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Sum of all the digits of the coefficient of `x^(5)` in the expansion of `(1+x^(2))^(5)(1+x)^(4)` is

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MOTION-BINOMIAL THEOREM -Exercise -3 ( Subjective )
  1. Prove that sqrt(C1) +sqrt(C2) +sqrt(C3)+...+sqrt(Cn)le 2^(n-1) +(n-1)/...

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  2. If C(r ) = (n!)/(r!(n - r)!), then prove that sqrt(C(1)) + sqrt(C(2)...

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  3. Sum of all the digits of the coefficient of x^(5) in the expansion of ...

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  4. Find the coefficient of x^(4) in the expansion of (1+x+x^(2)+x^(3))^(1...

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  5. Find the coefficients of x^(4) in the expansions of (2 - x + 3x^(2...

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  6. Let a = (72!)/(36!)^2-1 , then (A) a is odd (B) a is divisible by 7...

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  7. find the sum of the series sum(r=0)^n(-1)^r *"^nCr[1/(2^r)+(3^r)/(2^(...

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  8. Given that (1+x+x^2)^n=a0+a1x+a2x^2+........+a(2n)x^(2n) find the val...

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  9. Given that (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+......+a(2n)x^(2n), f...

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  10. Given that (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+......+a(2n)x^(2n), f...

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  11. If n(j(r))=((1-xn)(1-x(n-1))(1-x^(n-2)).......(1-x^(n-r+1)))/((1-x)(1-...

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  12. Prove that sum(k=0)^n ^nCk sinKx.cos(n-K)x=2^(n-1)sin nx

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  13. The expressions 1+x,1+x+x^2,1+x+x^2+x^3.............1+x+x^2+.............

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  14. Find the coefficients of x^(6) in the expansion of (ax^(2) + bx +...

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  15. Find the coefficient of x^2 y^3 z^4 in the expansion of (ax-by+cz)^9

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  16. Find the coefficient of x^2 y^3 z^4 in the expansion of (ax -by +cx...

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  17. If sum(r=0)^(2n)ar(x-2)^r=sum(r=0)^(2n)br(x-3)^ra n dak=1 for all kgeq...

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  18. Show that the integral part in each of the following is odd. n in N. ...

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  19. Show that the integral part in each of the following is even. n in N....

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  20. Show that the integer next above (sqrt(3)+1)^(2m) contains 2^(m+1) as ...

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