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If $x_{1}, x_{2}, x_{3}, \dots, x_{13}$ are in A.P. then the value of $|\begin{array}{ccc} e^{x_{1}} & e^{x_{4}} & e^{x_{7}} \\ e^{x_{4}} & e^{x_{7}} & e^{x_{10}} \\ e^{x_{7}} & e^{x_{10}} & e^{x_{13}} \end{array}|$ is

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Correct option is B

Taking ex 1 common from R1, ex4 common from R2 and ex7 from R3, we get Δ=ex1+x4+x7Δ1where Δ1=1e3de6d1e3de6d1e3de6d=0where d is common difference of A.P. ∴Δ=0

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If x1,x2,x3,…,x13 are in A.P. then the value of ex1ex4ex7ex4ex7ex10ex7ex10ex13 is

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If $x_{1}, x_{2}, x_{3}, \dots, x_{13}$ are in A.P. then the value of $|\begin{array}{ccc} e^{x_{1}} & e^{x_{4}} & e^{x_{7}} \\ e^{x_{4}} & e^{x_{7}} & e^{x_{10}} \\ e^{x_{7}} & e^{x_{10}} & e^{x_{13}} \end{array}|$ is