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Question

Find the term which has the exponent of x as 8 in the expansion of x523x3x10

A
T2
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B
T3
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C
T4
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D
Does not exist
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Solution

The correct option is C Does not exist
Given, x523x3x10

General term,

Tr+1=nCrxnryr

Tr+1=10Cr(x52)10r(3x3x)r

Tr+1=10Cr(x)255r2(3)rx72r

Tr+1=10Cr(3)r(x)256r

given the exponent of x as 8

256r=8

258=6r

6r=17

r=176

since r is a fraction number which is not possible. Hence, the term which has the exponents of x as 8 in the expansion of x523x3x10
does not exist.

1072451_397165_ans_0f44ba23094d4f2daab452aa97c2bcd2.png

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