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Calculus and Linear Algebra — Minor 1 2026 question paper

MMMUT Electronics and Communication Engineering previous year question paper for Calculus and Linear Algebra (BSM 101), semester 1, Minor 1 2026. All 11 questions are listed below, each with a written answer on Nexsus.

Paper details

  • Subject: Calculus and Linear Algebra (BSM 101)
  • Branch: Electronics and Communication Engineering
  • Semester: 1
  • Exam: Minor 1 2026
  • Questions: 11

Questions asked in Calculus and Linear Algebra Minor 1 2026

  1. Q1(a). Verify Lagrange mean value theorem for the function f(x) = tan^-1(x) in the interval [0,1]. [5 marks]
  2. Q1(a)2. If y = tan^-1(x), find y0(0).
  3. Q1(b). If u = sin^-1[(x^2 + y^2)/(x^2 + y^2)], then find x^2 + (y^2u)/(y^2z) + 2xy * ∂^2u/∂x∂y + y^2 * ∂^2u/∂y^2. [3 marks]
  4. Q1(b)3. The Temperature T at any point (x,y,z) in space is T(x,y,z) = kxyz^2, k is positive constant. Find the highest temperature on the surface of sphere x^2 + y^2 + z^2 = 1.
  5. Q1(c). If u,v,w are the roots of the cubic equation (λ - x)^3 + (2 - y)^3 + (x - z)^4 = 0 in x, then find x^2 + y^2 + z^2 = 1. [3 marks]
  6. Q2(a). Show that every square matrix can be uniquely written as a sum of Hermitian and skew Hermitian matrix. [4 marks]
  7. Q2(a)2. Determine the value of k such that following system of linear equations kx + y + z = 1, x + ky + z = 1, x + y + kz = 1 has (i) unique solution (ii) no solution (iii) infinite solutions.
  8. Q2(b). Find the eigen values and eigen vector of the matrix. [3 marks]
  9. Q2(b)3. Find the rank of the matrix.
  10. Q2(b)4. State the Cayley-Hamilton theorem. Verify this theorem for the matrix A = [[1, 2], [-1, 3]]. Hence express A^6 - 4A^5 + 8A^4 - 12A^3 + 14A^2 as linear polynomial in A.
  11. QQ.1. Attempt any Two parts of the following. Q.1(a) is compulsory.