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Find the coefficient of a^3b^4c^5 in (ab...

Find the coefficient of `a^3b^4c^5` in `(ab+bc+ca)^6`

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The co-efficient of a^(3)b^(4)c^(5) in the expansion of (bc+ca+ab)^(6) is

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If (a-b), (b-c), (c-a) are in GP then prove that (a+b+c)^2 =3(ab+bc+ca)..

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PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. If n in I^+ show 2^(3n+3) -7n -8 is divisible by 49.

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  2. Find the coefficient of x^7 in (1+3x-2x^3)^10

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  3. Find the coefficient of a^3b^4c^5 in (ab+bc+ca)^6

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  4. Expand (x^2+(3/x))^4 , xne0

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  5. Compute (98)^5

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  6. Using binomial theorem prove that 6^n-5n always leaves remainder I whe...

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  7. Find a, if 17th and 18th terms in the expansions of (2+a)^50 are equal...

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  8. Find the coefficient of x^6y^3 in the expansion of (x+2y)^9

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  9. Use the principle of mathematical induction to show that 5^(2+1)+3^(n+...

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  10. Prove by mathematical induction that sum(r=0)^n "^nCr = n cdot 2^(n-1)

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  11. For ninN, prove that ((n+1)/2)^ngt n!

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  12. Using mathematical induction to show that p^(n+1) +(p+1)^(2n-1) is div...

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  13. Prove by induction that the integer next greater than (3+sqrt5)6n is d...

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  14. Using the principle of mathematical induction show that tan^(-1)(x/(1+...

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  15. Prove by induction that (1+x1)(1+x2)(1+x3)…….(1+xn) ge 1+x1+x2+……+xn

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  16. Use induction to prove that 3^(2n)-1 is not exactly divisible by 2^(n+...

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  17. (x+sqrt(x^3-1))^5+(x-sqrt(x^3-1))^5 is a polynomial of degree

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  18. if the coefficients of x^7 & x^8 in the expansion (2+x/3)^n are equal ...

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  19. The term independent of x in (sqrt(x/3)+sqrt(3/(2x^2)))^10 is

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  20. The total number of terms in the expansion of (x+y)^(100)+(x-y)^(100) ...

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