CBSE Class 12 Mathematics contains zero fluff; every mark corresponds to an explicit algebraic step.
1. Maxima and Minima Word Problems (5 Marks)
Draw the geometric figure, express the quantity to be optimized in terms of a single variable using constraints, calculate $\frac{dy}{dx} = 0$, and prove the second derivative condition ($\frac{d^2y}{dx^2} < 0$ for maximum, $> 0$ for minimum). Skipping the second derivative test costs 1 full mark.
2. Matrix Method for System of Equations
Writing $AX = B \implies X = A^{-1}B$. Calculate $|A|$ first; if $|A| = 0$, test $(\text{adj } A)B$. If $|A| \neq 0$, calculate all 9 cofactors systematically to construct $\text{adj } A$.
