English

If 20cr + 1 = 20cr − 1 , Then R is Equal to (A) 10 (B) 11 (C) 19 (D) 12 - Mathematics

Advertisements
Advertisements

Question

If 20Cr + 1 = 20Cr − 1 , then r is equal to

Options

  • 10

  • 11

  •  19

  • 12

MCQ

Solution

10

\[r + 1 + r - 1 = 20\] [∵\[{}^n C_x =^n C_y \Rightarrow n = x + y or x = y\]]
\[\Rightarrow 2r = 20\]
\[ \Rightarrow r = 10\]
shaalaa.com
  Is there an error in this question or solution?
Chapter 17: Combinations - Exercise 17.5 [Page 25]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 17 Combinations
Exercise 17.5 | Q 4 | Page 25

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?


How many three-digit numbers are there with no digit repeated?


How many three-digit numbers are there?


How many 9-digit numbers of different digits can be formed?


How many 3-digit numbers are there, with distinct digits, with each digit odd?


How many four digit different numbers, greater than 5000 can be formed with the digits 1, 2, 5, 9, 0 when repetition of digits is not allowed?


A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.


24Cx = 24C2x + 3, find x.


If n +2C8 : n − 2P4 = 57 : 16, find n.


If α = mC2, then find the value of αC2.


In how many ways can a football team of 11 players be selected from 16 players? How many of these will

include 2 particular players?


From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?


A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. In how many ways can he choose the 7 questions?


In a village, there are 87 families of which 52 families have at most 2 children. In a rural development programme, 20 families are to be helped chosen for assistance, of which at least 18 families must have at most 2 children. In how many ways can the choice be made?


A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (i) no girl?


A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (ii) at least one boy and one girl? 


A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has(iii) at least 3 girls? 


A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?


A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: atmost 3 girls?


Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.


A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular side and two on the other side. In how many ways can they be seated?


If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to


The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want to attend the party together is


If n + 1C3 = 2 · nC2 , then n =


The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is


Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3


Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.


Find the value of 15C4 


Find the value of 15C4 + 15C5 


Answer the following:

A question paper has 6 questions. How many ways does a student have to answer if he wants to solve at least one question?


If α = mC2, then αCis equal to.


A student has to answer 10 questions, choosing atleast 4 from each of Parts A and B. If there are 6 questions in Part A and 7 in Part B, in how many ways can the student choose 10 questions?


We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?


A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if they can be of any colour


In how many ways can a football team of 11 players be selected from 16 players? How many of them will include 2 particular players?


Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is ______.


All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is ______.


There are (n + 1) white and (n + 1) black balls each set numbered 1 to (n + 1). The number of ways in which the balls can be arranged in row so that the adjacent balls are of different colours is ______.


From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×