If the coefficient of x7 in the expansion of  ax2+1bx11 and the coefficient of x– 7 is the expansion of ax−1bx211are equal, then

If the coefficient of x7 in the expansion of  ax2+1bx11 and the coefficient of x– 7 is the expansion of ax1bx211are equal, then

  1. A

    ab = 1

  2. B

    ab = 11

  3. C

    ab = 5 

  4. D

    ab = 6

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    Solution:

    Tr+1,the(r+1) th  term in the expansion ax2+1bx11is 

    Tr+1=11Crax211r1bxr=11Cra11rbrx223r

    For the coefficient of x7,set 223r=7  r=5

    Coefficient of x7 in ax2+1bx11 is  11C5a6b5

    Next, tr + 1, the (r + 1)th term in the expansion of ax1bx211is 

    tr+1=11Cr(ax)11r1bx2r

    =11Cra11rbr(1)rx113r

    For the coefficient of x7, set 113r=7r=6

    Coefficient of  x7 in the expansion of =11C6a5b6

    We are given   11C5a6b5=11C6a5b6ab=1

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