ISC Class 12 Mathematics Important Topics 2027
Last updated:
Every topic ranked by how often and how recently it was asked in 4 board + 5 official sample papers (2023–2027). Teal tags = board papers, orange tags = official sample papers.
Top 10 most important topics
| # | Topic | Chapter | Asked in | Importance |
|---|---|---|---|---|
| 1 | homogeneous differential equation | Differential Equations | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026Sample 2027 | ★★★★★ |
| 2 | solve system using matrix method | Determinants | Board 2024Board 2026Sample 2024Sample 2025Sample 2026Sample 2027 | ★★★★★ |
| 3 | second order derivatives, prove relation | Continuity, Differentiability and Differentiation | Board 2023Board 2024Board 2025Board 2026Sample 2023Sample 2025Sample 2026 | ★★★★☆ |
| 4 | definite integral using property | Integrals | Board 2024Board 2025Board 2026Sample 2023Sample 2026 | ★★★★☆ |
| 5 | Bayes theorem | Probability | Board 2023Board 2024Board 2025Sample 2023Sample 2026Sample 2027 | ★★★★☆ |
| 6 | related rates of change | Applications of Derivatives | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2027 | ★★★★☆ |
| 7 | sum formula of tan-inverse | Inverse Trigonometric Functions | Board 2023Sample 2025Sample 2026Sample 2027 | ★★★☆☆ |
| 8 | probability distribution and expectation | Probability | Board 2024Sample 2024Sample 2025Sample 2026 | ★★★☆☆ |
| 9 | definite integral of modulus function | Integrals | Board 2023Board 2024Board 2026Sample 2023Sample 2024 | ★★★☆☆ |
| 10 | classify a relation | Relations and Functions | Sample 2024Sample 2025Sample 2026 | ★★☆☆☆ |
Chapter-wise important topics
Relations and Functions · Relations and Functions
| classify a relation asked 3× | Sample 2024Sample 2025Sample 2026 | ★★☆☆☆ |
| properties of a relation asked 2× | Board 2024Sample 2027 | ★★☆☆☆ |
| finding inverse of a function asked 3× | Board 2023Board 2024Board 2026 | ★★☆☆☆ |
| smallest equivalence relation asked 2× | Board 2025Sample 2023 | ★☆☆☆☆ |
| graph of a function and its inverse asked 1× | Sample 2027 | ★☆☆☆☆ |
| domain, invertibility, inverse function asked 1× | Sample 2027 | ★☆☆☆☆ |
| symmetric relation and its inverse asked 1× | Sample 2026 | ★☆☆☆☆ |
| many-one function from a graph asked 1× | Sample 2026 | ★☆☆☆☆ |
| proving one-one and onto asked 2× | Board 2023Board 2024 | ★☆☆☆☆ |
| intersection/union of equivalence relations asked 1× | Sample 2025 | ★☆☆☆☆ |
| onto function from a graph asked 1× | Sample 2025 | ★☆☆☆☆ |
| one-one and onto over different domains asked 1× | Sample 2024 | ★☆☆☆☆ |
| condition for invertibility asked 1× | Sample 2024 | ★☆☆☆☆ |
| number of bijections between sets asked 1× | Board 2026 | ★☆☆☆☆ |
| symmetry of a relation asked 1× | Board 2026 | ★☆☆☆☆ |
| range of a function asked 1× | Board 2026 | ★☆☆☆☆ |
| equivalence relation check asked 1× | Sample 2023 | ★☆☆☆☆ |
| one-one and onto classification asked 1× | Sample 2023 | ★☆☆☆☆ |
| inverse function, domain and range asked 1× | Sample 2023 | ★☆☆☆☆ |
| existence of one-one functions asked 1× | Board 2025 | ★☆☆☆☆ |
