मराठी

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

Advertisements
Advertisements

प्रश्न

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

पर्याय

  • 12

  •  8

  •  6

  •  10

  • 14

MCQ
Advertisements

उत्तर

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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 17: Combinations - Exercise 17.5 [पृष्ठ २६]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 17 Combinations
Exercise 17.5 | Q 21 | पृष्ठ २६

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

If nC8 = nC2, find nC2.


Determine n if  `""^(2n)C_3 : ""^nC_3 = 12 : 1`


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?


Since the  number has to be greater than 8000, the thousand's place can be filled by only two digits, i.e. 8 and 9.
Now, the hundred's place can be filled with the remaining 4 digits as the repetition of the digits is not allowed.
The ten's place can be filled with the remaining 3 digits.
The unit's place can be filled with the remaining 2 digits.
Total numbers that can be formed = `2xx4xx3xx2=48`


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


Evaluate the following:

35C35


Evaluate the following:

\[\sum^5_{r = 1} {}^5 C_r\]

 


If 8Cr − 7C3 = 7C2, find r.


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?


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;


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.


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 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?


How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?


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?


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


If C (n, 12) = C (n, 8), then C (22, n) is equal to


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


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


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


Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 5 green balls, and 7 blue balls so that 3 balls of every colour are drawn.


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?


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 from the lot.


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


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 they must all be of the same colour.


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 ______.


The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is ______.


The total number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two signs ‘–’ occur together is ______.


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

A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed is ______.


If number of arrangements of letters of the word "DHARAMSHALA" taken all at a time so that no two alike letters appear together is (4a.5b.6c.7d), (where a, b, c, d ∈ N), then a + b + c + d is equal to ______.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×