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
उत्तर
This statement is False.
Explanation:
Required number of lines = 12C2 – 5C2 + 1
APPEARS IN
संबंधित प्रश्न
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?
How many A.P.'s with 10 terms are there whose first term is in the set {1, 2, 3} and whose common difference is in the set {1, 2, 3, 4, 5}?
How many three-digit numbers are there with no digit repeated?
How many different five-digit number licence plates can be made if
the first-digit cannot be zero, but the repetition of digits is 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:
35C35
If 15Cr : 15Cr − 1 = 11 : 5, find r.
If α = mC2, then find the value of αC2.
How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?
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 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: at least 3 girls?
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines
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?
Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.
If 20Cr = 20Cr−10, then 18Cr is equal to
If nCr + nCr + 1 = n + 1Cx , then x =
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?
Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 5 green balls, and 7 blue balls so that 3 balls of every colour are drawn.
In a small village, there are 87 families, of which 52 families have atmost 2 children. In a rural development programme 20 families are to be chosen for assistance, of which atleast 18 families must have at most 2 children. In how many ways can the choice be made?
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.
Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is ______.
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is ______.
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 ______.
If some or all of n objects are taken at a time, the number of combinations is 2n – 1.
A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. He can choose the seven questions in 650 ways.
There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of:
| C1 | C2 |
| (a) One book of each subject; | (i) 3968 |
| (b) At least one book of each subject: | (ii) 60 |
| (c) At least one book of English: | (iii) 3255 |
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 ______.
Number of selections of at least one letter from the letters of MATHEMATICS, is ______.
A badminton club has 10 couples as members. They meet to organise a mixed double match. If each wife refers to p artner as well as oppose her husband in the match, then the number of different ways can the match off will be ______.
