List of top Mathematics Questions asked in Kerala Plus Two(Class 12)

Express the matrix $A = \begin{bmatrix} 2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3 \end{bmatrix}$ as a sum of symmetric and skew-symmetric matrices.
Find the shortest distance between the lines $\vec{r} = (\hat{i} + 2\hat{j} + 3\hat{k}) + \lambda(\hat{i} - 3\hat{j} + 2\hat{k})$ and $\vec{r} = (4\hat{i} + 5\hat{j} + 6\hat{k}) + \mu(2\hat{i} + 3\hat{j} + \hat{k})$.
Evaluate $\displaystyle \int \frac{dx}{\sqrt{x^2 + 2x + 2}}$.
Solve the differential equation $\displaystyle \frac{dy}{dx} + \frac{y}{x} = x^2$.
If $P(E) = 0.6$, $P(F) = 0.3$ and $P(E \cap F) = 0.2$, find $P(E|F)$ and $P(F|E)$.
Find the area of the region bounded by the curve $y^2 = x$ and the lines $x = 1$, $x = 4$ and the $x$-axis.
Prove that the function $f(x) = |x|$ is continuous but not differentiable at $x = 0$.
Solve the LPP graphically: Minimize $Z = 5x + 10y$ subject to $x + 2y \le 120$, $x + y \ge 60$, $x, y \ge 0$.