Advertisements
Advertisements
प्रश्न
if `1/(6!) + 1/(7!) = x/(8!)`, find x
Advertisements
उत्तर
`1/(6!) + 1/(7!) = x/(8!)`
⇒ `1/(6!) + 1/(7 xx 6!) = x/(8 xx 7 xx 6!)`
⇒ `1/(6!) (1 + 1/7) = x/(8 xx 7 xx 6!)`
⇒ `1 + 1/7 = x/(8 xx 7)`
⇒ `8/7 = x/(8 xx 7)`
⇒ x = `(8 xx 8 xx 7)/7`
∴ x = 64
APPEARS IN
संबंधित प्रश्न
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
Find n if n – 1P3 : nP4 = 1 : 9
Find x in each of the following:
How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
Evaluate each of the following:
8P3
Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?
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 permutations of n different things taking r at a time when 3 particular things are to be included is
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is
The product of r consecutive positive integers is divisible by
If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are
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 five digits telephone numbers can be constructed using the digits 0 to 9 If each number starts with 67 with no digit appears more than once?
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
Evaluate the following.
`((3!)! xx 2!)/(5!)`
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?
How many ways can the product a2 b3 c4 be expressed without exponents?
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
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 of these 6-digit numbers are even?
If the letters of the word FUNNY are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, find the rank of the word FUNNY
If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?
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
There are 10 persons named P1, P2, P3, ... P10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
The total number of 9 digit numbers which have all different digits is ______.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, 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 |
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Determine the number of words which have at least one letter repeated.
