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Calculus and Linear Algebra — Minor 2 2021 question paper

MMMUT Electrical Engineering previous year question paper for Calculus and Linear Algebra (BSM-01), semester 1, Minor 2 2021. All 10 questions are listed below, each with a written answer on Nexsus.

Paper details

  • Subject: Calculus and Linear Algebra (BSM-01)
  • Branch: Electrical Engineering
  • Semester: 1
  • Exam: Minor 2 2021
  • Questions: 10

Questions asked in Calculus and Linear Algebra Minor 2 2021

  1. Q1(a)(i). Evaluate following integral by changing the order of integration ∫₀^√2-x² ∫₀^x (y / (x² + y²)) dydx [6 marks]
  2. Q1(a)(ii). Evaluate ∫₀¹ ∫₀^(1 - x³)⁵ dx
  3. Q1(b). Evaluate ∫₀^log2 ∫₀^x ∫₀^x+y e^(x+y+z) dx dy dz [4 marks]
  4. Q1(c). Show that Γ(m + 1/2) = (√π / 2^(2m-1)) Γ(2m) [4 marks]
  5. Q2(a)(I). In what direction from the point (1, 1,-2), the directional derivative of φ = x² - 2y² + 4z² is maximum? Also find the maximum value of directional derivative. [6 marks]
  6. Q2(a)(II). Show that div(grad rⁿ) = ∇²rⁿ = n(n + 1)rⁿ⁻²
  7. Q2(b). Evaluate ∫∫s F · ds if F = 4yî + 18zî – xk and S is the surface of the plane 3x + 2y + 6z = 6 contained in the first octant. [4 marks]
  8. Q2(c). Show that rⁿ î is solenoidal if n = -3 and irrotational for all values of n. Here 7 = xî + yî + zk and r = |7|. [4 marks]
  9. QQue 2.. Attempt any Two parts of the following. Q. 2 (a) is compulsory
  10. QQue1.. Attempt any Two parts of the following. Q. 1 (a) is compulsory.