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There are 10 points in a plane and 4 of ...

There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is `4` b. `40` c. `38` d. 39

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To solve the problem of finding the number of straight lines that can be formed by 10 points in a plane where 4 of them are collinear, we can follow these steps: ### Step 1: Calculate the total number of lines from 10 points To find the number of straight lines that can be formed by any two points, we use the combination formula \( nC2 \), where \( n \) is the total number of points. Here, \( n = 10 \): \[ \text{Total lines} = \binom{10}{2} = \frac{10 \times 9}{2} = 45 ...
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RD SHARMA-COMBINATIONS-Solved Examples And Exercises
  1. If \ ^(20)C(r+1)=\ \ ^(20)C(r-1),\ t h e n\ r is equal to a. 10 b. 11 ...

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  2. If C(n , 12)=C(n ,8),\ t h e n\ C(22 , n) is equal to a. 231 b. 210 c....

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  3. If \ ^ C1=\ \ ^n 2 then 2m=n m=(n-1) d. 2n=m(m-1)

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  4. If \ ^n C(12)=\ \ ^n C8 then n = a. 20 b. 12 c. 6 d. 30

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  5. If \ ^n Cr+\ ^n C(r-1)=\ \ ^(n+1)Cx ,\ t h e n x = r b. r-1 c. n d. r...

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  6. If \ ^(a^2-a)C2=\ \ ^(a^2-a)C4\ t h e n= 2 b. 3 c. 4 d. none of ...

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  7. \ ^5C1+\ ^5C2+\ ^5C3+\ ^5C4+\ ^5C5 is equal to 30 b. 31 c. 32 d. 33

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  8. Total number of words formed by 2 vowels and 3 consonants taken from 4...

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  9. There are 12 points in a lane. The number of the straight lines joinin...

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  10. There persons enter a railway compartment. If there are 5 seats vacant...

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  11. In how many ways can a committee of 5 be made out of 6 men and 4 women...

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  12. There are 10 points in a plane and 4 of them are collinear. The number...

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  13. There are 13 players of cricket, out of which 4 are bowlers. In how ...

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  14. The number of ways in which a host lady can invite for a party of 8 ou...

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  15. How many different committees of 5 can be formed from 6 men and 4 wome...

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  16. The number of diagonals that can be drawn by joining the vertices of a...

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  17. If \ ^(43)C(r-6)=\ ^(43)C(3r+1)\ then the value of r is 12 b. 8 c. 6 ...

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  18. A lady gives a dinner party for six guests. The number of ways in whic...

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  19. If \ ^(n+1)C3=2.\ \ ^n C2\ t h e n= 3 b. 4 c. 6 d. 5

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  20. The number of parallelograms that can be formed form a set of four ...

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