Calculus and Linear Algebra — Major (End Semester) 2022 question paper
MMMUT Electronics and Communication Engineering previous year question paper for Calculus and Linear Algebra (BSM-101), semester 1, Major (End Semester) 2022. All 16 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: Major (End Semester) 2022
Questions: 16
Questions asked in Calculus and Linear Algebra Major (End Semester) 2022
Q1(a). If x = r cosθ, y = r sinθ, then show that [2 marks]
Q1(b). If u = sin nx + cos nx, then show that [2 marks]
Q1(c). Find the sum and product of all the Eigen values of the matrix [2 marks]
Q1(d). Compute the area bounded by the parabola y = x^2 + 2 and the straight lines x = 0, x = 1, x+y = 0. [2 marks]
Q1(e). Evaluate ∫∫x sin^2 x cos^2 x dx. [2 marks]
Q1(f). Find the directional derivative of → in direction of F, where → = xi + yj + zk and F = 1. [2 marks]
Q1(g). Show that curl(grad φ) = 0. Here φ is the scalar point function. [2 marks]
Q2(a). If u, v, w are the roots of the cubic equation (2-x)^2 + (A-y)^2 + (A-z)^2 = 0 in 2, then find [2 marks]
Q2(b). 1+L+I = 1, then prove that [2 marks]
Q2(c). Given 2=x^2% (g) + y*h (l), prove that [2 marks]
Q3(a). Find the inverse of following matrix by using elementary operations [2 marks]
Q3(b). Discuss the consistency of the following system of equations for various values of 2 [2 marks]