← All papers
2025 Paper 1
- Q1a Bases and dimension; coordinates in a basis 10 marks Linear Algebra · asked 7× in 13 yrs
- Q1b Rank and nullity; rank-nullity theorem 10 marks Linear Algebra · asked 7× in 13 yrs
- Q1c Maxima and minima of single-variable functions 10 marks Calculus · asked 7× in 13 yrs
- Q1d Differentiability 10 marks Calculus · asked 3× in 13 yrs
- Q1e Cone 10 marks Analytic Geometry · asked 14× in 13 yrs
- Q2a Matrix of a linear transformation 15 marks Linear Algebra · asked 10× in 13 yrs
- Q2b Mean-value theorems (Rolle, Lagrange, Cauchy) 15 marks Calculus · asked 3× in 13 yrs
- Q2c-i Cylinder 10 marks Analytic Geometry · asked 4× in 13 yrs
- Q2c-ii Shortest distance between two skew lines 10 marks Analytic Geometry · asked 4× in 13 yrs
- Q3a Row and Column Reduction; Echelon Form 15 marks Linear Algebra
- Q3b Sphere 15 marks Analytic Geometry · asked 17× in 13 yrs
- Q3c-i Double integrals 10 marks Calculus · asked 10× in 13 yrs
- Q3c-ii Partial derivatives 10 marks Calculus · asked 8× in 13 yrs
- Q4a Sphere 15 marks Analytic Geometry · asked 17× in 13 yrs
- Q4b Partial derivatives 15 marks Calculus · asked 8× in 13 yrs
- Q4c-i Eigenvalues and eigenvectors 12 marks Linear Algebra · asked 9× in 13 yrs
- Q4c-ii Quotient Vector Space V/W 8 marks Linear Algebra
- Q5a First-order higher-degree ODEs 10 marks ODEs · asked 5× in 13 yrs
- Q5b Formulation of differential equations 10 marks ODEs · asked 2× in 13 yrs
- Q5c Central force motion and Kepler's laws 10 marks Dynamics & Statics · asked 6× in 13 yrs
- Q5d Common catenary 10 marks Dynamics & Statics · asked 4× in 13 yrs
- Q5e Gradient: definition, geometric meaning, computation 10 marks Vector Analysis · asked 6× in 13 yrs
- Q6a Properties of Laplace transform (linearity, shift, derivative, convolution) 15 marks ODEs · asked 3× in 13 yrs
- Q6b Simple harmonic motion (free, damped, forced) 15 marks Dynamics & Statics · asked 8× in 13 yrs
- Q6c-i Gradient: definition, geometric meaning, computation 10 marks Vector Analysis · asked 6× in 13 yrs
- Q6c-ii Vector identities (curl of grad, div of curl, product rules) 10 marks Vector Analysis · asked 3× in 13 yrs
- Q7a Stability of equilibrium (energy criterion) 15 marks Dynamics & Statics · asked 5× in 13 yrs
- Q7b Line integrals 15 marks Vector Analysis · asked 8× in 13 yrs
- Q7c-i First-order higher-degree ODEs 10 marks ODEs · asked 5× in 13 yrs
- Q7c-ii Euler-Cauchy equation 10 marks ODEs · asked 8× in 13 yrs
- Q8a Method of variation of parameters 15 marks ODEs · asked 11× in 13 yrs
- Q8b Gauss divergence theorem 15 marks Vector Analysis · asked 9× in 13 yrs
- Q8c Constrained motion 20 marks Dynamics & Statics · asked 7× in 13 yrs