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x = 1 + (3 ) /(1 ! ) xx (1 )/(6) + (...

` x = 1 + (3 ) /(1 ! ) xx (1 )/(6) + ( 3 xx 7 ) /(2 ! ) ( (1 )/(6) ) ^ 2 + (3 xx 7 xx 11 ) /(3 ! ) ((1 )/(6))^ 3 + … rArr x ^4 = `

A

`81 `

B

`54 `

C

`27`

D

`8`

Text Solution

Verified by Experts

The correct Answer is:
C
` x = 1 + (3 ) /(1! ) xx (1 )/(6) + (3 xx 7 ) /(2 ! ) ((1 )/(6))^ 2 + (3 xx 7 xx 11 ) /(3 ! ) ((1 )/(6))^(3) + … `
` x = (1 - y ) ^(-p//q ) `
` p = 3, p + q = 7, (y ) /(q) = (1 )/(6) `
` q = 4 `
` (y) /(4) = (1 )/(6)`
` rArr y = (4 ) /(6)`
` therefore y = (2 ) /(3)`
` x = (1 - (2 ) /(3) ) ^(-3//4)`
` rArr x = ((1)/(3)) ^( -3/4)`
` rArr x = 3^(3//4)`
` rArr x = 4 sqrt(27)`
` therefore x ^ 4 = 27 `
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SIA PUBLICATION-BINOMIAL THEOREM AND PARTIAL FRACTIONS -Problems
  1. x = 1 + (3 ) /(1 ! ) xx (1 )/(6) + ( 3 xx 7 ) /(2 ! ) ( (1 )/(6) ...

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  2. If |x| is so small that x ^ 2 and higher power of x may be...

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  3. The coefficient of x ^n in the expansion of (1 ) /(x ^2 - 5x...

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  4. If |x| lt 1 then the coefficient of x ^ 5 in the expansi...

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  5. If the coefficients of x ^(9), x ^( 10) , x ^ ( 11 ) in the e...

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  6. If (a + bx ) ^ ( -3 ) = (1 ) /(27) + (1 ) /(3) x + …, ...

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  7. The term independent of x in the expansions of (sqrtx - (2...

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  8. If (2x ^ 3 + x ^ 2 - 5 ) /( x ^4 - 25 ) = (Ax + B)/( x ^ 2...

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  9. The term independent of x ( x gt 0, x ne 1 ) in the expansion...

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  10. If x is small, so that x ^ 2 and higher powers can be negl...

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  11. If (1 ) /(x ^ 4 + x ^ 2 + 1 ) = (Ax + B)/(x ^ 2 + x + 1 ) +...

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  12. If ab ne 0 and the sum of coefficients of x ^ 7 and x ^ ...

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  13. (1)/(x (x - 1 ) (x + 2 ) …. (x + n)) = (A0 )/( x ) + (A 1 )/(x +...

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  14. If the coefficients of r^(th) and ( r + 1 ) ^(th) terms in...

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  15. (x ^ 2 + x + 1 ) /((x - 1) (x -2) (x -3)) = (A)/(x-1) + (B)/(x-2)...

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  16. If (1 + 2x + 3x^2 ) ^(10) = a 0 + a 1 x + a 2 x ^ 2 + … + a...

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  17. For |x| lt (1)/(5) the coefficient of x ^ 3 in the expans...

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  18. if (3x ^ 2 + x + 1 )/((x - 1 ) ^4) = (a)/((x - 1 )) +(b)/((x -1)...

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  19. The coefficient of x ^(24) in the expansion of (1 + x^ 2 )^...

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  20. If x is numerically so small so that x ^ 2 and higher...

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