Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
Given that out of 20 lines, no two lines are parallel and no three lines are concurrent.
Therefore, number of point of intersection
= 20C2 ......[∵ For any point of intersection, we need two lines]
= `(20*19)/(2*1)`
= 190
Hence, the required number of points = 190.
APPEARS IN
संबंधित प्रश्न
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 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?
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 with no digit repeated?
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 different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5 when repetition of digits is not allowed?
Evaluate the following:
n + 1Cn
If nC4 = nC6, find 12Cn.
If 15Cr : 15Cr − 1 = 11 : 5, find r.
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 professor is included.
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.
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?
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?
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: atmost 3 girls?
A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
Find the number of ways in which : (a) a selection
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?
There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.
If 15C3r = 15Cr + 3 , then r is equal to
If 20Cr + 1 = 20Cr − 1 , then r is equal to
If mC1 = nC2 , then
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
If n + 1C3 = 2 · nC2 , then n =
Find n if `""^6"P"_2 = "n" ""^6"C"_2`
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.
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 ______.
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 words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike 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 ______.
A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides is
