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The value of sum(r=0)^(20)r(20-r)(^(20)C...

The value of `sum_(r=0)^(20)r(20-r)(`^(20)C_r)^2` is equal to ?

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. The coefficients of three consecutive terms of (1+x)^(n+5) are in the ...

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  2. If (1-x)^(-n)=a0+a1x+a2x^2++ar x^r+ ,t h e na0+a1+a2++ar is equal to ...

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  3. The value of sum(r=0)^(20)r(20-r)(^(20)Cr)^2 is equal to ?

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  4. The coefficient of x^(10) in the expansion of (1+x^(2)-x^(3))^(8) is

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  5. If the term independent of x in the (sqrt(x)-k/(x^2))^(10) is 405, the...

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  6. The coefficient of x^2y^3 in the expansion of (1-x+y)^(20) is (a)(20 !...

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  7. The coefficient of x^5 in the expansion of (x^2-x-2)^5 is

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  8. The coefficient of a^8b^4c^9d^9 in (a b c+a b d+a c d +b c d)^(10) is

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  9. If the coefficient of x^(7)in [ax^(2) + (1/bx)]^(11) equals the coeffi...

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  10. If (1+x)^5=a0+a1x+a2x^2+a3x^3+a4x^4+a5x^5, then the value of (a0-a2+a4...

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  11. The coefficient of x^n in the expansion of (1+x)(1-x)^n is

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  12. The coefficient of x^(28) in the expansion of (1+x^(2)-x^(6))^(30) is

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  13. The coefficient of x^(n) in (1+x)^(101) (1-x+x^(2))^(100) is nonzero, ...

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  14. prove that sum(r=0)^n(-1)^r^n Cr. [1/(2^r)+(3^r)/(2^(2r))+(7^r)/(2^(...

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  15. In the expansion of (7^(1//3)+11^(1//9))^(6561) ,

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  16. If for z as real or complex, (1+z^2+z^4)^8=C0+C1z^2+C2z^4+...+C(16)z^(...

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  17. The sum of the coefficient in the expansion of (1+ax-2x^(2))^(n) is

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  18. if the 4^(th) term in the expansion of (ax+1)^(n) is 5//2, then

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  19. Number of values of r satisfying the equation ,^69C(3r-1) -^(69)C(r^2)...

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  20. If (4+sqrt(15))^n=I+f,where n is an odd natural number, I is an intege...

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