| identity vs reflexive relation asked 1× | Board 2024 | ★☆☆☆☆ |
| vertical line test for a function asked 1× | Board 2024 | ★☆☆☆☆ |
| reflexive/symmetric/transitive check asked 1× | Board 2023 | ★☆☆☆☆ |
| domain of inverse function equals range asked 1× | Board 2023 | ★☆☆☆☆ |
Inverse Trigonometric Functions · Relations and Functions
| sum formula of tan-inverse asked 4× | Board 2023Sample 2025Sample 2026Sample 2027 | ★★★☆☆ |
| solving inverse trig equation asked 3× | Board 2024Sample 2025Sample 2026 | ★★☆☆☆ |
| range of inverse trig expression asked 1× | Sample 2027 | ★☆☆☆☆ |
| complementary inverse identity, equal roots asked 1× | Sample 2027 | ★☆☆☆☆ |
| principal values of inverse trig functions asked 2× | Board 2024Sample 2023 | ★☆☆☆☆ |
| complementary inverse trig identity asked 1× | Sample 2026 | ★☆☆☆☆ |
| identity tan-inverse plus cot-inverse asked 2× | Board 2023Board 2025 | ★☆☆☆☆ |
| range condition for inverse tan equation asked 1× | Sample 2025 | ★☆☆☆☆ |
| evaluate trig of inverse-trig expression asked 1× | Sample 2024 | ★☆☆☆☆ |
| domain of inverse trig function asked 1× | Sample 2024 | ★☆☆☆☆ |
| composition of inverse trig functions asked 1× | Sample 2024 | ★☆☆☆☆ |
| principal value branch identities asked 1× | Board 2026 | ★☆☆☆☆ |
| principal value of inverse secant asked 1× | Board 2026 | ★☆☆☆☆ |
| inverse trig substitution and proof asked 1× | Board 2026 | ★☆☆☆☆ |
| sum of inverse functions, solve asked 1× | Board 2026 | ★☆☆☆☆ |
| sum of inverse cosines, prove identity asked 1× | Sample 2023 | ★☆☆☆☆ |
| graph, domain/range, identities, evaluation asked 1× | Board 2025 | ★☆☆☆☆ |
| sum of inverse sines, prove identity asked 1× | Board 2024 | ★☆☆☆☆ |
Matrices · Algebra
| matrix multiplication application asked 2× | Board 2025Sample 2027 | ★★☆☆☆ |
| non-commutativity of matrix multiplication asked 1× | Sample 2027 | ★☆☆☆☆ |
| product of non-singular and matrix equals zero asked 1× | Sample 2026 | ★☆☆☆☆ |
| power of a scalar matrix asked 1× | Sample 2026 | ★☆☆☆☆ |
| skew-symmetric matrix condition asked 2× | Board 2023Board 2025 | ★☆☆☆☆ |
| symmetric and skew-symmetric matrix asked 1× | Sample 2025 | ★☆☆☆☆ |
| transpose and matrix operations asked 1× | Sample 2024 | ★☆☆☆☆ |
| symmetric matrix condition asked 1× | Sample 2024 | ★☆☆☆☆ |
| counting matrices with restricted entries asked 1× | Board 2026 | ★☆☆☆☆ |
| power of a triangular matrix asked 1× | Sample 2023 | ★☆☆☆☆ |
| decomposition into symmetric and skew-symmetric asked 1× | Sample 2023 | ★☆☆☆☆ |
| powers of a nilpotent matrix asked 1× | Board 2025 | ★☆☆☆☆ |
| inverse of matrix powers and determinant of inverse asked 1× | Board 2025 | ★☆☆☆☆ |
| commuting matrices and powers asked 1× | Board 2024 | ★☆☆☆☆ |
| symmetric/skew-symmetric matrix property asked 1× | Board 2024 | ★☆☆☆☆ |
Determinants · Algebra
| solve system using matrix method asked 6× | Board 2024Board 2026Sample 2024Sample 2025Sample 2026Sample 2027 | ★★★★★ |
| scalar multiplication of rows/columns asked 2× | Sample 2025Sample 2026 | ★★☆☆☆ |
| determinant of cofactor matrix asked 2× | Sample 2025Sample 2026 | ★★☆☆☆ |
