SPSC-Mathematics

Mathematics serves as the definitive filter in the Sindh Public Service Commission (SPSC) examinations, acting as the primary differentiator between successful candidates and those who fall short of the merit list. In competitive environments—ranging from SPSC screening tests to high-stakes entrance exams like MDCAT, ECAT, and HEC-related assessments—mathematical proficiency is not merely about calculation; it is about logical reasoning, analytical speed, and the ability to solve complex problems under strict time constraints. At Professional Academy (MM Online), we recognize that mastering SPSC-Mathematics requires moving beyond rote memorization. Our curated quiz is designed to sharpen your quantitative aptitude by focusing on high-yield topics, including arithmetic operations, algebraic structures, geometry, and statistical interpretation. These are the core pillars that frequently appear in the SPSC syllabus, yet they remain the most common stumbling blocks for applicants. To excel, your preparation strategy must pivot from passive reading to active problem-solving. We advise students to prioritize conceptual clarity over shortcut hacks; understanding the "why" behind a formula ensures you can navigate variations in question phrasing during the actual exam. Use this assessment to identify your knowledge gaps and refine your mental processing speed. By integrating rigorous practice with our expert-led insights, you are not just preparing for a test—you are building the cognitive foundation required for a successful career in the public sector. Engage with this module to benchmark your readiness and elevate your analytical performance.

Practice questions

  1. The value of determinant of
    • triangular matrix is:
    • Sum of diagonal elements
    • Product of diagonal elements
    • Zero
  2. If derivative of
    • function is zero, the function is:
    • Increasing
    • Decreasing
    • Constant
  3. The integral of ( e^x dx ) is:
    • ( e^x +
    • ( xe^x )
    • ( \ln x )
    • ( \frac{1}{x} )
  4. Q.
    • matrix is invertible if its determinant is:
    • Zero
    • Non-zero
    • One only
  5. The rank of identity matrix of order n is:
    • 0
    • 1
    • n
    • n−1
  6. The derivative of ( \ln x ) is:
    • ( x )
    • ( \frac{1}{x} )
    • ( e^x )
    • ( \ln x )
  7. Eigenvectors correspond to:
    • Scalars
    • Eigenvalues
    • Determinants
    • Functions
  8. The Laplace transform of ( e^{at} ) is:
    • ( \frac{1}{s+a} )
    • ( \frac{1}{s-a} )
    • ( s-a )
    • ( s+a )
  9. Q.
    • continuous function has:
    • No limit
    • Limit exists
    • No derivative
  10. If vectors are orthogonal, their dot product is:
    • 1
    • −1
    • 0
    • ∞
  11. The inverse of identity matrix is:
    • Zero matrix
    • Identity matrix
    • Scalar matrix
    • Singular matrix
  12. The degree of differential equation is defined when equation is:
    • Linear
    • Polynomial in derivatives
    • Constant
    • Continuous
  13. Integration is inverse of:
    • Multiplication
    • Division
    • Differentiation
    • Addition
  14. Divergence measures:
    • Rotation
    • Spread
    • Gradient
    • Direction
  15. Curl measures:
    • Rotation
    • Divergence
    • Gradient
    • Scalar
  16. Nullity of matrix is related to:
    • Rank
    • Determinant
    • Trace
    • Eigenvalue
  17. Trace of matrix is sum of:
    • All elements
    • Diagonal elements
    • Rows
    • Columns
  18. Fourier transform converts function into:
    • Time domain
    • Frequency domain
    • Space domain
    • Vector domain
  19. Unit vector magnitude is:
    • 0
    • 1
    • −1
    • ∞
  20. Q.
    • square matrix with all zero elements is called:
    • Identity matrix
    • Scalar matrix
    • Zero matrix
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