Question

There are 15 points in a plane of which exactly 8 are collinear. Find the number of straight lines obtained by joining there points.   

Solution

Correct option is

78

For line we require two points. Therefore the numbers of lines which we can obtained is 16C2 = 105. Since 8 of these points lie on a straight line, we lose 8C2 = 28 lines and get just one line on which these points lie. Therefore, the number of lines is 105 – 28 + 1 = 78.

SIMILAR QUESTIONS

Q1

A five digit number divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is

Q2

The number of ways in which a mixed double game can be arranged from amongst 9 married couple if no husband and wife play in the same game is 

Q3

The number of times the digit 3 will be written when listing the integers from 1 to 1000 is

Q4

The number of positive integers n such that 2n divides n! is

Q5

A class contains 4 boys and g girls. Every Sunday five students, including at least three boys go for a picnic to Appu Ghar, a different group being sent every week. During, the picnic, the class teacher gives each girl in the group a doll. If the total number of dolls distributed was 85, then value of g is    

Q6

The sum of the factors of 9! Which are odd and are of the form 3m + 2, where m is a natural number is 

Q7

Sum of all three digit numbers (no digit being zero) having the property that all digit are perfect squares, is

Q8

Let S = {1, 2, 3, ... n}. if X denote the set of all subsets of S containing exactly two elements, then the value of   

Q9

Let a be a factor of 120, then the number of integral solution of x1x2x3 = a is 

Q10

If n is the number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any quation find n/40.