Question

If \(x_{1}, x_{2}, x_{3}, x_{4}\) are in GP, then we subtract 2, 4, 7, 8 from \(x_{1}, x_{2}, x_{3}, x_{4}\) respectively, then the resultant numbers are in AP, then the value of \(\frac{1}{24}\left(x_{1} \cdot x_{2} \cdot x_{3} \cdot x_{4}\right)\) is

(1) \(\frac{2^{4}}{3^{8}}\)

(2) \(\frac{2^{3}}{3^{9}}\)

(3) \(\frac{2}{3^{9}}\)

(4) \(\frac{2}{3^{8}}\)  

Answer 1

Correct option is: (2) \(\frac{2^{3}}{3^{9}}\)  

\(=\frac{1}{24} \times\left(\frac{1}{9}\right)^{4} \times(-2)^{6}\)

\(=\frac{2^{3}}{3^{9}}\)