THEORY EXAMINATION 2024-25 ENGINEERING MATHEMATICS-I
B.Tech
Engineering
53 downloads
₹29.00
📄 Question Paper Overview
The examination is for the 2024-25 academic session, with a total duration of 3 hours and a Maximum Marks (M.Marks) of 70.
Subject: Engineering Mathematics-I
Subject Code: BAS103
Level: B.Tech (SEM I) Theory Examination
Time: 3 HRS
Max Marks: 70
Identification Code: QP25DP2_290
Date/Time of Print: 03-Mar-2025 9:02:08 AM
🔢 Structure and Content
The paper is divided into three sections (A, B, and C), covering core areas of Engineering Mathematics, including Linear Algebra, Differential Calculus, Integral Calculus, and Vector Calculus.
Section A: Short Answer Questions (Total Marks: 14)
Consists of seven compulsory questions (Q. No. 1, parts a-g), each carrying 2 marks.
Questions require brief answers, direct computations, or statements of definitions/theorems (K1, K2, K3, K4 levels).
Topics covered:
Finding eigen values of a specific $2\times 2$ matrix.
Verifying Euler's theorem for homogeneous functions ($x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y}$).
Difference between total and partial derivatives.
Applications of Jacobians.
Statement of Liouville’s Theorem (in the context of calculus/integrals).
Evaluating a simple double integral.
Proving $\text{curl } \vec{r} = 0$.
Section B: Medium Answer Questions (Total Marks: 21)
Requires attempting any three out of five given questions (Q. No. 2, parts a-e).
Each question carries 7 marks.
These questions primarily involve standard derivations, finding series, or applying theorems (K2, K3, K4, K5 levels).
Topics covered:
Finding non-singular matrices P and Q to reduce a matrix A to its Normal Form (Linear Algebra).
Finding the $n^{th}$ derivative of $\tan^{-1}(x/a)$ (Differential Calculus).
Finding the volume of the largest rectangular parallelepiped inscribed in an ellipsoid (Maxima/Minima, Application of Multivariable Calculus).
Applying Dirichlet’s theorem to evaluate a triple integral over an ellipsoid.
Showing that the vector $\vec{F} = f(r)\vec{r}$ is irrotational (Vector Calculus).
Section C: Long Answer/Numerical Questions (Total Marks: 35)
Consists of five main questions (Q. No. 3 to Q. No. 7).
In each of the five questions, candidates must attempt any one part (a or b), with each part carrying 7 marks.
The questions are analytical, descriptive, or involve extensive calculations/proofs (K1 to K5 levels).
Q. No.
Topic Area
Part (a)
Part (b)
3
Linear Algebra
Find eigen values and eigen vectors of a given $3\times 3$ matrix $\text{A}$.
Discuss the existence and nature of the solution for a given system of linear equations for all values of $\text{K}$.
4
Differential Calculus
Trace the curve $y^2(a+x) = x^2(3a-x)$.
Prove the relation $\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = f''(r) + \frac{1}{r} f'(r)$, where $u = f(r)$ and $r^2 = x^2 + y^2$.
5
Multivariable Calculus
Find the Jacobian $\frac{\partial(x, y, z)}{\partial(u, v, w)}$ given $u=xyz$, $v=x^2+y^2+z^2$, $w=x+y+z$.
Find the maxima and minima of the function $\sin x + \sin y + \sin(x+y)$.
6
Integral Calculus
Find the area inside the circle $r=2a \cos\theta$ and outside the circle $r=a$ (Polar Coordinates).
Change the order of integration and then evaluate the given double integral.
7
Vector Calculus
Show that $\text{div}(\text{grad } r^n) = n(n+1)r^{n-2}$.
Verify Stokes' theorem for the vector field $\vec{F} = (x^2+y^2)\hat{i} - 2xy\hat{j}$ over a rectangle bounded by $x=0, x=a, y=0, y=b$.
File Size
175.61 KB
Uploader
Ajay sahu
Download
Continue to the SuGanta to download this note securely.
This is Kishan Kumar Dubey. I have done my schooling from CBSE, graduation from CSJMU, post graduation from ASU and appear in B.Ed. from MGKVP on aided seat.
I have 2 years experience in academic class (Future Shapers C...
I have 10+ years of experience in teaching maths physics and chemistry for 10th 11th 12th and intermediate students all my students till today are 90% grade. Even an average student got 90%
I am an experienced teacher ,worked with many reputed institutions Mount Carmel Convent , Chandrapur Maharashtra India, St Paul’s H.S Hyderabad, Fiitjee school Narayanaguda.
I have handled students of different age gr...
Hi, I’m Shifna Sherin! I believe that every student has the potential to excel in Math with the right guidance. I offer dedicated tutoring for 10th-grade students, covering everything from foundational basics to advanced...
Excellence in Language. Leadership in Results.
With over 18 years of distinguished experience, Réussi Academy of Language stands as a trusted name in foreign language and communication training. Foun...
IGS Institute provide classes for SSC, Bank, Railway, Police, NDA, Airforce Group X and Group Y, Teaching exams. IGS - Institute for Government Services providing classes since 2018 to the students.
