हिंदी

Write the Maximum Number of Points of Intersection of 8 Straight Lines in a Plane. - Mathematics

Advertisements
Advertisements

प्रश्न

Write the maximum number of points of intersection of 8 straight lines in a plane.

उत्तर

We know that two lines are required for one point of intersection.
∴ Number of points of intersection =\[{}^8 C_2 = \frac{8}{2} \times \frac{7}{1} = 28\]

shaalaa.com
Factorial N (N!) Permutations and Combinations
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 17: Combinations - Exercise 17.4 [पृष्ठ २४]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 17 Combinations
Exercise 17.4 | Q 7 | पृष्ठ २४

संबंधित प्रश्न

Convert the following products into factorials: 

(n + 1) (n + 2) (n + 3) ... (2n)


If (n + 1)! = 90 [(n − 1)!], find n.


If P (9, r) = 3024, find r.


If P(11, r) = P (12, r − 1) find r.


If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.


If n +5Pn +1 =\[\frac{11 (n - 1)}{2}\]n +3Pn, find n.


In how many ways can five children stand in a queue?


From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?


Four books, one each in Chemistry, Physics, Biology and Mathematics, are to be arranged in a shelf. In how many ways can this be done?


In how many ways can the letters of the word 'FAILURE' be arranged so that the consonants may occupy only odd positions?


In how many ways can the letters of the word 'STRANGE' be arranged so that

the vowels come together?

 


In how many ways can the letters of the word 'STRANGE' be arranged so that

the vowels occupy only the odd places?


How many permutations can be formed by the letters of the word, 'VOWELS', when
each word begins with E?


In how many ways can a lawn tennis mixed double be made up from seven married couples if no husband and wife play in the same set?


Find the number of words formed by permuting all the letters of the following words:
INTERMEDIATE


Find the number of words formed by permuting all the letters of the following words:

INDIA


Find the number of words formed by permuting all the letters of the following words:

PAKISTAN


Find the number of words formed by permuting all the letters of the following words:

RUSSIA


Find the number of words formed by permuting all the letters of the following words:
EXERCISES


Find the total number of arrangements of the letters in the expression a3 b2 c4 when written at full length.


How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?


How many number of four digits can be formed with the digits 1, 3, 3, 0?


In how many ways can the letters of the word 'ARRANGE' be arranged so that the two R's are never together?


How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.


How many words can be formed from the letters of the word 'SERIES' which start with S and end with S?


In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?


Find the total number of ways in which six '+' and four '−' signs can be arranged in a line such that no two '−' signs occur together.


In how many ways can the letters of the word
"INTERMEDIATE" be arranged so that:the vowels always occupy even places?


Prove that the product of 2n consecutive negative integers is divisible by (2n)!


Prove that: 4nC2n : 2nCn = [1 · 3 · 5 ... (4n − 1)] : [1 · 3 · 5 ... (2n − 1)]2.


Evaluate

\[^ {20}{}{C}_5 + \sum^5_{r = 2} {}^{25 - r} C_4\]

Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:

\[\frac{^{n}{}{C}_r}{^{n}{}{C}_{r - 1}} = \frac{n - r + 1}{r}\]

How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if  all letters are used at a time 


How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?


Write the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.


Write the number of ways in which 5 red and 4 white balls can be drawn from a bag containing 10 red and 8 white balls.


Write the number of ways in which 12 boys may be divided into three groups of 4 boys each.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×