सही विकल्प: A

1² + 3² + 5² + ....... + 19² = (1² + 2² + 3² + 4² + ..... + 18² + 19²) - (2² + 4² + ... 18²)

Use the formula given in the question ,
1² + 2² + 3² + ........ + a² = a(a + 1)(2a + 1) ÷ 6

1² + 3² + 5² + ....... + 19² = 19(19 + 1)(38 + 1) ÷ 6 - 4(1² + 2² + 3² + ..... + 9²)
1² + 3² + 5² + ....... + 19² = 19 x 20 x 39 ÷ 6 - 4 x 9 x 10 x 19 ÷ 6
1² + 3² + 5² + ....... + 19² = 2470 - 1140 = 1330