Matrices & Determinants
Matrices And Determinants
nta_abhyas_2025
Grade 12
Question:
Let $pq^3 + q q^3 + r z^2 + xz + t = \begin{vmatrix} x^2+3x-1 & x+3 \\ 2x & -2x & -4 \\ 3 & x & 3 \end{vmatrix}$ be an identity, where $p, q, r, s$ and $t$ are constants, then the value of $s$ is equal to
Step-by-Step Solution
Key Concept: Use implicit differentiation to find derivatives when variables are mixed in an equation.
Differentiating the given equation $4y^3 + 3x^2 + 2xy + x = \ldots$ with respect to $x$, we apply implicit differentiation to find $\frac{dy}{dx}$. Setting $\frac{dy}{dx} = 0$ and substituting values gives us critical information. Substituting $x = 1$ and solving yields $s = 64 - 3 + 10 = 71$.
Correct Answer: 71