<p>Fifth term of a G.P. is 2, then the product of its 9 terms is</p>
Step-by-Step Solution
Key Concept: In a G.P., the product of 9 terms equals the 5th term raised to the 9th power, since the 5th term is the middle term.
<p><strong>Step 1:</strong> In a G.P., if \(a_5 = 2\), then \(ar^4 = 2\) where \(a\) is the first term and \(r\) is the common ratio.</p><p><strong>Step 2:</strong> The product of 9 terms of a G.P. is: \(P = a_1 \cdot a_2 \cdot a_3 \cdots a_9\)</p><p><strong>Step 3:</strong> Using the property that in a G.P., \(a_i \cdot a_{10-i} = (a_5)^2\) (terms equidistant from the middle), the product of 9 terms is: \(P = (a_5)^9 = 2^9 = 512\)</p><p>∴ Answer is B.</p>
Correct Answer: B