Advertisements
Advertisements
प्रश्न
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
Advertisements
उत्तर
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
संबंधित प्रश्न
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
Find n if n – 1P3 : nP4 = 1 : 9
Find r if `""^5P_r = ""^6P_(r-1)`
How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
(i) 4 letters are used at a time,
(ii) all letters are used at a time,
(iii) all letters are used but first letter is a vowel?
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
Find x in each of the following:
Find x in each of the following:
A customer forgets a four-digits code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6 and 9. Find the largest possible number of trials necessary to obtain the correct code.
How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10 ?
How many numbers of four digits can be formed with the digits 1, 2, 3, 4, 5 if the digits can be repeated in the same number?
Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together ?
The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is
If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is
If (n+2)! = 60[(n–1)!], find n
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
Evaluate the following.
`(3! + 1!)/(2^2!)`
The number of permutation of n different things taken r at a time, when the repetition is allowed is ______.
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
Find the distinct permutations of the letters of the word MISSISSIPPI?
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 distinct 6-digit numbers are there?
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?
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
Find the number of permutations of n different things taken r at a time such that two specific things occur together.
The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
The total number of 9 digit numbers which have all different digits is ______.
Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:
| C1 | C2 |
| (a) Boys and girls alternate: | (i) 5! × 6! |
| (b) No two girls sit together : | (ii) 10! – 5! 6! |
| (c) All the girls sit together | (iii) (5!)2 + (5!)2 |
| (d) All the girls are never together : | (iv) 2! 5! 5! |
Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find
| C1 | C2 |
| (a) How many numbers are formed? | (i) 840 |
| (b) How many number are exactly divisible by 2? | (i) 200 |
| (c) How many numbers are exactly divisible by 25? | (iii) 360 |
| (d) How many of these are exactly divisible by 4? | (iv) 40 |
The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______.
If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.
