The document contains the questions from the Fourth Semester B.E. Degree Examination in Engineering Mathematics - IV. It has two parts, Part A and Part B, with multiple choice questions in each part. Some of the questions in Part A ask students to use numerical methods like Picard's method, Euler's modified method, and Runge-Kutta method of fourth order to solve initial value problems and solve systems of simultaneous equations. Other questions in Part B involve topics like analytic functions, harmonic functions, and Legendre polynomials. Students are required to solve five full questions by selecting at least two from each part.