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Engineering Mathematics II — Minor 2024 question paper

MMMUT Mechanical Engineering previous year question paper for Engineering Mathematics II (BSM-160), semester 2, Minor 2024. All 15 questions are listed below, each with a written answer on Nexsus.

Paper details

  • Subject: Engineering Mathematics II (BSM-160)
  • Branch: Mechanical Engineering
  • Semester: 2
  • Exam: Minor 2024
  • Questions: 15

Questions asked in Engineering Mathematics II Minor 2024

  1. Q1. Attempt any three parts of the following.
  2. Q1(a). Solve by the method of variation of parameter x^2*d^2y/dx^2-x*dy/dx-y = x^2*e^x [4 marks]
  3. Q1(b). State and prove the orthogonality of Legendre's polynomial. [4 marks]
  4. Q1(c). Solve x^2*y'' - (x^2 + 2x)*y' + (x + 2)*y = x^3*e^x [4 marks]
  5. Q1(d). Using method of Frobenius, obtain the series solution in power of x for x*d^2y/dx^2 + dy/dx - y = 0 [4 marks]
  6. Q2. Attempt any three parts of the following.
  7. Q2(a). Solve d^2y/dx^2 - 2x*dy/dx + (x^2 + 2)*y = e^(1/2*(x^2 + 2x)) [3 marks]
  8. Q2(b). Solve d^2y/dx^2 - 2*dy/dx + 2*y = e^x*tan(x) [3 marks]
  9. Q2(c). Solve [D^2 + 2D + 1]*y = e^(-x)/x^2 + 3^x + cos(2x - 1) [3 marks]
  10. Q2(d). Solve the simultaneous differential equation: dx/dt + dy/dt - 2y = 2*cos(t) - 7*sin(t), dx/dt - dy/dt + 2x = 4*cos(t) - 3*sin(t) [3 marks]
  11. Q3. Attempt any three parts of the following.
  12. Q3(a). Prove that x^2*J_n'' = (n^2 - n - x^2)*J_n + x*J_(n+1), where n is positive integer. [3 marks]
  13. Q3(b). Show that d/dx(J_n^2 + J_(n+1)^2) = 2*(n/x*J_n^2 - (n+1)/x*J_(n+1)^2) [3 marks]
  14. Q3(c). Prove that ∫(-1 to 1) x*P_n*P_n' = 2n/(2n+1) and ∫(0 to 2π) √π*x*J_1/2(2x) dx = 1 [3 marks]
  15. Q3(d). Show that ∫(-1 to 1) (1 - x^2)*P_n'*P_m' dx = {0, m ≠ n; 2n(n+1)/(2n+1), m = n} [3 marks]