Relations, Functions & ITF

1. Equivalence Relation proofs (Reflexive, Symmetric, Transitive).
2. Bijective functions: Proving \(f(x)\) is one-one and onto.
3. Principal value branch of Inverse Trig Functions.
4. ITF Simplification:
   \(\tan^{-1}\left(\frac{\cos x}{1-\sin x}\right)\)

Matrices & Determinants

1. Matrix Method: Solving 3-variable linear equations. 5 Marks
2. Properties of Determinants (proving identities).
3. Inverse of a matrix using Adjoint method.
4. Finding the area of a triangle using determinants.

Calculus (Part I & II)

Weightage: ~35 Marks | High Priority

1. Continuity: Finding unknown \(k\) at a point.
2. Parametric Differentiation: \(\frac{dy}{dx}\) for functions of \(t\) or \(\theta\).
3. Maxima & Minima: Applied word problems (Cylinder/Sphere). Case Study
4. Definite Integrals: Properties like:
   \[\int_0^a f(x)dx = \int_0^a f(a-x)dx\]
5. Area Under Curve: Area between two parabolas or a circle and line. 5 Marks
6. Differential Equations: Integrating Factor (I.F.) and Homogeneous forms.

Vectors & 3D Geometry

1. Scalar Triple Product and Projection of vectors.
2. Shortest Distance: Between two skew lines. Guaranteed
3. Equation of a plane passing through three non-collinear points.
4. Angle between a line and a plane.

LPP & Probability

1. LPP Graphical: Feasible region and optimal solution. 5 Marks
2. Bayes’ Theorem: Inverse probability problems. Case Study
3. Probability distribution and Mean of a random variable.