मराठी

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

Advertisements
Advertisements

प्रश्न

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

पर्याय

  • 10

  • 11

  •  19

  • 12

MCQ

उत्तर

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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 17: Combinations - Exercise 17.5 [पृष्ठ २५]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 17 Combinations
Exercise 17.5 | Q 4 | पृष्ठ २५

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.


In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?


Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.


Prove that

\[\frac{1}{9!} + \frac{1}{10!} + \frac{1}{11!} = \frac{122}{11!}\]

A letter lock consists of three rings each marked with 10 different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock?


How many A.P.'s with 10 terms are there whose first term is in the set {1, 2, 3} and whose common difference is in the set {1, 2, 3, 4, 5}?


How many three-digit numbers are there?


How many three-digit odd numbers are there?


How many different five-digit number licence plates can be made if

the first-digit cannot be zero, but the repetition of digits is allowed?


How many different numbers of six digits each can be formed from the digits 4, 5, 6, 7, 8, 9 when repetition of digits is not allowed?


Serial numbers for an item produced in a factory are to be made using two letters followed by four digits (0 to 9). If the letters are to be taken from six letters of English alphabet without repetition and the digits are also not repeated in a serial number, how many serial numbers are possible?


A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?


In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?


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? 


Find the number of (i) diagonals


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 the selection be made?


Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.


In how many ways can one select a cricket team of eleven from 17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers?


In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?


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: exactly 3 girls?


If 15C3r = 15Cr + 3 , then r is equal to


5C1 + 5C2 5C3 + 5C4 +5C5 is equal to


There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is


There are 20 straight lines in a plane so that no two lines are parallel and no three lines are concurrent. Determine the number of points of intersection.


There are 3 wicketkeepers and 5 bowlers among 22 cricket players. A team of 11 players is to be selected so that there is exactly one wicketkeeper and at least 4 bowlers in the team. How many different teams can be formed?


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?


All the letters of the word ‘EAMCOT’ are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is ______.


If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?


A convex polygon has 44 diagonals. Find the number of its sides.


A committee of 6 is to be chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee ______.


Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on other side of the table. The number of ways in which the seating arrangements can be made is `(11!)/(5!6!) (9!)(9!)`.


There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:

C1 C2
(a) In how many ways committee: can be formed (i) 10C2 × 19C3 
(b) In how many ways a particular: professor is included (ii) 10C2 × 19C2
(c) In how many ways a particular: lecturer is included (iii) 9C1 × 20C3
(d) In how many ways a particular: lecturer is excluded (iv) 10C2 × 20C3

A badminton club has 10 couples as members. They meet to organise a mixed double match. If each wife refers to p artner as well as oppose her husband in the match, then the number of different ways can the match off will be ______.


There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row so that the balls are with numbers in ascending or descending order is equal to ______.


Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear 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×