Mathematics (B.Arch.): Calculus, Coordinate Geometry and 3D Vectors
The Mathematics section of JEE Main Paper 2A carries 25 questions - 20 MCQs and 5 numerical-value questions - for 100 marks. The NTA syllabus tracks Class 11–12 core mathematics, with a strong B.Arch slant toward coordinate geometry, 3D geometry, vectors and calculus.
High-yield blocks
- Coordinate geometry: straight lines, circles, parabola, ellipse, hyperbola; focus-directrix and eccentricity conditions.
- 3D geometry: direction cosines, line and plane equations, angle between line and plane, shortest distance.
- Vectors: dot and cross products, scalar triple product, coplanarity, area and volume.
- Calculus: limits, continuity, differentiability, tangents/normals, maxima-minima, definite integrals, differential equations.
- Algebra and probability: matrices/determinants, binomial, sequences, permutations/combinations, conditional probability.
Worked example
Find the plane through A(1,2,3), B(2,0,1), C(3,1,0). Take AB=(1,−2,−2) and AC=(2,−1,−3). The normal is AB×AC = (4,−1,3). Using A: 4(x−1) −1(y−2) +3(z−3)=0, so 4x − y + 3z − 11 = 0. Check B: 8−0+3−11=0. Check C: 12−1+0−11=0. The cross product is the key step: it produces a vector perpendicular to both direction vectors, hence normal to the plane.
Traps
A plane needs a point and a normal, not two points. In a cross product, a sign slip in the j-component changes the answer; write the determinant with the middle term negated. For conics, check eccentricity before choosing a formula: e=1 parabola, e<1 ellipse, e>1 hyperbola. In definite integrals, reversing limits changes the sign; in probability without replacement, update the denominator. Numerical-value answers should be entered as positive decimals/integers as instructed - do not add units.