Engineering Mathematics-1 — Minor 2026 question paper
MMMUT Information Technology previous year question paper for Engineering Mathematics-1 (BSM-110), semester 1, Minor 2026. All 15 questions are listed below, each with a written answer on Nexsus.
Paper details
Subject: Engineering Mathematics-1 (BSM-110)
Branch: Information Technology
Semester: 1
Exam: Minor 2026
Questions: 15
Questions asked in Engineering Mathematics-1 Minor 2026
Q1. If u = f(2x - 3y, 3y - 4z, 4z - 2x), then prove that 1/2 ∂u/∂x + 1/3 ∂u/∂y + 1/4 ∂u/∂z = 0. [4 marks]
Q1. Attempt any three parts of the following.
Q1(b). If u, v, w are the roots of the cubic equation (λ - x)^3 + (λ - y)^3 + 4 (λ - z)^3 = 0 in λ, find Jacobian of u, v, w with respect to x, y and z. [4 marks]
Q1(c). Find the rank of the matrix....... [4 marks]
Q1(d). Using elementary transformations, find the inverse of the matrix A = [9 7 3; 5 -1 4; 3 4 1]. [4 marks]
Q2. Attempt any three parts of the following.
Q2(a). Expand ...... [3 marks]
Q2(b). if u=.... [3 marks]
Q2(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 [3 marks]
Q2(d). Determine λ and μ such that the equations x + y + z = 6, x + 2y + 3z = 10 and x + 2y + λz = μ have (i) no solution (ii) a unique solution (iii) infinite number of solutions. [3 marks]
Q3. Attempt any three parts of the following.
Q3(a). Verify Cayley-Hamilton theorem for the matrix ....... [3 marks]
Q3(b). Expand f(x, y) = tan^(-1) (xy) in Taylor's series about the (1, -1) up to the second-degree terms and hence evaluate f(1, 0.9). [3 marks]
Q3(c). Examine for minimum and maximum values of the function u = sin x + sin y + sin(x + y) [3 marks]
Q3(d). Find the eigen values and corresponding eigen vectors of the following matrix.... [3 marks]