JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

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Analyzing +4 | -1

Let

a_1, a_2, a_3, \ldots, a_{10}

be in G.P. with

a_i>0

for

i=1,2,3, \ldots, 10

and

S

be the set of pairs

(r, k), r, k \in N

for which

D=\left|\begin{array}{lll}\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{array}\right|=0

Then the number of elements in

S

, is

View answer and explanation

Correct option: A

Infinity many

Option A (Infinity many) is correct because the determinant D is always zero for all values of r and k, making the set S infinitely large.

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