Let a1- a2- a3- a10 be in G-P- with a1 - 0 for i - 1- 2-10 and S be the set of pairs r- k- r k - N the set of natural numbers for which loge a1r a2k loge a2r a3k loge a3r a4k loge a4r a5k loge a5r a6k loge a6r a7k loge a7r a8k loge a8r a9k loge a9r a10k -0Then the number of elements in S- is -

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Byju's Answer

Standard XII

Mathematics

Definition of Relations

Let a1, a2,...

Question

Let $a_{1}, a_{2}, a_{3}, . . . ., a_{10}$ be in G.P. with $a_{1} > 0$ for $i = 1, 2, . . .10$ and $S$ be the set of pairs $(r, k), r k \in N$ (the set of natural numbers) for which
$∣ ∣ ∣ ∣ ∣ \begin{matrix} {log}_{e} a_{1}^{r} a_{2}^{k} & {log}_{e} a_{2}^{r} a_{3}^{k} & {log}_{e} a_{3}^{r} a_{4}^{k} {log}_{e} a_{4}^{r} a_{5}^{k} & {log}_{e} a_{5}^{r} a_{6}^{k} & {log}_{e} a_{6}^{r} a_{7}^{k} {log}_{e} a_{7}^{r} a_{8}^{k} & {log}_{e} a_{8}^{r} a_{9}^{k} & {log}_{e} a_{9}^{r} a_{10}^{k} \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0$
Then the number of elements in $S$ , is :

Infinitely many

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Solution

The correct option is A Infinitely many

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