Advertisements
Advertisements
प्रश्न
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 12C2 – 5C2.
विकल्प
True
False
Advertisements
उत्तर
This statement is False.
Explanation:
Required number of lines = 12C2 – 5C2 + 1
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?
How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?
Compute:
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 9-digit numbers of different digits can be formed?
Evaluate the following:
35C35
Evaluate the following:
n + 1Cn
From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?
Find the number of diagonals of , 1.a hexagon
Find the number of diagonals of (ii) a polygon of 16 sides.
How many triangles can be obtained by joining 12 points, five of which are collinear?
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?
We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can the selection be made?
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?
Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.
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?
If 20Cr = 20Cr−10, then 18Cr is equal to
Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points is
If 43Cr − 6 = 43C3r + 1 , then the value of r 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 n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
There are 20 straight lines in a plane so that no two lines are parallel and no three lines are concurrent. Determine the number of points of intersection.
Answer the following:
A question paper has 6 questions. How many ways does a student have to answer if he wants to solve at least one question?
In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?
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 ______.
We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?
In how many ways can a football team of 11 players be selected from 16 players? How many of them will include 2 particular players?
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 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 at least three girls.
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.
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 ______.
A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box if at least one black ball is to be included in the draw is ______.
There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:
| C1 | C2 |
| (a) In how many ways committee: can be formed | (i) 10C2 × 19C3 |
| (b) In how many ways a particular: professor is included | (ii) 10C2 × 19C2 |
| (c) In how many ways a particular: lecturer is included | (iii) 9C1 × 20C3 |
| (d) In how many ways a particular: lecturer is excluded | (iv) 10C2 × 20C3 |
All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is ______.
