If 3x-2y=10 and xy=11, the value of $$27x^3-8y^3$$​ is

Correct option is A

Given:
3x - 2y = 10 and xy=11

Formula used:
​$$(a - b)^3 = a^3 - b^3 - 3ab(a - b) \\$$​​
Solution: 
​$$3x - 2y = 10 \\\text{Taking a cube on both sides of the above equation:} \\(3x - 2y)^3 = 10^3 \\27x^3 - 8y^3 - 3(3x)(2y)(3x - 2y) = 1000 \\27x^3 - 8y^3 - 18(xy)(3x - 2y) = 1000 \\\text{Substitute: } 3x - 2y = 10, \, xy = 11 \\27x^3 - 8y^3 - 18 \cdot 11 \cdot 10 = 1000 \\27x^3 - 8y^3 - 1980 = 1000 \\27x^3 - 8y^3 = 1980 + 1000 \\27x^3 - 8y^3 = 2980 \\\textbf{Hence, the value of } 27x^3 - 8y^3 \text{ is } 2980.$$​​