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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 15 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: 15

Questions asked in Calculus and Linear Algebra Minor 1 2026

  1. Q1(a). Show that the functions u = 2, = tan"*x + tan"*y are functionally related. Hence find the relation between them. [2 marks]
  2. Q1(a)(i). Show that the nth derivative of Far is 1)8 sin**19, where 8 = tan -19 [1 marks]
  3. Q1(a)(ii). If (cx - az, cy - bz) = D, then show that - + b = C [1 marks]
  4. Q1(b). Find the shortest and longest distance from the point (1, 2, - 1) to the sphere x=+y? +22 = 24 [2 marks]
  5. Q1(b)(i). Show that the nth derivative of Far is 1)8 sin**19, where 8 = tan -19 [1 marks]
  6. Q1(b)(ii). If (cx - az, cy - bz) = D, then show that - + b = C [1 marks]
  7. Q1(c). Find the Taylor series expansion of f(x, y) - cot xy in powers of 0.5) and G2) up to the second defitorerm. Hence substitute f(-0.4. 2.2) approximately. [2 marks]
  8. Q2(a). Verify Cayley-Hamilton theorem for matrix A and hence find matrix A8 - SA? + 7A• - 345 + 8A* - 5.43 + BA2 - 2A + 1 [4 marks]
  9. Q2(a)(i). Verify Cayley-Hamilton theorem for matrix A [2 marks]
  10. Q2(a)(ii). Find matrix A8 - SA? + 7A• - 345 + 8A* - 5.43 + BA2 - 2A + 1 [2 marks]
  11. Q2(b). Reduce the matrix 0-1 -1 2 1 j to the normal form. Hence find the rank. [4 marks]
  12. Q2(c). Solve the system of equations 2x+y +iz + 2y +z= 9 and x + 2y + 2z = 11, 'by finding the inverse using elementary transformations [4 marks]
  13. Q2(d). Find all the eigen values and eigen vectors of fo lowing matrix A = 3 -4 4 1 -2 1 -1 3 14 10|3 [4 marks]
  14. QQ.1. Show that the functions u = 2, = tan"*x + tan"*y are functionally related. Hence find the relation between them. (IC) Find the shortest and longest distance from the point (1, 2, - 1) to the sphere x=+y? +22 = 24
  15. QQ.2. Verify Cayley-Hamilton theorem for matrix A and hence find matrix A8 - SA? + 7A• - 345 + 8A* - 5.43 + BA2 - 2A + 1 If matrix A = г2 0 1 1 1 0 2