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Consider the binomial expansion of R = ...

Consider the binomial expansion of ` R = (1 + 2x )^(n) = I = f ` , where I
is the integral part of R and f is the fractional part of R , n `in` N .
Also , the sum of coefficient of R is 2187.
If ith term is the greatest term for `x= 1/3`, then `i` equal

A

4

B

5

C

6

D

7

Text Solution

Verified by Experts

The correct Answer is:
a
Here , ` (1 + 2)^(n) = 2187`
` 3^(n) = 2187 = 3^(7) rArr n = 7`
At ` x = (1)/(sqrt(2)) , R = (sqrt(2) + 1)^(7) = I + f `
Here , `m= |((n +1)(x))/(1 + x)| `
` = | ((7+1)(2xx(1)/(3)))/(1 + 2 xx(1)/(3))| = - (8xx(2)/(3))/((5)/(3)) = (16)/(5) = 3.2`
` T_([m]+1) = T_(3+1) = T_(4)`
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ARIHANT MATHS-BIONOMIAL THEOREM-Exercise (Passage Based Questions)
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  5. Find the modulus of the complex number (2 + 3i)/(2 - 3i)

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  6. If a is the remainder when 5^(40) is divided by 11 and b is the rem...

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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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  13. Find the value of |(1 + i)/(1-i)|

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

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

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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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