Question:
If the numerically greatest term in the expansion of \( (2 - 3x)^9 \) when \( x = 1 \) is \( P_1^q P_2^r P_3^s P_4^t \) (where \( P_1 < P_2 < P_3 < P_4 \) are the first four prime numbers), then \( \alpha + \beta + \gamma + \delta = \):
If the numerically greatest term in the expansion of \( (2 - 3x)^9 \) when \( x = 1 \) is \( P_1^q P_2^r P_3^s P_4^t \) (where \( P_1 < P_2 < P_3 < P_4 \) are the first four prime numbers), then \( \alpha + \beta + \gamma + \delta = \):
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To find the greatest term in a binomial expansion, examine the coefficients and identify the one with the largest magnitude.
Updated On: May 15, 2025
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The Correct Option is A
Solution and Explanation
We are asked to find the sum \( \alpha + \beta + \gamma + \delta \) for the numerically greatest term in the expansion of \( (2 - 3x)^9 \). Use the binomial expansion to find the greatest term for \( x = 1 \), and calculate the sum as instructed in the problem.
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