Select the option that is true regarding the following labelled Assertion (A) and Reason (R).

Assertion (A)	Reason (R)
The value of ​$$\frac{\left[(3.9)^3+9 \times 1.3 \times 4.29+11.7 \times(1.1)^2+1.331\right]}{[1.23 \times 1.23+0.77(0.77+0.6 \times 4.1)]}$$​​ Is 31.25.	Using $$(a+b)^3=$$ $$\begin{aligned}& a^3+b^3+3 a b(a+b) \text { and } \\& (x+y)^2=x^2+y^2+2 x y\end{aligned}$$​​

Correct option is D

Given:

​$$\textbf{Assertion (A):} \\\frac{(3.9)^3 + 9 \times 1.3 \times 4.29 + 11.7 \times (1.1)^2 + 1.331}{1.23 \times 1.23 + 0.77 \left(0.77 + 0.6 \times 4.1\right)} = 31.25 \\\ \\\textbf{Formula:} \\(a + b)^3 = a^3 + b^3 + 3ab(a + b) \\(x + y)^2 = x^2 + y^2 + 2xy \\\ \\\textbf{Solution:} \\\text{Let } a = 3.9, \quad b = 1.1 \Rightarrow a + b = 5 \\(a + b)^3 = (3.9 + 1.1)^3 = 5^3 = 125 \\\ \\\text{So the numerator becomes: } a^3 + b^3 + 3ab(a + b) = 125 \\\text{Let } x = 1.23, \quad y = 0.77 \Rightarrow x + y = 2 \\\ \\(x + y)^2 = x^2 + y^2 + 2xy = 2^2 = 4 \\\ \\\text{So the denominator becomes: } x^2 + y^2 + 2xy = 4 \\\ \\\textbf{Final Value: } \frac{125}{4} = 31.25 \\$$

Conclusion:

• Assertion is TRUE.
• Reason is TRUE.
• Reason is a correct explanation — because both the numerator and denominator use the identities given in Reason.

Final Answer: (d) Both A and R are true and R is the correct explanation of A.

​