English

If Ncr + Ncr + 1 = N + 1cx , Then X = (A) R (B) R − 1 (C) N (D) R + 1

Advertisements
Advertisements

Question

If nCr + nCr + 1 = n + 1Cx , then x =

Options

  •  r

  • r − 1

  • n

  • r + 1

MCQ
Advertisements

Solution

r + 1

\[n_{C_r} + n_{C_{r + 1}} = n + 1_{C_x}\] [Given]
We have:
\[{}^n C_r +^n C_{r + 1} = {}^{n + 1} C_x \]
[∵\[{}^n C_r +^n C_{r - 1} = {}^{n + 1} C_r\]]
\[\Rightarrow {}^{n + 1} C_{r + 1} = {}^{n + 1} C_x\]
\[\Rightarrow r + 1 = x\] [∵ \[{}^n C_x =^n C_y \Rightarrow n = x + y\ \text{or} x = y\]]
shaalaa.com
  Is there an error in this question or solution?
Chapter 17: Combinations - Exercise 17.5 [Page 25]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 17 Combinations
Exercise 17.5 | Q 8 | Page 25

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?


Compute:

\[\frac{11! - 10!}{9!}\]

In how many ways can an examinee answer a set of ten true/false type questions?


There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?


A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?


If 15Cr : 15Cr − 1 = 11 : 5, find r.


If 16Cr = 16Cr + 2, find rC4.


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

 exclude 2 particular players?


How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;


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


Find the number of diagonals of (ii) a polygon of 16 sides.


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(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?


Find the number of (ii) triangles


In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?


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


If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =


Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?


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


How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?
(a) 6
(b) 20
(c) 60
(d) 120


The value of\[\left( \ ^{7}{}{C}_0 + \ ^{7}{}{C}_1 \right) + \left( \ ^{7}{}{C}_1 + \ ^{7}{}{C}_2 \right) + . . . + \left( \ ^{7}{}{C}_6 + \ ^{7}{}{C}_7 \right)\] is


Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?


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 `""^6"P"_2 = "n" ""^6"C"_2`


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 ______.


The straight lines l1, l2 and l3 are parallel and lie in the same plane. A total numbers of m points are taken on l1; n points on l2, k points on l3. The maximum number of triangles formed with vertices at these points are ______.


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 group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has at least three girls.


Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.


15C8 + 15C915C615C7 = ______.


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 ______.


The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` is ______.


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 ______.


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


The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4, (repetition of digits is not allowed) and are multiple of 3 is?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×