Question

Numerically greatest term in the expansion of \( (5 + 3x)^6 \), when \( x = 1 \), is:

• A. \( 3^5 \times 5^3 \)
• B. \( 3^3 \times 5^5 \)
• C. \( 3^2 \times 5^5 \)
• D. \( 3^4 \times 5^4 \)

Hint:

For binomial expansions, to find the greatest term, evaluate the terms for different values of \( r \) and check which one gives the highest value.

Answer 1

The Correct Option is B

We need to find the numerically greatest term in the expansion of \( (5 + 3x)^6 \). The general term in the binomial expansion of \( (5 + 3x)^6 \) is: \( T_r = \binom{6}{r} 5^{6-r} (3x)^r \) 

Step 1: Substitute \( x = 1 \) into the general term: \( T_r = \binom{6}{r} 5^{6-r} 3^r \) 

Step 2: The term will be greatest when the powers of 3 and 5 are balanced. After solving, the greatest term occurs when \( r = 3 \), and the value is \( 3^3 \times 5^5 \).