Question

Find the sum of first 90 even natural numbers.

• A. \(8180\)
• B. \(8190\)
• C. \(9180\)
• D. \(8100\)
• E. \(8150\)

Answer 1

The Correct Option is B

Concept: Sum of first \(n\) even natural numbers: \[ 2 + 4 + 6 + \cdots + 2n = n(n+1) \]
Step 1: Identify \(n\).
\[ n = 90 \]
Step 2: Apply formula.
\[ \text{Sum} = n(n+1) = 90 \times 91 \]
Step 3: Calculate.
\[ 90 \times 91 = 8190 \]
Step 4: Option analysis.

• (A) 8180: Incorrect calculation $\times$
• (B) 8190: Correct \checkmark
• (C) 9180: Wrong multiplication $\times$
• (D) 8100: Missing extra term $\times$
• (E) 8150: Incorrect result $\times$

Conclusion:
Thus, the correct answer is
Option (B).