GIKI Admission Test 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 GIKI Admission Test, not a summary of it.

1. 1

   Number Systems, Sets & Functions

   4 topics

   • Real and Complex Numbers
   • Sets and Relations
   • Functions
   • Polynomials and Linear Equations
2. 2

   Matrices & Determinants

   4 topics

   • Matrix Operations
   • Determinants and Their Properties
   • Inverse of a Matrix
   • Solution of Simultaneous Equations
3. 3

   Quadratic Equations

   4 topics

   • Solution of Quadratic Equations
   • Nature of Roots
   • Relationship Between Roots and Coefficients
   • Equations Reducible to Quadratic Form
4. 4

   Sequences & Series

   4 topics

   • Arithmetic Progression
   • Geometric Progression
   • Harmonic Progression
   • Sum to Infinity of Geometric Series
5. 5

   Permutations, Combinations & Probability

   4 topics

   • Permutations
   • Combinations
   • Basic Probability
   • Elementary Statistics
6. 6

   Mathematical Induction & Binomial Theorem

   4 topics

   • Principle of Mathematical Induction
   • Binomial Theorem for Positive Integral Index
   • Binomial Series for Rational Index
   • Applications of Binomial Expansion
7. 7

   Trigonometry

   5 topics

   • Angles and Their Measurement
   • Trigonometric Functions and Identities
   • Trigonometric Equations
   • Inverse Trigonometric Functions
   • Solution of Triangles and Applications
8. 8

   Differential Calculus

   4 topics

   • Limits and Continuity
   • Differentiation Rules
   • Derivatives of Trigonometric, Exponential and Logarithmic Functions
   • Maxima, Minima and Rate of Change
9. 9

   Integral Calculus

   4 topics

   • Indefinite Integration
   • Methods of Integration
   • Definite Integrals
   • Area Under Curves and Volumes
10. 10

    Analytic Geometry

    3 topics

    • Coordinate Geometry and Straight Lines
    • Circle
    • Conic Sections
11. 11

    Vectors

    4 topics

    • Vectors in Plane and Space
    • Scalar (Dot) Product
    • Vector (Cross) Product
    • Scalar Triple Product

Mathematics flashcards for GIKI Admission Test

21 of 50 cards from the Mathematics deck — real questions with worked answers.

1. What is a complex number, and what are its real and imaginary parts in the form z = a + bi?

   A complex number is a number of the form z = a + bi where a and b are real numbers and i = √(-1). Here 'a' is the real part Re(z) and 'b' is the imaginary part Im(z).

2. What is the conjugate of a complex number z = a + bi, and what is the product of z with its conjugate?

   The conjugate is z̄ = a - bi. Their product z·z̄ = a² + b², which is a non-negative real number equal to |z|².

3. What is the modulus of a complex number z = a + bi?

   The modulus is |z| = √(a² + b²), the distance of the point (a, b) from the origin in the Argand plane.

4. Classify the real number system: how do natural, whole, integer, rational, and irrational numbers relate?

   Natural numbers ⊂ Whole numbers ⊂ Integers ⊂ Rational numbers. Rationals (expressible as p/q, q≠0) together with irrationals (non-terminating, non-repeating decimals like √2, π) form the real numbers.

5. What is the difference between a rational and an irrational number?

   A rational number can be written as p/q with integers p, q (q≠0) and has a terminating or repeating decimal. An irrational number cannot be expressed as such a fraction and has a non-terminating, non-repeating decimal.

6. Define the union and intersection of two sets A and B.

   A ∪ B is the set of all elements in A or B (or both). A ∩ B is the set of elements common to both A and B.

7. What is the difference of sets A − B, and what is the complement of a set A?

   A − B is the set of elements in A but not in B. The complement A' (or Aᶜ) is the set of all elements in the universal set U that are not in A.

8. State De Morgan's Laws for sets.

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

9. For finite sets, what is the formula for the number of elements in A ∪ B (inclusion–exclusion)?

   n(A ∪ B) = n(A) + n(B) − n(A ∩ B).

10. How many subsets does a set with n elements have, and how many of them are proper subsets?

    A set with n elements has 2ⁿ subsets and 2ⁿ − 1 proper subsets (excluding the set itself).

11. What is a relation from set A to set B?

    A relation from A to B is any subset of the Cartesian product A × B; i.e., a set of ordered pairs (a, b) with a ∈ A and b ∈ B.

12. Define reflexive, symmetric, and transitive relations.

    Reflexive: (a, a) ∈ R for all a. Symmetric: if (a, b) ∈ R then (b, a) ∈ R. Transitive: if (a, b) ∈ R and (b, c) ∈ R then (a, c) ∈ R. A relation that is all three is an equivalence relation.

13. What is a function, and how does it differ from a general relation?

    A function from A to B is a relation that assigns to each element of A exactly one element of B. Unlike a general relation, no element of the domain may map to more than one image.

14. Define the domain, codomain, and range of a function.

    Domain: the set of all input values (A). Codomain: the set B into which the function maps. Range: the set of actual output values, a subset of the codomain.

15. Distinguish between one-to-one (injective), onto (surjective), and bijective functions.

    Injective: distinct inputs give distinct outputs. Surjective: every element of the codomain is an image of some input. Bijective: both injective and surjective (one-to-one correspondence).

16. What is the condition for a function f to have an inverse, and what does the inverse satisfy?

    A function has an inverse if and only if it is bijective. The inverse f⁻¹ satisfies f⁻¹(f(x)) = x and f(f⁻¹(y)) = y, effectively swapping domain and range.

17. What is a polynomial of degree n in one variable?

    A polynomial of degree n is an expression aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀ where aₙ ≠ 0 and the exponents are non-negative integers.

18. State the Remainder Theorem.

    When a polynomial P(x) is divided by (x − a), the remainder equals P(a).

19. State the Factor Theorem.

    (x − a) is a factor of polynomial P(x) if and only if P(a) = 0.

20. What is the order (or dimension) of a matrix, and when is a matrix called square?

    The order of a matrix is m × n where m is the number of rows and n the number of columns. A matrix is square when m = n (equal rows and columns).

21. Under what condition can two matrices be multiplied, and what is the order of the product?

    Matrices A (m × n) and B (p × q) can be multiplied only if n = p. The product AB has order m × q.

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