Q)(A)20   (B)2   (C)1   (D)7

Asked by araima2001 | 16th Mar, 2017, 09:11: AM

Expert Answer:

begin mathsize 16px style In space the space expansion space of space open parentheses fraction numerator 3 straight x squared over denominator 2 end fraction minus fraction numerator 1 over denominator 3 straight x end fraction close parentheses to the power of 9 space the space independent space term space of space straight x space is comma
straight T subscript straight r plus 1 end subscript equals open parentheses table row 9 row straight r end table close parentheses open parentheses fraction numerator 3 straight x squared over denominator 2 end fraction close parentheses to the power of 9 minus straight r end exponent open parentheses fraction numerator negative 1 over denominator 3 straight x end fraction close parentheses to the power of straight r
space space space space space space space space space equals space open parentheses table row 9 row straight r end table close parentheses open parentheses 3 over 2 close parentheses to the power of 9 minus straight r end exponent straight x to the power of 18 minus straight r end exponent space open parentheses negative 1 close parentheses to the power of straight r space straight x to the power of negative straight r end exponent
space space space space space space space space space space equals open parentheses table row 9 row straight r end table close parentheses open parentheses 3 over 2 close parentheses to the power of 9 minus straight r end exponent space open parentheses negative 1 close parentheses to the power of straight r space straight x to the power of 18 minus 2 straight r end exponent space
As space term space should space be space independent space of space straight x comma
18 minus 2 straight r equals 0
rightwards double arrow straight r equals 6
Hence comma space only space one space term space in space the space expansion space of space open parentheses fraction numerator 3 straight x squared over denominator 2 end fraction minus fraction numerator 1 over denominator 3 straight x end fraction close parentheses to the power of 9.
Also comma space open parentheses 2 straight x squared plus straight x plus 18 close parentheses space has space only space one space term space which space is space independent space of space straight x comma
we space will space have space only space one space term space in space the space expansion space of space open parentheses 2 straight x squared plus straight x plus 18 close parentheses open parentheses fraction numerator 3 straight x squared over denominator 2 end fraction minus fraction numerator 1 over denominator 3 straight x end fraction close parentheses to the power of 9.
Answer space is space 1.

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Answered by Sneha shidid | 16th Mar, 2017, 04:17: PM