RTU Kota B.Tech 1st Year Engineering Mathematics-II Question Paper 2025

RTU Engineering Mathematics-II 2025 Paper Review

Preparing for the Rajasthan Technical University B.Tech Engineering Mathematics-II exam requires intensive practice and a strong grasp of formulas. The 2025 paper tests your ability to solve complex calculus and differential equation problems. Reviewing this paper shows you exactly how examiners structure the questions and allocate marks among the syllabus modules. This preparation allows you to approach your semester exam confidently.

Understanding the Exam Pattern

The RTU theory examination is a three hour paper worth 70 marks. The paper consists of three distinct sections.

• Part A: This section contains ten compulsory questions worth two marks each. You must solve very short numerical problems or state theorems under 30 words.
• Part B: You will find seven questions here. You must answer five of them. Each question is worth four marks. Your answers require multi step calculations.
• Part C: This section offers five major questions. You need to answer three. Each question carries ten marks. These require lengthy mathematical proofs and detailed problem solving.

Core Topics Evaluated in the Paper

The 2025 question paper covers several critical modules. Focus your study time on these specific areas to maximize your score.

Matrices

You must calculate the rank of a matrix by reducing it to normal form or echelon form. Practice finding eigenvalues and eigenvectors for 3x3 matrices. Examiners frequently ask you to verify the Cayley Hamilton theorem and use it to find the inverse of a given matrix.

Ordinary Differential Equations

This section carries high weightage. You need to solve first order exact differential equations. Practice higher order linear differential equations with constant coefficients. You must master the method of variation of parameters and solve Cauchy Euler homogeneous equations.

Partial Differential Equations

Study Lagrange linear equations and Charpit method for non linear equations. You will see questions asking you to find the complementary function and particular integral for homogeneous linear partial differential equations with constant coefficients.

Multiple Integration

Practice evaluating double and triple integrals. Examiners consistently ask you to change the order of integration in double integrals. You must know how to apply multiple integrals to calculate the area of plane curves and the volume of solid figures using polar and cylindrical coordinates.

Vector Calculus

You need to calculate the gradient of a scalar field, as well as the divergence and curl of a vector field. Memorize the statements and formulas for Green theorem, Gauss divergence theorem, and Stokes theorem. Expect a ten mark question asking you to verify one of these theorems for a given vector function over a specific surface.

Answer Writing Strategy for High Marks

RTU evaluators look for clear logical steps and correct final answers. Use a blue pen for your calculations and a black pen for writing final answers and theorem statements.

In Part A, answer directly. If the question asks for the statement of Stokes theorem, write the exact mathematical formula. Keep your answers factual and precise.

In Part B, show your working clearly. When calculating the rank of a matrix, state the row or column operations you apply at each step. This practice allows the evaluator to follow your logic easily.

In Part C, detail is essential. When solving a ten mark differential equation, write down the auxiliary equation, find the roots clearly, and state the rules used for the particular integral. Write out every single step in your integrations. The university marking system awards step by step marks even if your final numerical answer contains an arithmetic error. Draw a box around your final calculated answers to make them visible.

Time Management During the Exam

Allocate 20 minutes to Part A. Spend 40 minutes on Part B. Reserve the remaining 120 minutes for the three long answer questions in Part C. Solving triple integrals or verifying Gauss divergence theorem takes significant time. This structure gives you 40 minutes per major question, allowing you to recheck your integration limits and verify your mathematical signs. Use the final 10 minutes to review your answers and ensure you copied the question data correctly from the paper.