If (1−y)(1+2x+4x2+8x3+16x4+32x5)=(1−y6) , (y ≠1), then a value of y/x is
A
1/2
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B
2
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C
25/24
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D
24/25
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Solution
The correct option is B2 1+2x+4x2+8x3+16x4+32x5 indicate the sum of a G.P. with a common ratio of 2x. Hence S=1+2x+4x2+8x3+16x4+32x5 =1((2x)6−1)2x−1 =64x6−12x−1 Hence (1−y)(1+2x+4x2+8x3+16x4+32x5)=(1−y6) 1+2x+4x2+8x3+16x4+32x5=1−y61−y (2x)6−12x−1=1−y61−y (2x)6−12x−1=y6−1y−1 Comparing x and y, gives us 2x=y Or yx=2