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Out of 18 points in a plane, no three ar...

Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the points.

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There are 11 points in a plane. No three of these lies in the same straight line except 4 points, which are collinear. Find, (i) the number of straight lines that can be obtained from the pairs of these points? (ii) the number of triangles that can be formed for which the points are their vertices?

There are 11 points in a plane. No three of these lies in the same straight line except 4 points, which are collinear. Find , (i) the number of straight lines that can be obtained from the pairs of these points ? (ii) the number of triangles that can be formed for which the points are their vertices ?

There are 8 points in a plane, no three of them are collinear .The number of triangles that can be formed is:

Find the mid points of the line segment joining the points .

There are 10 points in a plane no three of which are collinear except 4 of them which lie on a line. The number of straight lines determined by them is

There are 10 points on a plane of which 5 points are collinear. Also, no three of the remaining 5 points are collinear. Then find (i) the number of straight lines joining these points: (ii) the number of triangles, formed by joining these points.

There are n points in a plane in which no large no three are in a straight line except m which are all i straight line. Find the number of (i) different straight lines, (ii) different triangles, (iii) different quadrilaterals that can be formed with the given points as vertices.

FULL MARKS-COMBINATORICS AND MATHEMATICAL INDUCTION-ADDITIONAL QUESTIONS
  1. How many 3-digit even numbers can be made using the digits 1,2,3,4,6,7...

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  2. If ""^(n-1)P(3): ""^(n)P(4)=1:9 find n.

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  3. Out of 18 points in a plane, no three are in the same line except five...

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  4. We wish to select 6 person from 8 but , if the person A is choosen , t...

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  5. How many 3-digit numbers can be made using digit 1,2,3,4,6,7 if no dig...

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  6. Find the number of 4-digit numbers that can be formed using the digits...

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  7. Iff ""^(5)P(r)=""^(6)P(r-1) find r.

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  8. How many words, with or without meaning , can be made from the letters...

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  9. A group consists of 4 girls and 7 boys. In how many ways can a team of...

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  10. A committee of 6 is to be choosen from 10 men and 7 women so as to con...

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  11. Using the digits 1,2,3,4,5,6,7 a number of 4 different digits is forme...

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  12. If ""^(22)P(r+1):^(20)P(r+2)=11:52, find r.

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  13. If ""^(nP(r)=""^(n)P(r+1) and ""^(n)C(r)=""^(n)C(r-1) find n and r.

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  14. A committee of 7 peoples has to be formed from 9 men and 4 women . In ...

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  15. In .^(2n)C(3) :.^(n)C(3) = 11 : 1 then n is

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  16. Find the number of ways of selecting 9 balls from 6 red balls, 5 white...

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  17. If 1/(7!)+1/(9!)=x/(10!), find x.

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  18. If ""^(n)C(4),^(n)C(5)" and "^(n)C(6) are in A.P. then find n.

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  19. Prove by induction the inequality (1+x)^(n) ge 1 + nx. whenever x is p...

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  20. Prove that 3^(2n)-1 is divisible by 8.

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