A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of (2(1/3) + (1/2(3)(1)3))10 is :

Question

A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of (2(1/3) + (1/2(3)(1)3))10 is : (A)  1: 4(16)(1/3) (B)  1: 2 (6)(1/3) (C)  2(36)(1/3): 1  (D)  4(36)(1/3): 1

Tardigrade Admin · Accepted Answer

(T5/T51) = (10C4(21/3)10-4 ( (1/2(3)1/3))4/10C4 ((1)2(3)1/3)10-4(21/3)4) = 4.(36)1/3

Q. A ratio of the $5^{t h}$ term from the beginning to the $5^{t h}$ term from the end in the binomial expansion of $(2^{\frac{1}{3}} + \frac{1}{2 ( 3 ) ^{\frac{1}{3}}})^{10}$ is :

$1 : 4 (16)^{\frac{1}{3}}$

$1 : 2 (6)^{\frac{1}{3}}$

$2 (36)^{\frac{1}{3}} : 1$

$4 (36)^{\frac{1}{3}} : 1$

$\frac{T _{5}}{T _{5}^{1}} = \frac{^{10} C _{4} ( 2 ^{1/3} ) ^{10 - 4} ( \frac{1}{2 ( 3 ) ^{1/3}} ) ^{4}}{^{10} C _{4} ( \frac{1}{2 ( 3 ) ^{1/3}} ) ^{10 - 4} ( 2 ^{1/3} ) ^{4}} = 4. (36)^{1/3}$

Q. A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of (231​+2(3)31​1​)10 is :

1:4(16)31​

1:2(6)31​

2(36)31​:1

4(36)31​:1