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UPTET Paper 2 Math and Science Model Test 1

Section: Mathematics and Science

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Question : 96 of 150

Marks: +1, -0

(1^{2}+2^{2}+3^{2}+.....+10^{2})=?

330
345
365
385

Solution:

Concept:

The sum of squares of the first n natural numbers can be calculated using a standard formula.

Explanation:

Use the formula:

\text{Sum} = \frac{n(n+1)(2n+1)}{6}

Here,

n = 10

.

Substitute the values:

\text{Sum} = \frac{10 \times (10+1) \times (2 \times 10 + 1)}{6}

Simplify inside:

10 \times 11 \times 21

Multiply:

10 \times 11 = 110

and

110 \times 21 = 2310

Divide by 6:

2310 \div 6 = 385

Answer:

Option D, 385

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