35 tough questions on reminder
Q1. The unit digit of 23 4 x 34 5 x 45 6 x 67 8 x 78 9 is
Q2. If 2 n can exactly divide p! then the value of n which is not possible :
a. 43 b. 44 c. 45 d. None of these
Find the reminders when
Q3. 6 6 6 . . . . . . Infinity is divided by 10.
Q4. 888222888222. . . . . up to 9235 digits divided by 53
Q5. 1 x 2 + 3 x 4 + 5 x 6 + 7 x 8 + . . . 10 terms divided by 19
Q6. 11 3 + 9 3 is divided by 7 3
Q7. 4 4 n + 3 is divided by 7
a. 0 b. 1 c. 5 d. None of these
Q8. 3 0 + 3 1 + 3 2 + . . . . .201 terms is divided by 13
a. 0 b. 12 c. 3 d. None of these
Q9. 1 3 + 2 3 + 3 3 + 1000 3 is divide by 13
Q10. 10 2 + 11 2 + 12 2 + . . . . 28 2 is divided by 19
Q11. 21 12 – 12 21 is divided by 7
Q12. 23 32 – 9 is divided by 16
Q13. 1 3 + 2 3 + 3 3 + 4 3 +. . 10 terms is divided by 1 2 + 2 2 + 3 2 + 4 2 + . . .10 terms
Q14. 3 37 + 4 37 is divided by 7
Q15. 10 3 + 9 3 is divided by 12 3?
Q16. 10 11 12 is divided by 13
Q17. 999 9 is divided by 99 9
Q18. 999 9 is divided by 99 9 an then by 9 9
Q19. 12121212. . . 300 times is divided by 99
Q20. 12233344455555…100 terms divided by 7
Q21. (10 3 + 9 3)752 is divided 12 12
Q22. 44444 + 3333 is divided by 7
Q23. 1! + 2! + 3! + . . . .70! divided by 100
Q24. 3456 is divided by 108?
Q25. 1 1 + 2 2 + 3 3 + . . . .100 100 is divided by 4?
Q26. 3 3 3 3 3 3 3 3 3. . .1001 digits. . . . divided by 1001
Q27. 4 + 44 + 444 +. . .100 terms. . divided by 7
Q28. 4 44 is divided by 15.
Q29. 37! 37! Divided by 100
Q30. 17 x 18 x 19 x . . . . 37 divided by 100
Q31. 4 101 is divided by 5
Q32. 1 3 + 2 3 + 3 3 + . . . . .99 3 is divided by 10
Q33. 2222 5555 + 5555 2222 is divided by 7
Q34. Find the sum of all two-digit numbers that give a reminder 4 when they are divided by 5
a. 98,270 b. 99,270 c. 1,02, 090
Q35. When 7179 and 9699 are divided by another natural number N, remainder obtained is same. How many values of N will be ending with one or more than zeroes?
a. 24 b. 124 c. 46 d. None of these
Q28. 4 44 is divided by 15.
ans(4^2)^22 =16^22 so reminder=1
Little Star
n/a
Divided by 10 means finding the last digit
n/a
1 x 2 + 3 x 4 + 5 x 6 + 7 x 8 + . . . 10 terms divided by 19
440 = 3 (mod 19)
n/a
Q33. 2222 5555 + 5555 2222 is divided by 7
2222 divided by 7 reminder =3
5555 divided by 7 reminder=4
now (4^2)1111 + (3^5)1111 so 16+243=259 divided by 7so reminder =0
Little Star
n/a
Q31. 4 101 is divided by 5
(4^2)^50 x 4 divided by 5 reminder=1*4=4
Little Star
n/a
Q6. 11 3 + 9 3 is divided by 7 3
ans 2
Little Star
n/a
Q14. 3 37 + 4 37 is divided by 7
ans a^n + b^n divided by a+b when n is odd
so reminder=0
Little Star
n/a
Q32. 1 3 + 2 3 + 3 3 + . . . . .99 3 is divided by 10
sum of cube=(n(n+1)/2)^2=99*99*100*100/4 divided by 10 so reminder= 0
Little Star
n/a
Thz a huge collection. . answers of few easier ones
Q6. 2
Q11. I think it shd be 12 21 - 21 12 . . answer 6
Q12. ans 8
'll post the other answers soon