Coefficients of Terms Equidistant from Beginning and End
The ratio of ...
Question
The ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of (213+12(2)13)10 is:
A
1:2(6)13
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B
2(36)13:1
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C
4(36)13:1
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D
1:4(16)13
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Solution
The correct option is C4(36)13:1 ⎛⎜⎝213+12(3)13⎞⎟⎠10
We know that 5th term from end will be 7th term from begining, ∴T5T7=10C4⋅(213)6⋅⎛⎜⎝12.(3)13⎞⎟⎠410C6⋅(213)4.⎛⎜⎝12⋅(3)13⎞⎟⎠6 =(213)2⎛⎜⎝12⋅(3)13⎞⎟⎠2 =223⋅22⋅3231 T5T7=4⋅(36)131 T5:T7=4⋅(36)13:1