SSC MTS 6 Feb 2026 Shift 3 Paper

Concept:The sum of squares of natural numbers from 1 to n is given by the formula $S_n = \frac{n(n+1)(2n+1)}{6}$. To find the sum from 11² to 45², subtract the sum from 1² to 10² from the sum from 1² to 45².Explanation:First, compute the sum of squares from 1 to 45 using the formula:$S_{45} = \frac{45 \times (45+1) \times (2 \times 45 + 1)}{6} = \frac{45 \times 46 \times 91}{6}$.Simplify: $45 \div 3 = 15$, $46 \div 2 = 23$, so $15 \times 23 \times 91 = 31395$.Next, compute the sum of squares from 1 to 10:$S_{10} = \frac{10 \times (10+1) \times (2 \times 10 + 1)}{6} = \frac{10 \times 11 \times 21}{6}$.Simplify: $10 \div 2 = 5$, $21 \div 3 = 7$, so $5 \times 11 \times 7 = 385$.Now subtract: required sum = $31395 - 385 = 31010$.Answer:$31010$ (Option D)