The greatest term in the expansion of 51+1520is :

The greatest term in the expansion of 51+1520

is :

  1. A

     20C5125

  2. B

     20C515

  3. C

     20C5

  4. D

     20C5(5)

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    Solution:

    We have 

    Tr+1=20Cr5(5)r=20Cr1(5)r1

    Suppose (r + 1)th term is the greatest term. Then

    Tr+1Tr>1 and Tr+1Tr+2>120rr+115>1 and r+219r5>120r>5r+5 and r5+25>19r1925<(5+1)r<20514(1925)(51)<r<14(205)(51)14(21529)<r<14(21525)

    4.48<r<5.49r=5,

     greatest term =20C5154=20C5125

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