Advertisements
Advertisements
प्रश्न
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 |
Advertisements
उत्तर
| C1 | C2 |
| (a) How many numbers are formed? | (i) 840 |
| (b) How many number are exactly divisible by 2? | (i) 360 |
| (c) How many numbers are exactly divisible by 25? | (iii) 40 |
| (d) How many of these are exactly divisible by 4? | (iv) 200 |
Explanation:
(a) Total of 4 digit number formed with 1, 2, 3, 4, 5, 6, 7
= 7P4
= `(7 xx 6 xx 5 xx 4 xx 3!)/(3!)`
= 840
(b) When a number is divisible by 2
= 4 × 5 × 6 × 3
= 360
(c) Total numbers which are divisible by 25 = 40
(d) Total numbers which are divisible by 4 (last two digits is divisible by 4) = 200
APPEARS IN
संबंधित प्रश्न
Is 3! + 4! = 7!?
Compute `(8!)/(6! xx 2!)`
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
Find x in each of the following:
Find x in each of the following:
Find x in each of the following:
Which of the following are true:
(2 +3)! = 2! + 3!
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?
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?
In how many ways can 5 different balls be distributed among three boxes?
Evaluate each of the following:
8P3
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 arrangements of the word "DELHI" in which E precedes I is
The number of ways to arrange the letters of the word CHEESE are
The number of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants is
In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is
How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?
If (n+2)! = 60[(n–1)!], find n
If nP4 = 12(nP2), find n.
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
Evaluate the following.
`((3!)! xx 2!)/(5!)`
The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:
If n is a positive integer, then the number of terms in the expansion of (x + a)n is:
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if the first four questions have three choices and the remaining have five choices?
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
What is the maximum number of different answers can the students give?
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
How will the answer change if each question may have more than one correct answers?
How many strings are there using the letters of the word INTERMEDIATE, if no two vowels are together
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
GARDEN
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
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! |
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 |
Let b1, b2, b3, b4 be a 4-element permutation with bi ∈ {1, 2, 3, .......,100} for 1 ≤ i ≤ 4 and bi ≠ bj for i ≠ j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of such permutations b1, b2, b3, b4 is equal to ______.
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 m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
