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Find coeff. of x^(25) in the expansion ...

Find coeff. of `x^(25)` in the expansion of `sum_(k=0)^(50)(-1)^(k)""^(50)C_(k)(2x-3)^(50-k)(2-x)^(k)`.

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The correct Answer is:
`""^50C_5(5)^25`
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AAKASH SERIES-BINOMIAL THEOREM-ADDITIONAL EXERCISE
  1. The term independent of x (x gt 0 , x ne 1) in the expansion of [((x+...

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  2. Find coeff. of x^(25) in the expansion of sum(k=0)^(50)(-1)^(k)""^(5...

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  3. If the 6th term in the expansion of ((1)/(x^(8//3))+x^2 log10 x)^8 is ...

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  4. Find the coefficient of x^6 in the expansion of (1+ x^2 - x^3)^8

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  5. Find the number of distinct terms in the expansion (x + 2y + 3z + ...

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  6. Find the number of distinct terms in the expansion (x+ y + z)^10+ ...

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  7. Find the coefficient of x^10 in the expansion of (1+2x)^21 + (1 + 2x)^...

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  8. The expansion [x+(x^3-1)^(1//2)]^5+[x-(x^3-1)^(1//2)]^5 is a polynomia...

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  9. If the middle term of the expansion of (1+x)^(2n) is the greatest term...

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  10. Show that the greatest coefficient in the expansion of ( x + y + z + w...

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  11. Find the sum of the coefficients of integral powers of x in (1+3sqrtx)...

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  12. If n is integer greater than 1 show that a -^n C1 (a - 1) +^n C2(a...

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  13. Prove that (C0)/(1)+ (C2)/(3) + (C4)/(5) + (C6)/(7) +…….= (2^n)/(n+ 1)

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  14. Prove that (1)/(1!(n-1)!) + (1)/(3!(n-3)!)+ (1)/(5!(n-5)!) + …….= ...

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  15. Show that sum(r = 0)^50 (""^100Cr).(""^200C(150+r)) = ""^300C50

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  16. Show that C0 + (C0 + C1) + (C0 +C1 + C2)+……. + (C0 + C1 + …+Cn)= (n+2...

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  17. If x > 0 , write the first negative term in the expansion of (1 + 2x)^...

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

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  19. Find the coefficient of x^6 in (1+ x + x^2 + x^3+…….oo)(1+x^2 +x^4 + x...

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  20. Find the coefficient of x^5 in (1 + x + x^2 + x^3)^5 (1+x+x^2 + x^3 + ...

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