हिंदी

The Product of R Consecutive Positive Integers is Divisible by , R ! , (R − 1) ! , (R + 1) ! , None of These.

Advertisements
Advertisements

प्रश्न

The product of r consecutive positive integers is divisible by

विकल्प

  • r !

  • (r − 1) !

  • (r + 1) !

  • none of these.

MCQ
Advertisements

उत्तर

r !
The product of r consecutive integers  is equal to r!, so it will be divisible by r!.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 16: Permutations - Exercise 16.7 [पृष्ठ ४७]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 16 Permutations
Exercise 16.7 | Q 16 | पृष्ठ ४७

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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?


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?


Find r if `""^5P_r = 2^6 P_(r-1)`


Find r if `""^5P_r = ""^6P_(r-1)`


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 three jobs I, II and III be assigned to three persons AB and C if one person is assigned only one job and all are capable of doing each job?


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 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?


Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.


Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?


Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?


The number of words that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places is


How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?


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 six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is


A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is


Find x if `1/(6!) + 1/(7!) = x/(8!)`


Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.


  1. In how many ways can 8 identical beads be strung on a necklace?
  2. In how many ways can 8 boys form a ring?

Evaluate the following.

`((3!)! xx 2!)/(5!)`


The number of permutation of n different things taken r at a time, when the repetition is allowed is ______.


If `""^(("n"  – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n


8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?


Find the distinct permutations of the letters of the word MISSISSIPPI?


In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?


A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?


How many strings are there using the letters of the word INTERMEDIATE, if all the 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 divisible by 4?


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


Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?


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 signals that can be sent by 6 flags of different colours taking one or more at a time 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 ______.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×