, 15, 18 and 20 soldiers and also in form of a solid square?

6) Find the least number which will leaves remainder 5 when divided by 8, 12, 16 and 20.

7) 7⁶ⁿ- 6⁶ⁿ, where n is an integer >0, is divisible by

8) After the division of a number successively by 3, 4 and 7, the remainder obtained is 2, 1 and 4 respectively. What will be remainder if 84 divide the same number?

9) Find the remainder when 2²⁵⁶ is divided by 17.

10) Find the remainder when 4⁹⁶ is divided by 6.