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

RTU Engineering Mathematics-I 2025 Paper Review

Preparing for the Rajasthan Technical University B.Tech Engineering Mathematics-I exam requires intensive practice and a strong grasp of formulas. The 2025 paper tests your ability to solve complex multivariable calculus and series 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 mathematical definitions 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 derivations 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.

Calculus, Sequences, and Series

You must understand improper integrals and the properties of Beta and Gamma functions. Expect numerical problems asking you to evaluate surface areas and volumes of revolutions using definite integrals. For sequences and series, practice the tests for convergence, such as the ratio test and the root test. You must also know how to expand exponential and trigonometric functions using Taylor's and Maclaurin's series.

Fourier Series

This is a highly scoring section. You need to calculate the Fourier coefficients using Euler's formula for given periodic functions. Practice expanding functions into half range sine and cosine series. Memorize Parseval's theorem and understand how to apply it to deduce the sums of infinite series.

Multivariable Calculus (Differentiation)

Examiners frequently test your ability to find partial derivatives and total derivatives. You must find the maxima, minima, and saddle points of functions of two variables. Practice Lagrange's method of multipliers for constrained optimization problems. You must also calculate the gradient, curl, and divergence of vector functions.

Multivariable Calculus (Integration)

You must practice evaluating double and triple integrals in Cartesian coordinates. A frequent ten mark question will ask you to change the order of integration in a double integral. You will also need to change variables from Cartesian to polar coordinates to find areas, volumes, and the center of mass for regions with variable densities.

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 formula statements.

In Part A, answer directly. If the question asks for Euler's formula for Fourier coefficients, write the exact mathematical equations. Keep your answers factual and precise.

In Part B, show your working clearly. When testing a series for convergence, state the specific convergence test you are applying before executing the steps. This practice allows the evaluator to follow your logic easily.

In Part C, detail is essential. When changing the order of integration for a ten mark question, draw the region of integration clearly using a pencil. Write out every single step in your integration. 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 multiple integrals or calculating Fourier coefficients 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.