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If .^(2n)C(3):^(n)C(3)=11:1, find the va...

If `.^(2n)C_(3):^(n)C_(3)=11:1`, find the value of n.

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To solve the problem, we need to find the value of \( n \) given the equation: \[ \frac{{^{2n}C_3}}{{^{n}C_3}} = \frac{11}{1} \] ### Step 1: Write the combinations in terms of factorials ...
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ARIHANT MATHS ENGLISH-PERMUTATIONS AND COMBINATIONS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. If .^(2n)C(3):^(n)C(3)=11:1, find the value of n.

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  2. There is a rectangular sheet of dimension (2m-1)xx(2n-1), (where m > 0...

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  3. If the letters of the word SACHIN are arranged in all possible ways...

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  4. lf r, s, t are prime numbers and p, q are the positive integers such t...

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  5. At an election a voter may vote for nany number of candidates , not gr...

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

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  7. The set S""=""{1,""2,""3,""........ ,""12) is to be partitioned into...

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  8. Consider all possible permutations of the letters of the word ENDEANOE...

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  9. How many different words can be formed by jumbling the letters in the ...

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  14. Statement-1: The number of ways of distributing 10 identical balls in ...

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  15. There are 10 points in a plane, out of these 6 are collinear. The numb...

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  16. The total number of ways in which 5 balls of differert colours can be ...

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  17. Let n denote the number of all n-digit positive integers formed by the...

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  18. Let a(n) denote the number of all n-digit numbers formed by the digits...

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  19. Assuming the balls to be identical except for difference in colours, t...

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  20. Let Tn be the number of all possible triangles formed by joining ve...

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  21. Consider the set of eight vector V={a hat i+b hat j+c hat k ; a ,bc in...

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