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STATEMENT -1 : There are 12 points in a ...

STATEMENT -1 : There are 12 points in a plane of which only 5 are collinear , then the number of straight lines obained by joining these points in pairs is `""^(12)C_(2) - ""^(5)C_(2)` .
STATEMENT-2: `""^(n +1)C_(r) - ""^(n-1)C_(r - 1) = ""^(n)C_(r) + ""^(n)C_(r - 2)`
STATEMENT -3 :2n persons may be seated at two round tables , n person seated at each , in `((2n)!)/(n^(2))` in differnet ways.

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""^(n) C_(r+1)+2""^(n)C_(r) +""^(n)C_(r-1)=

For ""^(n) C_(r) + 2 ""^(n) C_(r-1) + ""^(n) C_(r-2) =

""^(n)C_(r+1)+^(n)C_(r-1)+2.""^(n)C_(r)=

""^(n)C_(r)+2""^(n)C_(r-1)+^(n)C_(r-2) is equal to

""^(n-2)C_(r)+2""^(n-2)C_(r-1)+""^(n-2)C_(r-2) equals :

n points are given of which r points are collinear, then the number of straight lines that can be found = (a) ""^(n)C_(2)-""^(r)C_(2) (b) ""^(n)C_(2)-""^(r)C_(2)+1 (c) ""^(n)C_(2)-""^(r)C_(2)-1 (d) None of these

.^(n)C_(r)+2.^(n)C_(r-1)+.^(n)C_(r-2)=

If ""^(n)C_r : ""^(n)C_(r+1) =1 : 2 and^(n)C_(r+1): ""^(n)C_(r+2) = 2 : 3 determine the values of n and r.

Find the sum sum_(r=1)^(n) r^(2) (""^(n)C_(r))/(""^(n)C_(r-1)) .

""^(n)C_(n-r)+3.""^(n)C_(n-r+1)+3.""^(n)C_(n-r+2)+""^(n)C_(n-r+3)=""^(x)C_(r)

VMC MODULES ENGLISH-PERMUTATION & COMBINATION-JEE ARCHIVE
  1. STATEMENT -1 : There are 12 points in a plane of which only 5 are coll...

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  2. The number of integers greater than 6000 that can be formed using the ...

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  3. How many different nine-digit numbers can be formed from the digits of...

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  4. An n-digit number is a positive number with exactly n digits. Nine hun...

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  5. In a college of 300 students, every student reads 5 newspapers and eve...

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  6. Eight chairs are numbered 1 to 8. Two women and three men wish to oc...

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  7. Ten different letters of an alphabet are given. Words with five letter...

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  8. let T(n) be the number of all possible triangels formed by joining ver...

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  9. Find the value of ""^(47)C4+ underset (r=1) overset( 5) sum ""^(52-r...

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  10. True or false 1. The product of any 2. r 3. 4. consecutive natural ...

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  11. The letters of the word COCHIN are permuted and all the permutation...

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  12. The number of arrangements of the letters of the word BANANA in whic...

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  13. The number of divisors of the form 4K + 2 , K ge 0 of the integers 24...

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  14. Find the number of ways in which six '+' and four '-' signs can be arr...

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  15. There are five balls of different colours and five boxes of colours sa...

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  16. The number of ways of choosing 10 objects out of 31 objects of which 1...

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  17. Suppose that 20 pillars of the same height have been erected along the...

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  18. Some identical balls are arranged in rows to form an equilateral trian...

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  19. There are m men and two women participating in a chess tournament. Eac...

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  20. A group of students comprises of 5 boys and n girls. If the number of ...

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  21. Let S be the set of all triangles in the xy-plane, each having one ver...

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