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If the second term of the expansion [a^(...

If the second term of the expansion `[a^(1/(13))+a/(sqrt(a^(-1)))]^n` is `14 a^(5//2)` , then the value of `(^n C_3)/(^n C_2)` is.

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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. The largest value of x for which the fourth tem in the expansion (5^(...

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  2. The number of values in set of values of r for which ^23 Cr+2.^(23)C(...

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  3. If the second term of the expansion [a^(1/(13))+a/(sqrt(a^(-1)))]^n is...

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  4. Given (1-2x+5x^2-10 x^3)(1+x)^n=1+a1x+a2x^2+ and thata1 ^2=2a2 then th...

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  5. Sum of last three digits of the number N=7^(100)-3^(100) is.

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  6. Let n be a positive integer and (1+x+x^2)^n=a0+a1x+ . . . . +a(2n)x^(2...

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  7. sum(r=1)^k(−3)^(r−1) .^(3n)C(2r−1)=0, where k=(3n)/2 and n is an even ...

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  8. The coefficient of the middle term in the binomial expansion in powers...

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  9. If in the expansion of (1+x)^n ,a ,b ,c are three consecutive coeffici...

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  10. If n and k are positive integers, show that 2^k( .^n C0)(.^n Ck)-2^(k-...

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  11. Prove that (25)^(n+1)-24n+5735 is divisible by (24)^2 for all n=1,2,.....

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  12. The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (a).(...

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  13. The coefficient x^5 in the expansion of (1+x)^(21)+(1+x)^(22)++(1+x)^...

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  14. If x^m occurs in the expansion (x+1//x^2)^(2n) , then the coefficient ...

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  15. If the coefficients of 5th, 6th , and 7th terms in the expansion of (1...

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  16. If (1+2x+x^2)^n=sum(r=0)^(2n)ar x^r ,then ar is a.(.^nC2)^2 b. .^n ...

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  17. In the expansion of (x^3-1/x^2)^n, n in N if sum of the coefficients o...

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  18. If the coefficients of rth and (r+1)t h terms in the expansion of (3+7...

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  19. In the expansion of (1+3x+2x^2)^6 , the coefficient of x^(11) is a. 14...

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  20. If n-1Cr=(k^2-3)^nC(r+1), then (a) (-oo,-2] (b) [2,oo) (c) [-sqrt3, s...

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