Advertisements
Advertisements
प्रश्न
Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is
विकल्प
24
30
125
100
Advertisements
उत्तर
24
In order to make a number divisible by 4, its last two digits must be divisible by 4, which in this case can be 12, 24, 32 or 52.
Since repetition of digits is not allowed, the remaining first two digits can be arranged in 3 x 2 ways in each case.
∴ Total number of numbers that can be formed = 4 x {3 x 2} = 24
APPEARS IN
संबंधित प्रश्न
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
How many 4-digit numbers are there with no digit repeated?
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 ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S.
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all 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?
Which of the following are true:
(2 × 3)! = 2! × 3!
In how many ways can three jobs I, II and III be assigned to three persons A, B and C if one person is assigned only one job and all are capable of doing each job?
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?
Evaluate each of the following:
8P3
Evaluate each of the following:
P(6, 4)
In how many ways can 4 letters be posted in 5 letter boxes?
Write the total number of possible outcomes in a throw of 3 dice in which at least one of the dice shows an even number.
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 ?
Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?
The number of permutations of n different things taking r at a time when 3 particular things are to be included is
The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants 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
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?
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
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?
Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?
Choose the correct alternative:
The product of r consecutive positive integers is divisible b
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.
In how many ways can 5 children be arranged in a line such that two particular children of them are always together
In how many ways 3 mathematics books, 4 history books, 3 chemistry books and 2 biology books can be arranged on a shelf so that all books of the same subjects are together.
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.
The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.
A five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done 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 |
