Mathematics I Importants Questions
BCA First Semester Mathematics I Importants Questions
UNIT 1: Logic, Relations, Functions & Graphs
Theory Type
- Elementary logic (contrapositive, converse, inverse statements)
- Definition and types of functions (bijective, one-one, onto)
- Exponential and logarithmic function definition + properties
- Real number system, field axioms, ordered axioms
- Types of relations (equivalence relation)
Numerical Type
- Domain and range finding of functions like √(a − x − x²)
- Solving inequalities like 3 + 2x − x² ≥ 0
- Complex number problems — proving x² + y² = 1
- Composite functions (fog, gof)
- Absolute value of complex numbers
- Proving bijective functions
- Logarithmic function identity problems
- Interval and modulus notation problems
UNIT 2: Sequence and Series
Theory Type
- Definition and properties of AP, GP, HP
- Relationship between AM, GM, HM — proving AM ≥ GM ≥ HM
- Maclaurin and Taylor series definition
Numerical Type
- Sum to n terms of arithmetic-geometric series like 1.3 + 3.5 + 5.7…
- Problems where AP terms form GP after addition — classic type
- Taylor series expansion of f(x) = x³ − 2x + 4 at a = 2
- Maclaurin series of cos x, sin x, eˣ
- Sum of infinite GP series
- Proving AM, GM, HM inequality with numbers
- If a,b,c,d are in GP prove related expressions also in GP
UNIT 3: Matrices and Determinants
Theory Type
- Definition and types of matrices
- Properties of determinants (without proof)
- Definition of singular and non-singular matrix
- Linear and orthogonal transformation concept
- Eigenvalues and Eigenvectors definition and concept
- Rank of a matrix definition
Numerical Type
- Finding inverse of 3×3 matrix
- Proving determinant identities like the xyz determinant
- Finding adjoint of matrix
- Expressing matrix as sum of symmetric and skew-symmetric
- Finding Eigenvalues and Eigenvectors of a 2×2 or 3×3 matrix
- Linear transformation problems — finding matrix of transformation
- Proving (AB)ᵀ = BᵀAᵀ
- Rank of matrix problems
- Characteristic equation problems
UNIT 4: Analytical Geometry
Theory Type
- Definition of conic sections (circle, parabola, ellipse, hyperbola)
- Standard equations and their parts
- Eccentricity and classification of conics
- Polar equations of circle, ellipse, parabola, hyperbola
Numerical Type
- Finding equation of ellipse given latus rectum and eccentricity
- Finding centre, vertices, foci, eccentricity of ellipse like 25x² + 4y² = 100
- Finding equation of hyperbola given focus and directrix
- Finding equation of parabola given focus and directrix
- Finding equation of circle passing through three points
- Converting polar equation to Cartesian
- Classifying conic by eccentricity
UNIT 5: Vector and Vector Space
Theory Type
- Definition of vector space and subspace
- Linear combination, linear dependence and independence
- Scalar product and vector product with geometrical interpretation
- Norm and orthogonality
Numerical Type
- Finding angle between two vectors
- Finding unit vector perpendicular to a plane through three points
- Proving cos(A−B) or cos(A+B) or sin(A+B) by vector method
- Finding area of parallelogram using cross product
- Finding volume of parallelepiped
- Linear dependence/independence of vectors
- Problems on scalar product, norm, orthogonality
UNIT 6: Permutations and Combinations
Theory Type
- Basic counting principle
- Relationship between permutation and combination formula
- Circular permutation concept
Numerical Type
- Word arrangement problems like ARRANGE, STRANGE, CALCULUS, PETROL, LOGIC, SUNDAY
- Forming numbers with given digits with conditions (less than 500, three digits etc.)
- Committee formation problems with conditions (at least one lady/girl etc.)
- Circular permutation (clock, round table)
- Combination problems like choosing questions from exam paper
- Selecting balls from bags
Don’t use our content without permission. 📸⚠️
Thank you for sharing you everyone! If you’d like to share your notes, lab reports, solution, assignments, projects, or any other academic materials, feel free to contact us through social media (Uni Bytes), email us at unibytesofficials@gmail.com.
We regularly provide updates on BCA news, results, exam routines, and other important information. Stay connected with Uni Bytes for all your academic needs
Don’t Forget to Follow Uni Bytes
