Advertisements
Advertisements
प्रश्न
Which of the following are true:
(2 +3)! = 2! + 3!
Advertisements
उत्तर
LHS = (2 +3)!
= 5!
= 120
RHS = 2! + 3!
= 2 + 6
= 8
Since LHS ≠ RHS,
Thus, (i) is false.
APPEARS IN
संबंधित प्रश्न
Evaluate 4! – 3!
Is 3! + 4! = 7!?
Compute `(8!)/(6! xx 2!)`
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
Find r if `""^5P_r = 2^6 P_(r-1)`
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
Evaluate each of the following:
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 all possible words that can be formed using the letters of the word 'MATHEMATICS'.
The number of arrangements of the word "DELHI" in which E precedes I 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
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
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
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
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?
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?
How many 6-digit telephone numbers can be constructed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each numbers starts with 35 and no digit appear more than once?
If n is a positive integer, then the number of terms in the expansion of (x + a)n is:
The number of ways to arrange the letters of the word “CHEESE”:
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:
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 can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?
8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?
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 vowels are never together
How many strings are there using the letters of the word INTERMEDIATE, if no two 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 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 even?
Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
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.
Suppose m men and n women are to be seated in a row so that no two women sit together. If m > n, show that the number of ways in which they can be seated is `(m!(m + 1)!)/((m - n + 1)1)`
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together 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 |
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 ______.
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 ______.
