NIMCET 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 NIMCET, not a summary of it.

1. 1

   Algebra

   8 topics

   • Sets and Functions
   • Relations and Functions
   • Matrices and Determinants
   • Quadratic Equations
   • Permutations and Combinations
   • Binomial Theorem
   • Complex Numbers
   • Sequences and Series
2. 2

   Calculus

   5 topics

   • Limits and Continuity
   • Differentiation
   • Integration
   • Application of Derivatives
   • Differential Equations
3. 3

   Vector Algebra

   3 topics

   • Vectors and Scalars
   • Dot and Cross Product
   • Vector Equations
4. 4

   Trigonometry

   3 topics

   • Trigonometric Ratios
   • Trigonometric Identities
   • Inverse Trigonometric Functions
5. 5

   Coordinate Geometry

   6 topics

   • Straight Lines
   • Conic Sections
   • Circles
   • Parabolas
   • Ellipses
   • Hyperbolas

Mathematics flashcards for NIMCET

21 of 55 cards from the Mathematics deck — real questions with worked answers.

1. In set theory, what is the formula for the number of subsets and the number of proper subsets of a set with n elements?

   Number of subsets = 2^n; number of proper subsets = 2^n − 1 (all subsets except the set itself).

2. State the De Morgan's laws for two sets A and B.

   (A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'.

3. For finite sets, what is the inclusion–exclusion formula for n(A ∪ B ∪ C)?

   n(A∪B∪C) = n(A)+n(B)+n(C) − n(A∩B) − n(B∩C) − n(C∩A) + n(A∩B∩C).

4. Define a function and distinguish between one-one (injective), onto (surjective), and bijective functions.

   A function maps each domain element to exactly one codomain element. Injective: distinct inputs give distinct outputs. Surjective: every codomain element is an image. Bijective: both injective and surjective.

5. If a relation R on a set is reflexive, symmetric, and transitive, what is it called, and what do these three properties mean?

   An equivalence relation. Reflexive: aRa for all a. Symmetric: aRb ⇒ bRa. Transitive: aRb and bRc ⇒ aRc.

6. How many relations exist from a set A with m elements to a set B with n elements?

   2^(mn), since each relation is a subset of A×B which has mn ordered pairs.

7. What is the formula for the determinant of a 2×2 matrix [[a, b], [c, d]]?

   det = ad − bc.

8. State the formula for the inverse of a non-singular matrix A in terms of its adjoint.

   A⁻¹ = (1/det A)·adj(A), valid when det A ≠ 0.

9. For a square matrix A of order n, how does det(kA) relate to det(A), and what is det(adj A)?

   det(kA) = kⁿ·det(A); det(adj A) = (det A)^(n−1).

10. For the quadratic ax² + bx + c = 0, state the sum and product of its roots.

    Sum of roots = −b/a; product of roots = c/a.

11. What does the discriminant D = b² − 4ac tell us about the roots of a quadratic equation?

    D > 0: two distinct real roots; D = 0: two equal (repeated) real roots; D < 0: two complex conjugate roots.

12. Give the quadratic formula for the roots of ax² + bx + c = 0.

    x = [−b ± √(b² − 4ac)] / (2a).

13. State the formulas for the number of permutations nPr and combinations nCr of r objects from n.

    nPr = n!/(n−r)!; nCr = n!/[r!(n−r)!].

14. How many distinct arrangements are there of n objects where there are repetitions of p, q, r identical items?

    n!/(p!·q!·r!).

15. State Pascal's rule relating combination numbers.

    nCr + nC(r−1) = (n+1)Cr.

16. State the binomial theorem for (a + b)ⁿ and the general (r+1)th term.

    (a+b)ⁿ = Σ_{r=0}^{n} nCr·a^(n−r)·b^r; the general term is T_{r+1} = nCr·a^(n−r)·b^r.

17. How do you find the term independent of x (constant term) in a binomial expansion?

    Write the general term T_{r+1}, set the total exponent of x to zero, solve for r, then substitute that r back into the term.

18. For the complex number z = a + bi, define its modulus and conjugate.

    Modulus |z| = √(a² + b²); conjugate z̄ = a − bi.

19. State Euler's form and De Moivre's theorem for a complex number.

    Euler/polar: z = r(cosθ + i sinθ) = r·e^(iθ). De Moivre: (cosθ + i sinθ)ⁿ = cos(nθ) + i sin(nθ).

20. What is the value of the four powers of i (i, i², i³, i⁴) and the property of the cube roots of unity?

    i = √−1, i² = −1, i³ = −i, i⁴ = 1. Cube roots of unity 1, ω, ω² satisfy 1 + ω + ω² = 0 and ω³ = 1.

21. State the nth term and sum of n terms of an arithmetic progression (AP) with first term a and common difference d.

    aₙ = a + (n−1)d; Sₙ = (n/2)[2a + (n−1)d] = (n/2)(a + l), where l is the last term.

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