| properties of determinants, factorization asked 2× | Board 2025Sample 2027 | ★★☆☆☆ |
| properties of determinants asked 3× | Board 2023Board 2024Board 2026 | ★★☆☆☆ |
| area of triangle using determinant asked 1× | Sample 2027 | ★☆☆☆☆ |
| skew-symmetric matrix of odd order is singular asked 1× | Sample 2025 | ★☆☆☆☆ |
| addition and scalar multiple of determinants asked 1× | Sample 2024 | ★☆☆☆☆ |
| skew-symmetric of odd order is singular asked 1× | Sample 2024 | ★☆☆☆☆ |
| determinant of scalar multiple asked 1× | Board 2026 | ★☆☆☆☆ |
| unique solution and non-singular matrix asked 1× | Board 2026 | ★☆☆☆☆ |
| solve equation from determinant expansion asked 1× | Board 2026 | ★☆☆☆☆ |
| A(adj A) = |A| I property asked 1× | Sample 2023 | ★☆☆☆☆ |
| row operations and splitting determinants asked 1× | Sample 2023 | ★☆☆☆☆ |
| inverse of matrix, solve system asked 1× | Sample 2023 | ★☆☆☆☆ |
| condition for unique solution of a system asked 1× | Board 2025 | ★☆☆☆☆ |
| determinant of scalar multiple of matrix asked 1× | Board 2023 | ★☆☆☆☆ |
| solve system using matrix inverse method asked 1× | Board 2023 | ★☆☆☆☆ |
Continuity, Differentiability and Differentiation · Calculus
| second order derivatives, prove relation asked 7× | Board 2023Board 2024Board 2025Board 2026Sample 2023Sample 2025Sample 2026 | ★★★★☆ |
| implicit differentiation asked 2× | Sample 2023Sample 2026 | ★★☆☆☆ |
| differentiability, find constants asked 1× | Sample 2027 | ★☆☆☆☆ |
| removable discontinuity and non-differentiability from graph asked 1× | Sample 2027 | ★☆☆☆☆ |
| chain rule, second order derivative change of variable asked 1× | Sample 2027 | ★☆☆☆☆ |
| differentiation of log and inverse trig, monotonicity asked 1× | Sample 2027 | ★☆☆☆☆ |
| continuity vs differentiability asked 1× | Sample 2026 | ★☆☆☆☆ |
| derivative at a point, find constant asked 1× | Sample 2026 | ★☆☆☆☆ |
| implicit/logarithmic differentiation asked 1× | Sample 2026 | ★☆☆☆☆ |
| continuity at a point, find constant asked 2× | Board 2023Board 2024 | ★☆☆☆☆ |
| continuity vs differentiability at a point asked 1× | Sample 2025 | ★☆☆☆☆ |
| derivative of modulus function asked 1× | Sample 2025 | ★☆☆☆☆ |
| logarithmic differentiation asked 1× | Sample 2025 | ★☆☆☆☆ |
| continuity interpretation from graphs asked 1× | Sample 2024 | ★☆☆☆☆ |
| continuity and differentiability from a graph asked 1× | Sample 2024 | ★☆☆☆☆ |
| chain rule from a table of values asked 1× | Sample 2024 | ★☆☆☆☆ |
| continuity and differentiability, find constants asked 1× | Sample 2024 | ★☆☆☆☆ |
| parametric differentiation, second order asked 1× | Sample 2024 | ★☆☆☆☆ |
| continuity and differentiability of log function asked 1× | Board 2026 | ★☆☆☆☆ |
| differentiability at a corner point asked 1× | Board 2026 | ★☆☆☆☆ |
| differentiation of infinite exponential asked 1× | Board 2026 | ★☆☆☆☆ |
| implicit differentiation of inverse trig relation asked 1× | Sample 2023 | ★☆☆☆☆ |
| points of discontinuity of rational function asked 1× | Sample 2023 | ★☆☆☆☆ |
| points of discontinuity of piecewise function asked 1× | Board 2025 | ★☆☆☆☆ |
