English

If 43cr − 6 = 43c3r + 1 , Then the Value of R is (A) 12 (B) 8 (C) 6 (D) 10 (E) 14 - Mathematics

Advertisements
Advertisements

Question

If 43Cr − 6 = 43C3r + 1 , then the value of r is

Options

  • 12

  •  8

  •  6

  •  10

  • 14

MCQ
Advertisements

Solution

12

\[r - 6 + 3r + 1 = 43\]  [∵ \[{}^n C_x =^n C_y \Rightarrow n = x + y or x = y\]]
\[\Rightarrow 4r - 5 = 43 \]
\[ \Rightarrow 4r = 48\]
\[ \Rightarrow r = 12\]
shaalaa.com
  Is there an error in this question or solution?
Chapter 17: Combinations - Exercise 17.5 [Page 26]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 17 Combinations
Exercise 17.5 | Q 21 | Page 26

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Compute:

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

A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of calendars should it prepare to serve for all the possibilities in future years?


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


There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?


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?


How many three-digit numbers are there?


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

first digit cannot be zero and the repetition of digits is not allowed,


In how many ways can six persons be seated in a row?


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.


If nC10 = nC12, find 23Cn.


How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?


There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:

a particular student is included.


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?


How many different selections of 4 books can be made from 10 different books, if
there is no restriction;


How many triangles can be obtained by joining 12 points, five of which are collinear?


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 (i) no girl?


Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king?


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?


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


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?


In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?


Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.


A business man hosts a dinner to 21 guests. He is having 2 round tables which can accommodate 15 and 6 persons each. In how many ways can he arrange the guests?


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 mC1 nC2 , then


There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is


Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.


If α = mC2, then αCis equal to.


In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.


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


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 two must be white and two red


If nC12 = nC8, then n is equal to ______.


There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C25C2.


There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of:

C1 C2
(a) One book of each subject; (i) 3968
(b) At least one book of each subject: (ii) 60
(c) At least one book of English: (iii) 3255

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 ______.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×