MHT CET Mathematics Syllabus

Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics in MHT CET, not a summary of it.

1. 1

   Algebra

   4 topics

   • Matrices and Determinants
     • Operations and types of matrices
     • Adjoint and inverse of a matrix
     • Solution of linear equations by matrix methods
   • Complex Numbers
     • Algebra of complex numbers and Argand diagram
     • Polar form and De Moivre's theorem
     • Cube roots of unity
   • Sequences and Series
     • Arithmetic, geometric and harmonic progressions
     • Sum to n terms and special series
   • Permutations, Combinations and Binomial Theorem
     • Fundamental principle of counting
     • Binomial theorem for positive integral index
     • General and middle terms
2. 2

   Trigonometry

   3 topics

   • Trigonometric Functions and Identities
     • Compound, multiple and submultiple angles
     • Transformation formulae
   • Trigonometric Equations
     • General solutions
     • Properties of triangles, sine and cosine rules
   • Inverse Trigonometric Functions
     • Domain, range and principal values
     • Properties and equations
3. 3

   Coordinate Geometry and Vectors

   4 topics

   • Straight Line and Circle
     • Forms of equation of a line and angle between lines
     • Equation of circle and tangent
   • Conic Sections
     • Parabola, ellipse and hyperbola
     • Standard equations and properties
   • Vectors
     • Scalar and vector products
     • Scalar triple product and applications
   • Three Dimensional Geometry
     • Direction cosines and direction ratios
     • Line and plane in space
4. 4

   Calculus

   4 topics

   • Limits, Continuity and Differentiability
     • Evaluation of limits and standard forms
     • Continuity and differentiability of functions
   • Differentiation and Applications
     • Derivatives of composite, implicit and parametric functions
     • Tangents, normals, maxima and minima
     • Rate of change and approximations
   • Integration
     • Methods of integration and standard integrals
     • Definite integrals and properties
   • Applications of Integrals and Differential Equations
     • Area under curves
     • Formation and solution of differential equations
5. 5

   Probability and Statistics

   3 topics

   • Probability
     • Conditional probability and Bayes' theorem
     • Random variables and probability distributions
     • Bernoulli trials and binomial distribution
   • Mathematical Logic
     • Statements, logical connectives and truth tables
     • Tautology, contradiction and quantifiers
   • Linear Programming
     • Formulation of LPP
     • Graphical solution and feasible region

Mathematics flashcards for MHT CET

21 of 60 cards from the Mathematics deck — real questions with worked answers.

1. In a 3x3 determinant, what is a cofactor C_ij and how does it relate to the minor M_ij?

   The cofactor C_ij = (-1)^(i+j) * M_ij, where M_ij is the minor (determinant of the 2x2 matrix left after deleting row i and column j).

2. What is the formula for the inverse of a non-singular square matrix A?

   A^(-1) = (1/|A|) * adj(A), where adj(A) is the adjoint (transpose of the cofactor matrix). It exists only when |A| ≠ 0.

3. For a square matrix A of order n, what is the relation between |adj A| and |A|?

   |adj A| = |A|^(n-1).

4. State the condition for a system of linear equations AX = B to have a unique solution (Cramer's Rule context).

   A unique solution exists when the coefficient determinant D = |A| ≠ 0. Then x_i = D_i / D, where D_i replaces the i-th column of D with the constants.

5. What is the value of i^n for n giving remainders 0,1,2,3 when divided by 4?

   i^0=1, i^1=i, i^2=-1, i^3=-i; the powers of i cycle with period 4 (use n mod 4).

6. For a complex number z = a + bi, what is its modulus |z| and conjugate z̄?

   |z| = √(a² + b²); conjugate z̄ = a - bi. Also z·z̄ = |z|² = a² + b².

7. State De Moivre's Theorem for (cosθ + i sinθ)^n.

   (cosθ + i sinθ)^n = cos(nθ) + i sin(nθ), valid for all integers n (and rational n giving one of the values).

8. What are the cube roots of unity and one key property they satisfy?

   The cube roots of unity are 1, ω, ω², where ω = (-1 + i√3)/2. They satisfy 1 + ω + ω² = 0 and ω³ = 1.

9. What is the nth term and sum of the first n terms of an Arithmetic Progression (AP)?

   nth term: t_n = a + (n-1)d. Sum: S_n = (n/2)[2a + (n-1)d] = (n/2)(a + l), where l is the last term.

10. What is the nth term and sum of n terms of a Geometric Progression (GP)?

    nth term: t_n = a·r^(n-1). Sum (r≠1): S_n = a(r^n - 1)/(r - 1). Infinite sum (|r|<1): S = a/(1 - r).

11. Give the formulas for the sum of the first n natural numbers, their squares, and their cubes.

    Σn = n(n+1)/2; Σn² = n(n+1)(2n+1)/6; Σn³ = [n(n+1)/2]².

12. What is the relationship between the Arithmetic Mean (A) and Geometric Mean (G) of two positive numbers, and their geometric link?

    A ≥ G (with equality iff the numbers are equal). For two numbers, G² = A·H (the GM is the geometric mean of AM and HM).

13. What is the formula for the number of permutations of n distinct objects taken r at a time?

    nPr = n! / (n - r)!

14. What is the formula for combinations nCr, and what is the relation between nCr and nP r?

    nCr = n! / [r!(n - r)!]; and nPr = nCr · r!.

15. State Pascal's rule relating combinations.

    nCr + nC(r-1) = (n+1)Cr.

16. What is the general (r+1)th term in the binomial expansion of (a + b)^n?

    T_(r+1) = nCr · a^(n-r) · b^r, for r = 0, 1, ..., n.

17. How many terms are there in the expansion of (a + b)^n and what is the sum of all binomial coefficients?

    There are (n + 1) terms; the sum of all binomial coefficients nC0 + nC1 + ... + nCn = 2^n.

18. State the three Pythagorean trigonometric identities.

    sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.

19. State the formulas for sin(A ± B) and cos(A ± B).

    sin(A±B) = sinA cosB ± cosA sinB; cos(A±B) = cosA cosB ∓ sinA sinB.

20. State the double angle formulas for cos 2θ (three forms).

    cos2θ = cos²θ - sin²θ = 1 - 2sin²θ = 2cos²θ - 1. Also sin2θ = 2 sinθ cosθ and tan2θ = 2tanθ/(1 - tan²θ).

21. What are the product-to-sum formulas for 2 sinA cosB and 2 cosA cosB?

    2 sinA cosB = sin(A+B) + sin(A-B); 2 cosA cosB = cos(A+B) + cos(A-B).

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