| logarithmic/implicit differentiation asked 1× | Board 2025 | ★☆☆☆☆ |
| differentiation of inverse trig after substitution asked 1× | Board 2025 | ★☆☆☆☆ |
| points of non-differentiability from a graph asked 1× | Board 2024 | ★☆☆☆☆ |
| derivative of standard functions asked 1× | Board 2024 | ★☆☆☆☆ |
| differentiation of a function w.r.t. another function asked 1× | Board 2023 | ★☆☆☆☆ |
Applications of Derivatives · Calculus
| related rates of change asked 6× | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2027 | ★★★★☆ |
| minimization of surface area asked 2× | Sample 2025Sample 2026 | ★★☆☆☆ |
| tangent parallel to a chord (mean value) asked 2× | Board 2024Sample 2026 | ★☆☆☆☆ |
| maxima, cylinder inscribed in sphere asked 2× | Sample 2023Sample 2024 | ★☆☆☆☆ |
| tangent parallel to x-axis asked 2× | Board 2025Sample 2024 | ★☆☆☆☆ |
| increasing/decreasing intervals asked 2× | Board 2023Sample 2025 | ★☆☆☆☆ |
| minimization word problem asked 2× | Board 2024Sample 2024 | ★☆☆☆☆ |
| sign of derivative and stationary point asked 1× | Sample 2027 | ★☆☆☆☆ |
| angle between curves, orthogonal asked 1× | Sample 2027 | ★☆☆☆☆ |
| local extrema when second derivative test fails asked 1× | Sample 2027 | ★☆☆☆☆ |
| monotonicity, extrema, normal to a curve asked 1× | Sample 2027 | ★☆☆☆☆ |
| related rates, monotonicity, rate of cost asked 1× | Sample 2027 | ★☆☆☆☆ |
| increasing function condition asked 1× | Sample 2026 | ★☆☆☆☆ |
| rate of change, maxima asked 1× | Sample 2026 | ★☆☆☆☆ |
| equation of tangent to a curve asked 1× | Sample 2025 | ★☆☆☆☆ |
| maxima, cone inscribed in sphere asked 1× | Sample 2025 | ★☆☆☆☆ |
| decreasing interval asked 1× | Sample 2024 | ★☆☆☆☆ |
| increasing/decreasing intervals from a graph asked 1× | Board 2026 | ★☆☆☆☆ |
| equation of normal to a curve asked 1× | Board 2026 | ★☆☆☆☆ |
| turning points, absolute maxima and minima asked 1× | Board 2026 | ★☆☆☆☆ |
| related rates, equal rates asked 1× | Sample 2023 | ★☆☆☆☆ |
| tangent line, derivative and value asked 1× | Sample 2023 | ★☆☆☆☆ |
| minimum distance from a line asked 1× | Sample 2023 | ★☆☆☆☆ |
| increasing/strictly increasing from a graph asked 1× | Board 2025 | ★☆☆☆☆ |
| minimum value of a function asked 1× | Board 2025 | ★☆☆☆☆ |
| turning points and derivative values asked 1× | Board 2025 | ★☆☆☆☆ |
| increasing intervals asked 1× | Board 2024 | ★☆☆☆☆ |
| maxima with perimeter constraint asked 1× | Board 2024 | ★☆☆☆☆ |
| slope of normal to a curve asked 1× | Board 2023 | ★☆☆☆☆ |
| maxima-minima with constraint asked 1× | Board 2023 | ★☆☆☆☆ |
| maxima-minima word problem asked 1× | Board 2023 | ★☆☆☆☆ |
Integrals · Calculus
| definite integral using property asked 6× | Board 2024Board 2025Board 2026Sample 2023Sample 2026 | ★★★★☆ |
| definite integral of modulus function asked 5× | Board 2023Board 2024Board 2026Sample 2023Sample 2024 | ★★★☆☆ |
| integration by substitution asked 4× | Board 2023Board 2025Sample 2024 | ★★☆☆☆ |
| integration using partial fractions asked 3× | Board 2023Board 2025Sample 2026 | ★★☆☆☆ |
