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Using the expansion in simplify (a+b)^6+...

Using the expansion in simplify `(a+b)^6+(a-b)^6`

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`2[a^6+15a^4b^2+15a^2b^4+b^6]`
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A N EXCEL PUBLICATION-BINOMIAL THEOREM-QUESTION BANK
  1. Consider the expansion of (3x^2-1/(2x^3))^10 Find the term independent...

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  2. Write the expansion of (a-b)^n, n is a positive integer

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  3. Using the expansion in simplify (a+b)^6+(a-b)^6

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  4. Find the value of (10.2)^6+(9.8)^6

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  5. What are the coefficients of (2r+1)^(th) and (r+2)^(th) terms in the e...

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  6. If these coefficients are equal , prove that r=14

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  7. Consider the expansion of (x+a)^n Find the (r+1)^(th)term in the expan...

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  8. Consider the expansion of (x+a)^n Find the 6th ,7th and 8th terms in t...

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  9. Consider the expansion of (x+a)^n If these are 112,7 and 1/4 respectiv...

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  10. Expand (1+ax)^n upto the third term if n is a positive integer

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  11. If the first three terms in the expansion of (1+ax)^n are 1,-21x and 2...

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  12. What is the coefficient of the (r+1)^(th) term in the expansion of (1+...

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  13. What is the coefficient of 5th, 6th and 7th terms in the expansion of ...

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  14. If they are in A.P, find the possible values of n

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  15. Expand 2^(3n) by writing 2^(3n)=(1+7)^n

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  16. Using binomial theorem prove that 2^(3n)-7n-1 is divisible by 49, wher...

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  17. prove the result ^(n+1)Cr=^nC(r-1)+^nCr

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  18. Prove that ""^(n+1)C(r+1)=(n+1)/(r+1)"^nCr

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  19. Prove that (C0+C1)(C1+C2)(C2+C3)...(C(n-1)+Cn)=(C0C1C2...C(n-1)(n+1)^n...

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  20. Prove that ""^(n+1)C(r+1)=(n+1)/(r+1)"^nCr

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