Pure Mathematics · 2023

CSS 2023 Pure Mathematics Paper

5 questions from this paper.

  1. Q1
    Define a Normal Subgroup. Prove that the intersection of two normal subgroups of a group G is a normal subgroup of G.
    Practice material Modern Algebra 20 marks
  2. Q2
    Find the eigenvalues and corresponding eigenvectors of the matrix A = [[1, 2, 0], [0, 2, 0], [-2, -2, -1]].
    Practice material Linear Algebra 20 marks
  3. Q3
    Find the equation of the tangent and normal to the ellipse x^2/a^2 + y^2/b^2 = 1 at a given point (x1, y1).
    Practice material Analytical Geometry 20 marks
  4. Q4
    Solve the differential equation (D^2 - 4D + 4)y = e^(2x) using the method of undetermined coefficients.
    Practice material Differential Equations 20 marks
  5. Q5
    Use Cauchy's Integral Formula to evaluate the integral of (sin z) / (z - pi/4)^2 dz around a circle |z| = 2.
    Practice material Complex Analysis 20 marks

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