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Engineering Mathematics-I — Major (End Semester) 2026 question paper

MMMUT Information Technology previous year question paper for Engineering Mathematics-I (BSM-110), semester 1, Major (End Semester) 2026. All 24 questions are listed below, each with a written answer on Nexsus.

Paper details

  • Subject: Engineering Mathematics-I (BSM-110)
  • Branch: Information Technology
  • Semester: 1
  • Exam: Major (End Semester) 2026
  • Questions: 24

Questions asked in Engineering Mathematics-I Major (End Semester) 2026

  1. Q1. Attempt any five parts of the following.
  2. Q1(a). Determine λ and μ such that the equations x+y+z=6 , x+2y+3z=10 and x+2y+λz= μ have a unique solution. [2 marks]
  3. Q1(b). Using elementary operation, reduce the following matrix into unit matrix [2 marks]
  4. Q1(c). Show that the equations 3x+4y+5z=a, 4x+5y+6z=b, 5x+6y+7z=c do not have solution unless a+b=2c and solve it in each case. [2 marks]
  5. Q1(d). If u=sin nx+cos nx , then show that...... [2 marks]
  6. Q1(e). If u=...... [2 marks]
  7. Q1(f). Examine f(x,y)=x^3+y^3-12x-3y+20 for its extreme points. Hence find its extreme value. [2 marks]
  8. Q1(g). If .............. then find J(u,v,w). [2 marks]
  9. Q2. Attempt any two parts of the following.
  10. Q2(a). (a). Evaluate ......(i).... (ii)..... [5 marks]
  11. Q2(b). Evaluate...... [5 marks]
  12. Q2(c). Find the volume and mass contained in the solid region of the positive octant of the surface ...... [5 marks]
  13. Q3. Attempt any two parts of the following.
  14. Q3(a). i. Evaluate the integral..... ii. Evaluate by changing it in polar coordinates:..... [5 marks]
  15. Q3(b). Evaluate..... [5 marks]
  16. Q3(c). Change the order of integration in...... [5 marks]
  17. Q4. Attempt any two parts of the following. [5 marks]
  18. Q4(a). i. Find a and b if the surfaces ...... [5 marks]
  19. Q4(b). Show that the vector field....... [5 marks]
  20. Q4(c). c) A fluid motion is given by .......... [5 marks]
  21. Q5. Attempt any two parts of the following.
  22. Q5(a). i. Find the directional derivative of ..... ii. Find a, b, c when ...... [5 marks]
  23. Q5(b). Verify Green theorem in a plane for ....... [5 marks]
  24. Q5(c). c) Verify Gauss divergence theorem for ...... [5 marks]