JEE Main 2019 Mathematics question
Let be in G.P. with for i = 1, 2, …, 10 and S be the set of pairs (r, k), r, k ∈ N (the set of natural numbers) for which \begin{vmatrix}\log_ea_1^ra_2^k & \log_ea_2^ra_3^k & \log_ea_3^ra_4^k\\ \log_ea_4^ra_5^k & \log_ea_5^ra_6^k & \log_ea_6^ra_7^k\\ \log_ea_7^ra_8^k & \log_ea_8^ra_9^k & \log_ea_9^ra_{10}^k\end{vmatrix} = 0. Then the number of elements in S, is:
Answer: (D)
Solution
Entries are in A.P. along rows and columns, so and the determinant is 0 for all r, k.