| integration using trigonometric simplification asked 3× | Board 2023Sample 2023Sample 2025 | ★★☆☆☆ |
| integration by parts asked 3× | Board 2024Board 2025Sample 2024 | ★★☆☆☆ |
| integration by substitution, find constant asked 2× | Board 2023Sample 2026 | ★☆☆☆☆ |
| integral of ex[f(x)+f'(x)] asked 2× | Board 2024Sample 2025 | ★☆☆☆☆ |
| integration by substitution/partial fractions asked 2× | Board 2023Sample 2025 | ★☆☆☆☆ |
| integration of trigonometric rational function asked 2× | Board 2025Board 2026 | ★☆☆☆☆ |
| integration by substitution, error analysis asked 1× | Sample 2027 | ★☆☆☆☆ |
| standard inverse trig integral asked 1× | Sample 2027 | ★☆☆☆☆ |
| definite integral of odd function, properties asked 1× | Sample 2027 | ★☆☆☆☆ |
| properties of definite integrals asked 1× | Sample 2027 | ★☆☆☆☆ |
| integration by parts and substitution asked 1× | Sample 2027 | ★☆☆☆☆ |
| integration of trigonometric functions asked 1× | Sample 2027 | ★☆☆☆☆ |
| integration after inverse-trig simplification asked 2× | Board 2023Sample 2024 | ★☆☆☆☆ |
| integration of exponential product asked 1× | Sample 2025 | ★☆☆☆☆ |
| definite integral of greatest integer function asked 1× | Sample 2025 | ★☆☆☆☆ |
| definite integral using properties asked 1× | Sample 2025 | ★☆☆☆☆ |
| integration of rational function asked 1× | Sample 2024 | ★☆☆☆☆ |
| integration by substitution to standard form asked 1× | Board 2026 | ★☆☆☆☆ |
| integration by parts of log function asked 1× | Sample 2023 | ★☆☆☆☆ |
| integration by parts / recognizing derivative asked 1× | Sample 2023 | ★☆☆☆☆ |
| integration of trigonometric function asked 1× | Sample 2023 | ★☆☆☆☆ |
| definite integral after simplification asked 1× | Board 2025 | ★☆☆☆☆ |
| definite integral of standard form asked 1× | Board 2024 | ★☆☆☆☆ |
| integration of linear over quadratic asked 1× | Board 2024 | ★☆☆☆☆ |
| definite integral of odd function over symmetric limits asked 1× | Board 2023 | ★☆☆☆☆ |
Application of Integrals · Calculus
| area of region as definite integral asked 1× | Sample 2027 | ★☆☆☆☆ |
| area using integration with a tangent line asked 1× | Sample 2027 | ★☆☆☆☆ |
| area between a line and a parabola asked 1× | Sample 2027 | ★☆☆☆☆ |
| area under a curve with sign change asked 1× | Sample 2026 | ★☆☆☆☆ |
| area under a modulus curve asked 1× | Sample 2025 | ★☆☆☆☆ |
| area between two parabolas, find parameter asked 1× | Sample 2024 | ★☆☆☆☆ |
| area under a semicircle asked 1× | Board 2026 | ★☆☆☆☆ |
| area between parabola and line, find parameter asked 1× | Sample 2023 | ★☆☆☆☆ |
| area under a curve asked 1× | Board 2025 | ★☆☆☆☆ |
| area of region bounded by lines asked 1× | Board 2025 | ★☆☆☆☆ |
| area bounded by parabola and line asked 1× | Board 2024 | ★☆☆☆☆ |
| area between two parabolas asked 1× | Board 2024 | ★☆☆☆☆ |
| area between curve and line asked 1× | Board 2023 | ★☆☆☆☆ |
Differential Equations · Calculus
| homogeneous differential equation asked 7× | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026Sample 2027 | ★★★★★ |
| linear differential equation asked 3× | Sample 2023Sample 2024Sample 2026 | ★★☆☆☆ |
