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The coefficient of x^(53) in the expansi...

The coefficient of `x^(53)` in the expansion of `sum_(m=0)^(100) ^100C_m(x-3)^(100-m) 2^m` is equal to

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. The coefficient of X^24in the expansion of (1+X^2 )^12(1+X^12)(1+X^24)

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  2. Find the sum of the GP 1+3+9+27+........ 12terms

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  3. The coefficient of x^(53) in the expansion of sum(m=0)^(100) ^100Cm(x-...

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  4. The coefficient of the term independent of x in the expansion of [((x+...

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  5. In the expansion of (1+x+x^3+x^4)^10, the coefficient of x^4 is a..^...

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  6. If coefficient of a^(2)b^(3)c^(4) in (a+b+c)^(m) (where m in N) is L (...

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  7. The last two digits of the number 3^(400) are: (A) 81 (B) 43 (C) ...

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  8. The expression (sqrt(2x^2+1)+sqrt(2x^2-1))^6 + (2/(sqrt(2x^2+1)+sqrt(2...

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  9. A GP has common ratio 3, last term 486, if the sum of its terms is 728...

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  10. If (1+2x+3x^2)^(10)=a0+a1x+a2x^2+.....+a(20)x^(20),t h e na1 equals a....

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  11. Find the number of integral terms in the expansion of (5^(1/2)+7^(1/8)...

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  12. For which of the following values of x ,5t h term is the numerically g...

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  13. For natural numbers m ,n ,if(1-y)^m(1+y)^n=1+a1y+a2y^2+... , and a1=a2...

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  14. If the middle term in the expansion of (x/2+2)^8 is 1120, then find t...

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  15. If (1+x)^n=C0+C1x+C2x^2+...+Cn x^n , t h e n C0-(C0+C1)+(C0+C1+C2)-(C0...

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  16. In the expansion of (x^(2) + 1 + (1)/(x^(2)))^(n), n in N,

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  17. The value of .^(n)C(1)+.^(n+1)C(2)+.^(n+2)C(3)+"….."+.^(n+m-1)C(m) is ...

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  18. If (1+x)^n=C0+C1x+C2 x^2+...+Cn x^n , n in N ,then C0-C1+C2-.....+(-1...

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  19. The 10th term of (3-sqrt((17)/4+3sqrt(2)))^(20) is (a) a irrational nu...

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  20. Find the geometric mean between2a and 8a^3

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