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

The coefficient of `x^(53)` in the expansion `sum_(m=0)^(100)^(100)C_m(x-3)^(100-m)2^m` is `^100 C_(47)` b. `^100 C_(53)` c. `-^(100)C_(53)` d. none of these

A

`""^(100)C_(47)`

B

`""^(100)C_(53)`

C

`-""^(100)C_(53)`

D

`-""^(100)C_(100)`

Text Solution

Verified by Experts

The correct Answer is:
c
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ML KHANNA-BINOMIAL THEOREM AND MATHEMATICAL INDUCTION -Self Assessment Test
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  5. If the coefficient of x^(7) and x^(8) in (2+(x)/(3))^(n) are equal, th...

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  6. The coefficient of x^(4) in the expansion of (1+x+x^(2)+x^(3))^(n) is

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  7. The greatest coefficient in the expansion of (1+ x)^(2n +1) is

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  8. The position of the term independent of x in the expansion of (sqrt((x...

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  9. In the expansion of (x+(2)/(x^(2)))^(15) , the term independent of x ...

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  11. If (1+ x)^(n) = C(0) + C(1) x + C(2)x^(2) + ...+ C(n)x^(n) , prove tha...

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  12. If C(0), C(1), C(2),.....,C(n) are binomial coefficients, (where C(r) ...

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  13. If (1+x-2x^2)^6=1+a1x+a2x^(12)++a(12)x^(12), then find the value of a2...

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  14. If (1 + x)^(n) = C(0) + C(1) x + C(2) x^(2) +… + C(n) x^(n) , prove th...

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  15. The coefficient of x^(n) in the expansion of (1-9 x + 20 x^(2))^(-1...

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  16. The number of integer terms in the expansion of (5^(1//2)+7^(1//6))^(...

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  17. Find the coefficient of x^5 in the expansion of (1+x^2)^5dot(1+x)^4i s...

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  18. Consider the expansion of ( 1+ x)^(2n+1) The coefficient of x^(99) ...

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  19. If the coefficient of x^(7) in (ax^(2)+(1)/(bx))^(11) is equal to the ...

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  20. The sum of the coefficeints of the polynominal (1 + x - 3x^(2))^(2163)...

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  21. Sum of coefficients in the expansion of (x+2y+z)^(10) is

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