JKBOSE Class 12 Mathematics

The Full 50 Question Masterlist

Complete Your Preparation: ➜ Class 12 Physics ➜ Class 12 Chemistry

Matrices & Determinants

Weightage: ~13 Marks | Focus: Matrix Method

Matrix Method: Solve the system of linear equations:
$$3x – 2y + 3z = 8$$ $$2x + y – z = 1$$ $$4x – 3y + 2z = 4$$
6 Marks Guaranteed
If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$, show that $A^2 – 5A + 7I = 0$. Find $A^{-1}$.
Using properties of determinants, prove that:
$$\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix} = abc(1 + \frac{1}{a} + \frac{1}{b} + \frac{1}{c})$$

Weightage: ~44 Marks | The King Section

Find $k$ so that $f(x)$ is continuous at $x = \frac{\pi}{2}$:
$$f(x) = \begin{cases} \frac{k \cos x}{\pi – 2x}, & x \neq \frac{\pi}{2} \\ 3, & x = \frac{\pi}{2} \end{cases}$$
Logarithmic Differentiation: Find $\frac{dy}{dx}$ if $x^y + y^x = 1$.
Definite Integrals: Evaluate using properties:
$$\int_0^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} dx$$
6 Marks
Area Under Curve: Find the area bounded by the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$.

Weightage: ~17 Marks | High Yield

Shortest Distance: Find the distance between lines:
$$\vec{r} = (\hat{i} + 2\hat{j} + \hat{k}) + \lambda(\hat{i} – \hat{j} + \hat{k})$$ $$\vec{r} = (2\hat{i} – \hat{j} – \hat{k}) + \mu(2\hat{i} + \hat{j} + 2\hat{k})$$
6 Marks
Find the unit vector perpendicular to both $\vec{a} + \vec{b}$ and $\vec{a} – \vec{b}$.
Find the equation of the plane passing through the intersection of two planes and a given point.

Weightage: ~16 Marks

LPP Graphical: Maximize $Z = 4x + y$ subject to $x + y \leq 50, 3x + y \leq 90$.
Bayes’ Theorem: Bag I has 3 red/4 black balls, Bag II has 5 red/6 black. If a drawn ball is red, find the probability it came from Bag II. 6 Marks

1. Integration: Always try to apply the property $\int_0^a f(x)dx = \int_0^a f(a-x)dx$ first. It solves most board-level questions.

2. Matrices: Double-check your Adjoint calculations. One sign mistake leads to zero marks in the final $A^{-1}$ result.

3. 3D Geometry: Memorize the formula for Shortest Distance; it is a guaranteed 6-mark visitor every year.