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A= (5/2+x/2)^n, B=(1+3x)^m Sum of coef...

`A= (5/2+x/2)^n, B=(1+3x)^m`
Sum of coefficients of expansion of B is 6561 . The difference of
the coefficient of third to the second term in the expansion of A is equal to 117 .
The value of m is

A

4

B

5

C

6

D

7

Text Solution

Verified by Experts

The correct Answer is:
c
Since , sum of coefficient of B is 6561 .
` therefore ((5)/(2) + (1)/(2))^(n) = 6561`
` rArr 3^(n) = 6561 rArr 3^(n) = 3^(8) `
` therefore n = 8 `
Coefficient ` (T_(3) - T_(2)) = 117`
` ""^(m)C_(2) 3^(2) - ""^(m)C_(1) 3^(1) = 117`
` rArr m = 6`
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ARIHANT MATHS ENGLISH-BIONOMIAL THEOREM-Exercise (Passage Based Questions)
  1. Consider (1 + x + x^(2))^(n) = sum(r=0)^(n) a(r) x^(r) , where a(0),...

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  2. Consider (1 + x + x^(2))^(n) = sum(r=0)^(n) a(r) x^(r) , where a(0),...

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  3. If (1+x+2x^(2))^(20) = a(0) + a(1)x^(2) "……" + a(40)x^(40), then follo...

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  4. If (1+x+2x^(2))^(20) = a(0) + a(1)x^(2) "……" + a(40)x^(40), then follo...

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  5. If (1 + x+ 2x^(2))^(20) = a(0) + a(1) x + a(2) x^(2) + …+ a(40) x^(40)...

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  6. Suppose ,m divided by n , then quotient q and remainder r {:("n)m(q"...

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  7. Suppose ,m divided by n , then quotient q and remainder r or m= n...

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  8. Suppose ,m divided by n , then quotient q and remainder r or m= n...

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  9. Consider the binomial expansion of R = (1 + 2x )^(n) = I + f , where...

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  10. Consider the binomial expansion of R = (1 + 2x )^(n) = I = f , where...

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  11. Consider the binomial expansion of R = (1 + 2x )^(n) = I = f , where...

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  12. If (x + a(1)) (x + a(2)) (x + a(3)) …(x + a(n)) = x^(n) + S(1) x^(n-1...

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  13. If (x + a(1)) (x + a(2)) (x + a(3)) …(x + a(n)) = x^(n) + S(1) x^(n-1...

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  14. If (x + a(1)) (x + a(2)) (x + a(3)) …(x + a(n)) = x^(n) + S(1) x^(n-1...

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  15. A= (5/2+x/2)^n, B=(1+3x)^m Sum of coefficients of expansion of B is ...

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  16. Sum of coefficients of expansion of B is 6561 . The difference of t...

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  17. Sum of coefficients of expansion of B is 6561 . The difference of t...

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  18. Let us consider the binomial expansion (1 + x)^(n) = sum(r=0)^(n) a(...

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  19. Let us consider the binomial expansion (1 + x)^(n) = sum(r=0)^(n) a(...

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  20. Let us consider the binomial expansion (1 + x)^(n) = sum(r=0)^(n) a(...

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