| variable separable asked 3× | Board 2023Sample 2023Sample 2026 | ★★☆☆☆ |
| linear differential equation in x asked 3× | Board 2023Board 2025Board 2026 | ★★☆☆☆ |
| order and degree of a differential equation asked 2× | Board 2024Sample 2026 | ★☆☆☆☆ |
| degree of a differential equation asked 2× | Sample 2023Sample 2025 | ★☆☆☆☆ |
| solution of DE representing a circle asked 1× | Sample 2027 | ★☆☆☆☆ |
| condition for homogeneity asked 1× | Sample 2024 | ★☆☆☆☆ |
| solution of linear differential equation asked 1× | Board 2026 | ★☆☆☆☆ |
| identify homogeneous differential equation asked 1× | Board 2025 | ★☆☆☆☆ |
| verify general solution of a DE asked 1× | Board 2025 | ★☆☆☆☆ |
| variable separable with partial fractions asked 1× | Board 2024 | ★☆☆☆☆ |
Vectors · Vector Algebra
| diagonals and sides of parallelogram asked 2× | Sample 2025Sample 2026 | ★★☆☆☆ |
| dot product of vectors from a cuboid asked 2× | Sample 2025Sample 2026 | ★★☆☆☆ |
| obtuse angle, dot product negative asked 2× | Sample 2025Sample 2026 | ★★☆☆☆ |
| product of cross products asked 1× | Sample 2027 | ★☆☆☆☆ |
| vector and scalar projection asked 1× | Sample 2027 | ★☆☆☆☆ |
| unit vector perpendicular to a plane asked 1× | Sample 2027 | ★☆☆☆☆ |
| position vector and foot of perpendicular asked 1× | Sample 2027 | ★☆☆☆☆ |
| scalar projection of one vector on another asked 2× | Board 2024Board 2026 | ★☆☆☆☆ |
| vector of given magnitude in a direction asked 2× | Board 2024Sample 2023 | ★☆☆☆☆ |
| relation between dot and cross product asked 2× | Board 2024Sample 2023 | ★☆☆☆☆ |
| magnitude of sum of unit vectors asked 1× | Sample 2026 | ★☆☆☆☆ |
| centroid and area using vectors asked 1× | Sample 2026 | ★☆☆☆☆ |
| dot product with perpendicular unit vector asked 1× | Sample 2025 | ★☆☆☆☆ |
| vector perpendicular to two vectors asked 1× | Sample 2025 | ★☆☆☆☆ |
| vector direction and notation asked 1× | Sample 2024 | ★☆☆☆☆ |
| cross product of unit vectors and angle asked 1× | Sample 2024 | ★☆☆☆☆ |
| cross product magnitude relation asked 1× | Sample 2024 | ★☆☆☆☆ |
| area of triangle from position vectors asked 1× | Sample 2024 | ★☆☆☆☆ |
| scalar multiple of a unit vector asked 1× | Board 2026 | ★☆☆☆☆ |
| area of parallelogram from adjacent sides asked 1× | Board 2026 | ★☆☆☆☆ |
| collinearity using vectors asked 1× | Board 2026 | ★☆☆☆☆ |
| magnitude of perpendicular vectors asked 1× | Board 2026 | ★☆☆☆☆ |
| perpendicular vectors, dot product zero asked 1× | Sample 2023 | ★☆☆☆☆ |
| section formula external division asked 1× | Sample 2023 | ★☆☆☆☆ |
| area of triangle from adjacent sides asked 1× | Sample 2023 | ★☆☆☆☆ |
| dot product identity asked 1× | Board 2025 | ★☆☆☆☆ |
| vector between points, projection, area asked 1× | Board 2025 | ★☆☆☆☆ |
| magnitude of a vector combination asked 1× | Board 2024 | ★☆☆☆☆ |
| cross product cancellation asked 1× | Board 2024 | ★☆☆☆☆ |
| cross product magnitude and angle asked 1× | Board 2023 | ★☆☆☆☆ |
| area of parallelogram from diagonals asked 1× | Board 2023 | ★☆☆☆☆ |
| perpendicular vectors dot product zero asked 1× | Board 2023 | ★☆☆☆☆ |
