Home
Class 14
MATHS
For any natural number n, if D (n) is th...

For any natural number n, if D (n) is the sum of all the digits of D(n) find the remainder when `sum_1^99` D(n) is divided by 99.

A

9

B

0

C

1

D

90

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MENSURATION

    QUANTUM CAT|Exercise QUESTION BANK|449 Videos

  • PERCENTAGES

    QUANTUM CAT|Exercise QUESTION BANK|271 Videos

Similar Questions

Explore conceptually related problems

Find the remainder when sum_(r=1)^(n)r! is divided by 15, if n ge5 .

Find the remainder when 5^(99) is divided by 13

If n is natural number,then find the remainder when (37)^(n+2)+(16)^(n+1)+(30)^(n) is divided by 7.

The sum of all two digit natural numbers which leave a remainder 5 when they are divided by 7 equal to

When n!+1 is divided by any natural number obtained is between 2 and n then remainder is

The sum of all digits of n for which sum _(r =1) ^(n ) r 2 ^(r ) = 2+2^(n+10) is :

Let S_(n) denote the sum of the cubes of the first n natural numbers and s_(n) denote the sum of the first n natural numbers.Then sum_(r=1)^(n)(S_(r))/(s_(r)) is equal to

QUANTUM CAT-NUMBER SYSTEM-QUESTION BANK
  1. Government has arrested 10 suspects who are believed to have more than...

    Text Solution

    |

  2. The sum of n terms of the series (1)/(sqrt(1) + sqrt3) + 1/(sqrt3 +...

    Text Solution

    |

  3. For any natural number n, if D (n) is the sum of all the digits of D(n...

    Text Solution

    |

  4. The digit 6 is written continuously 225 times to form a natural number...

    Text Solution

    |

  5. If n is always a natural number, how many terms in the following seque...

    Text Solution

    |

  6. The average marks of 140 students are 45 . If the average of passed st...

    Text Solution

    |

  7. The average age of 8 persons in a committee is increased by 2 years wh...

    Text Solution

    |

  8. If p, q are the positive integers and r, s, t are prime numbers such t...

    Text Solution

    |

  9. How many factors of the number 16! Don't have their unit digit 5?

    Text Solution

    |

  10. In Mahabalipuram Temple there are some magical bells which tolls 18 ti...

    Text Solution

    |

  11. Three numbers p, q, r are such that p^q = q^r, where p, q, r > 1 then ...

    Text Solution

    |

  12. If (p^2)/(q^2) + (q^2)/(p^2) =1, then the value of (p^6 +q^6) is

    Text Solution

    |

  13. If a^2+b^2+c^2+d^2 = 1, then the maximum value of a.bc.d is :

    Text Solution

    |

  14. The value of n in the expression n^2 - 2(n!) + n = 0 for every n in N ...

    Text Solution

    |

  15. The average weight of 8 men is increased by 1.5 kg when one of the men...

    Text Solution

    |

  16. The value of (n!)^(n) if n + (n - 1) + (n - 2) = n(n - 1)(n - 2), wher...

    Text Solution

    |

  17. If (n)^3-(n)^2-n = n, then the number of values of n that satisfy the ...

    Text Solution

    |

  18. If k = (k1, k2, k3, ...., kn) in I and k1k2k3 + k2k3k4 + k3k4k5 + .......

    Text Solution

    |

  19. The given relation n^(n - 1) + n^(n - 1) = (n^2 +1)^(2) - (n^2 + 1) is...

    Text Solution

    |

  20. The smallest possible number that can be expressed as the sum of cube ...

    Text Solution

    |