Advertisements
Advertisements
Question
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
Advertisements
Solution
Every number after 6! (i.e. 7! onwards) till 200! will consist a power of 2 and 7, which will be exactly divisible by 14.
So, we need to divide only the sum till 6!.
1! + 2! + 3! + 4! + 5! + 6! = 1 + 2 + 6 + 24 + 120 + 720 = 873
When 873 is divided, the remainder would be same as when 1! + 2! + 3! + ... + 200! is divided by 14.
Remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 = Remainder obtained when 873 is divided by 14 = 5
APPEARS IN
RELATED QUESTIONS
Evaluate 8!
Find r if `""^5P_r = 2^6 P_(r-1)`
Find r if `""^5P_r = 2^6 P_(r-1)`
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
Find x in each of the following:
How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, 5 when a digit may be repeated any number of times?
How many 5-digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?
Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.
How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is
Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is
If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is
The product of r consecutive positive integers is divisible by
The number of arrangements of the letters of the word BHARAT taking 3 at a time is
The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is
English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X and Y. How many symmetric three letters passwords can be formed using these letters?
- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
Find the rank of the word ‘CHAT’ in the dictionary.
Evaluate the following.
`(3! + 1!)/(2^2!)`
The possible outcomes when a coin is tossed five times:
If n is a positive integer, then the number of terms in the expansion of (x + a)n is:
The total number of 9 digit number which has all different digit is:
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?
How many ways can the product a2 b3 c4 be expressed without exponents?
In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
How many strings are there using the letters of the word INTERMEDIATE, if all the vowels are together
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are even?
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are divisible by 4?
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is ______.
How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
| C1 | C2 |
| (a) 4 letters are used at a time | (i) 720 |
| (b) All letters are used at a time | (ii) 240 |
| (c) All letters are used but the first is a vowel | (iii) 360 |
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do no occupy odd places is ______.
