Advertisements
Advertisements
प्रश्न
Find x in each of the following:
Advertisements
उत्तर
\[\frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!}\]
\[ \Rightarrow \frac{1}{6!} + \frac{1}{7(6!)} = \frac{x}{8!}\]
\[ \Rightarrow \frac{7 + 1}{7(6!)} = \frac{x}{8!}\]
\[ \Rightarrow \frac{8}{7!} = \frac{x}{8!}\]
\[ \Rightarrow \frac{8}{7!} = \frac{x}{8 \times 7!}\]
\[ \Rightarrow x = 64\]
APPEARS IN
संबंधित प्रश्न
How many 4-digit numbers are there with no digit repeated?
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
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?
In how many ways can 7 letters be posted in 4 letter boxes?
Evaluate each of the following:
8P3
Evaluate each of the following:
Evaluate each of the following:
P(6, 4)
In how many ways can 4 letters be posted in 5 letter boxes?
Write the number of arrangements of the letters of the word BANANA in which two N's come together.
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 different signals which can be given from 6 flags of different colours taking one or more at a time, is
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, 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?
How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
Evaluate the following.
`(3! + 1!)/(2^2!)`
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
The number of permutation of n different things taken r at a time, when the repetition is allowed is ______.
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
How many ways can the product a2 b3 c4 be expressed without exponents?
A coin is tossed 8 times, how many different sequences of heads and tails are possible?
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?
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 5-digit telephone numbers having atleast one of their digits repeated is ______.
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is `""^(n - m)"P"_(r - m) xx ""^r"P"_m`.
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 |
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 ______.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
Number of words from the letters of the words BHARAT in which B and H will never come together is ______.