| unit vector in given direction asked 1× | Board 2023 | ★☆☆☆☆ |
| dot product identity, magnitude asked 1× | Board 2023 | ★☆☆☆☆ |
Three-dimensional Geometry · Three-dimensional Geometry
| direction cosines sum of squares asked 2× | Sample 2025Sample 2026 | ★★☆☆☆ |
| plane containing a line and a point asked 2× | Sample 2025Sample 2026 | ★★☆☆☆ |
| point of intersection of two lines asked 1× | Sample 2027 | ★☆☆☆☆ |
| angle between a line and a plane asked 1× | Sample 2027 | ★☆☆☆☆ |
| equation of plane from normal direction asked 1× | Sample 2027 | ★☆☆☆☆ |
| parallel planes, line normal to plane, intersection asked 1× | Sample 2027 | ★☆☆☆☆ |
| line normal to a plane through points asked 1× | Sample 2026 | ★☆☆☆☆ |
| area of triangle with base on a line asked 1× | Sample 2026 | ★☆☆☆☆ |
| distance of plane from origin asked 1× | Sample 2025 | ★☆☆☆☆ |
| line parallel to plane, distance asked 1× | Sample 2025 | ★☆☆☆☆ |
| sum of squares of direction cosines asked 1× | Sample 2024 | ★☆☆☆☆ |
| intercepts of a plane asked 1× | Sample 2024 | ★☆☆☆☆ |
| equation of a line through origin asked 1× | Sample 2024 | ★☆☆☆☆ |
| distance of point from planes, angle between planes asked 1× | Sample 2024 | ★☆☆☆☆ |
| line with equal angles, intersection with plane asked 1× | Sample 2024 | ★☆☆☆☆ |
| direction cosines of a line through two points asked 1× | Board 2026 | ★☆☆☆☆ |
| equation of plane in intercept form asked 1× | Board 2026 | ★☆☆☆☆ |
| condition for intersecting lines asked 1× | Board 2026 | ★☆☆☆☆ |
| distance of point from plane, image/reflection asked 1× | Board 2026 | ★☆☆☆☆ |
| relation between two planes asked 1× | Sample 2023 | ★☆☆☆☆ |
| plane parallel to a coordinate plane asked 1× | Sample 2023 | ★☆☆☆☆ |
| intersection of two lines asked 1× | Sample 2023 | ★☆☆☆☆ |
| equation of plane with intercept condition asked 1× | Sample 2023 | ★☆☆☆☆ |
| angle between two planes asked 1× | Board 2025 | ★☆☆☆☆ |
| collinearity of three points in space asked 1× | Board 2025 | ★☆☆☆☆ |
| cartesian form and parallel line asked 1× | Board 2025 | ★☆☆☆☆ |
| plane through three points asked 1× | Board 2025 | ★☆☆☆☆ |
| plane through points parallel to an axis asked 1× | Board 2025 | ★☆☆☆☆ |
| direction cosines identity asked 1× | Board 2024 | ★☆☆☆☆ |
| distance of a point from coordinate planes asked 1× | Board 2024 | ★☆☆☆☆ |
| plane through three points, line, distance asked 1× | Board 2024 | ★☆☆☆☆ |
| distance of a point from a plane asked 1× | Board 2023 | ★☆☆☆☆ |
| equation of plane with equal intercepts asked 1× | Board 2023 | ★☆☆☆☆ |
| plane perpendicular to two planes asked 1× | Board 2023 | ★☆☆☆☆ |
| line perpendicular to two lines asked 1× | Board 2023 | ★☆☆☆☆ |
Linear Programming · Linear Programming
| LPP formulation and solution asked 3× | Board 2024Board 2026Sample 2024 | ★★☆☆☆ |
| graphical LPP, optimal solutions asked 2× | Sample 2025Sample 2026 | ★★☆☆☆ |
| multiple optimal solutions, objective value asked 1× | Sample 2027 | ★☆☆☆☆ |
| existence and multiplicity of optimal solutions asked 1× | Sample 2027 | ★☆☆☆☆ |
