मराठी

Find the Number of (I) Diagonals

Advertisements
Advertisements

प्रश्न

Find the number of (i) diagonals

Advertisements

उत्तर

A decagon has 10 sides.
(i)  Number of diagonals =\[\frac{n \left( n - 3 \right)}{2} = \frac{10 \left( 10 - 3 \right)}{2} = 35\]

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 17: Combinations - Exercise 17.2 [पृष्ठ १६]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 17 Combinations
Exercise 17.2 | Q 21.1 | पृष्ठ १६

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Determine n if  `""^(2n)C_3 : ""^nC_3 = 11: 1`


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.


How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?


If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?


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?


Prove that

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

A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?


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?


Given 7 flags of different colours, how many different signals can be generated if a signal requires the use of two flags, one below the other?


How many three-digit odd numbers are there?


How many four-digit numbers can be formed with the digits 3, 5, 7, 8, 9 which are greater than 7000, if repetition of digits is not allowed?


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.


Evaluate the following:

n + 1Cn


If nC4 = nC6, find 12Cn.


24Cx = 24C2x + 3, find x.


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


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?


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?


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


If nC12 = nC8 , then n =


There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?


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


A student finds 7 books of his interest, but can borrow only three books. He wants to borrow Chemistry part II book only if Chemistry Part I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.


Find the value of 80C2


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?


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 ______.


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 must all be of the same colour.


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.


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


The number of ways in which we can choose a committee from four men and six women so that the committee includes at least two men and exactly twice as many women as men is ______.


To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is 5C3 × 20C9.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×