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The smallest natural number n, such that...

The smallest natural number n, such that the coefficient of x in the expansion of `(x^(2) + (1)/(x^(3)))^(n)` is `.^(n)C_(23)`. Is:

A

35

B

38

C

23

D

58

Text Solution

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The correct Answer is:
B
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ALLEN-Solutions of Triangle & Binomial Theorem-EXERCISE (J-M)
  1. The sum of coefficient of integral powers of x in the binomial expansi...

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  2. The value of (.^(21)C(1) - .^(10)C(1)) + (.^(21)C(2) - .^(10)C(2)) + (...

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  3. The sum of the co-efficients of all odd degree terms in the expansion ...

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  4. If the fractional part of the number (2^(403))/(15) is (k)/(15) then k...

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  5. The positive value of lambda for which the coefficient of x^(2) in the...

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  6. The sum of the real values of x for which the middle term in the binom...

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  7. The value of r for which .^(20)C(r ), .^(20)C(r - 1) .^(20)C(1) + .^...

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  8. Let (x+10)^(50)+(x-10)^(50)=a(0)+a(1)x+a(2)x^(2)+...+a(50)x^(50) for a...

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  9. Let Sn=1+q+q^2 +...+q^n and Tn =1+((q+1)/2)+((q+1)/2)^2+...((q+1)/2)^n...

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  10. Ratio of the 5^(th) term from the beginning to the 5^(th) term from th...

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  11. The number of irrational terms in expansion (7^(1/5)-3^(1/10))^60 is ...

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  12. The sum of the series .^(20)C(0)-.^(20)C(1)-.^(20)C(2)-.^(20)C(3)+…+,....

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  13. If some three consecutive coefficeints in the binomial expanison of (x...

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  14. If the coefficients of x^(2) and x^(3)are both zero, in the expansion ...

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  15. The smallest natural number n, such that the coefficient of x in the e...

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  16. If .^(20)C(1)+(2^(2)).^(20)C(2)+(3^(2)).^(20)C(3)+……..+(20^(2)).^(20)C...

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  17. The term independent of x in the expansion of (1/60-(x^(8))/81).(2x^(...

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