| formulate constraints and optimize asked 1× | Sample 2027 | ★☆☆☆☆ |
| graphical maximization asked 2× | Board 2023Sample 2024 | ★☆☆☆☆ |
| read constraints from feasible region, optimize asked 1× | Sample 2026 | ★☆☆☆☆ |
| graphical solution of LPP asked 1× | Sample 2023 | ★☆☆☆☆ |
| LPP formulation and minimization asked 1× | Sample 2023 | ★☆☆☆☆ |
| LPP formulation and graphical solution asked 1× | Board 2025 | ★☆☆☆☆ |
Probability · Probability
| Bayes theorem asked 6× | Board 2023Board 2024Board 2025Sample 2023Sample 2026Sample 2027 | ★★★★☆ |
| probability distribution and expectation asked 4× | Board 2024Sample 2024Sample 2025Sample 2026 | ★★★☆☆ |
| probability without replacement asked 3× | Board 2025Sample 2025Sample 2026 | ★★☆☆☆ |
| probability using combinations asked 2× | Sample 2025Sample 2026 | ★★☆☆☆ |
| conditional probability and complements asked 2× | Sample 2025Sample 2026 | ★★☆☆☆ |
| total probability and Bayes theorem asked 2× | Board 2026Sample 2025 | ★☆☆☆☆ |
| conditional probability asked 2× | Sample 2023Sample 2024 | ★☆☆☆☆ |
| conditional probability relations asked 1× | Sample 2027 | ★☆☆☆☆ |
| probability distribution, sum of probabilities asked 1× | Sample 2027 | ★☆☆☆☆ |
| probability of consecutive events asked 1× | Sample 2027 | ★☆☆☆☆ |
| Bayes theorem (Monty Hall) asked 1× | Sample 2027 | ★☆☆☆☆ |
| repeated independent trials asked 1× | Sample 2026 | ★☆☆☆☆ |
| geometric distribution / repeated trials asked 1× | Sample 2025 | ★☆☆☆☆ |
| independence and mutual exclusivity asked 1× | Sample 2024 | ★☆☆☆☆ |
| at least one via complement asked 1× | Sample 2024 | ★☆☆☆☆ |
| transfer of balls, Bayes theorem asked 1× | Sample 2024 | ★☆☆☆☆ |
| transfer of items, total probability asked 1× | Sample 2024 | ★☆☆☆☆ |
| addition theorem for mutually exclusive events asked 1× | Board 2026 | ★☆☆☆☆ |
| testing independence of events asked 1× | Board 2026 | ★☆☆☆☆ |
| transfer of balls, total probability asked 1× | Board 2026 | ★☆☆☆☆ |
| probability distribution and mean asked 1× | Board 2026 | ★☆☆☆☆ |
| conditional probability of complements asked 1× | Sample 2023 | ★☆☆☆☆ |
| independent events, contradiction asked 1× | Sample 2023 | ★☆☆☆☆ |
| dependent events, at least two asked 1× | Sample 2023 | ★☆☆☆☆ |
| probability distribution, expectation, game asked 1× | Sample 2023 | ★☆☆☆☆ |
| conditional probability, mutually exclusive events asked 1× | Board 2025 | ★☆☆☆☆ |
| expected value of a random variable asked 1× | Board 2025 | ★☆☆☆☆ |
| odds and independent events asked 1× | Board 2025 | ★☆☆☆☆ |
| at least one event via complement asked 1× | Board 2024 | ★☆☆☆☆ |
| conditional probability and addition theorem asked 1× | Board 2024 | ★☆☆☆☆ |
| independent events with replacement asked 1× | Board 2023 | ★☆☆☆☆ |
| independent events, complement asked 1× | Board 2023 | ★☆☆☆☆ |
| independent events, exactly/at least two asked 1× | Board 2023 | ★☆☆☆☆ |
| probability distribution and mean of random variable asked 1× | Board 2023 | ★☆☆☆☆ |
Importance = how often a topic was asked × how recent, with extra weight for the latest official sample paper.