The number of rational terms in the expansion of (1+2+53)6 is

The number of rational terms in the expansion of (1+2+53)6 is

  1. A

    7

  2. B

    11

  3. C

    12

  4. D

    13

    Fill Out the Form for Expert Academic Guidance!l



    +91



    Live ClassesBooksTest SeriesSelf Learning



    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    A term in the expansion  of (1+2+53)6 is of the form

    6!r!s!(6rs)!(1)6rs(2)r(53)s

    =6!r!s!(6rs)!2r/25s/3

    This term will be rational if 2r/2,and 5s/3 are both rational
    numbers. This is possible if and only if r is a multiple of 2
    and s is a multiple of 3. Possible values of r are 0, 2, 4 and
    6 whereas the possible values of s are 0, 3 and 6. Also note that

    For 0r+s6. s can take value 0, 3 or 6.

    For r=0 s can take value 0 or 3.

    For r = 4, s can take value 0.

    For r = 6, s can take value 0.

    Thus, the number of rational terms is 3 + 2 + 1 + 1 = 7

    Chat on WhatsApp Call Infinity Learn

      Talk to our academic expert!



      +91


      Live ClassesBooksTest SeriesSelf Learning




      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.