#1Repeated 3 Times[5 Marks]Derivatives and its Applications
State Leibnitz's theorem. If $y = (x^2 - 1)^n$, then use the Leibnitz's theorem to prove $(x^2 - 1)y_{n+2} + 2xy_{n+1} - n(n+1)y_n = 0$.
Appeared in:2083 Baishakh2082 Shrawan2081 Bhadra
ENSH 101Bachelor in Agriculture Engineering · Semester 12 Papers Available
Engineering Mathematics I
Past examination question papers and complete curriculum syllabus for Engineering Mathematics I (ENSH 101), Bachelor in Agriculture Engineering Semester 1 under Institute of Engineering (IOE), Tribhuvan University.
Past Question Papers (PDF)
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Most Frequently Asked Questions
Top recurring IOE board exam questions for Engineering Mathematics I with verified mark schemes, formula notation, and recurrence frequency.
Showing 30 of 30 top repeated questions
Derivatives and its Applications
9 Questions#2Repeated 3 Times[5 Marks]Derivatives and its Applications
State L'Hospital's Rule and evaluate $\lim_{x \to 0} \left(\frac{\sin x}{x}\right)^{1/x^2}$.
Appeared in:2083 Baishakh2082 Shrawan2081 Bhadra
#3Repeated 3 Times[5 Marks]Derivatives and its Applications
Assuming the validity of expansion, apply Maclaurin's theorem to expand $\log(1 + \tan x)$ as far as the term in $x^3$.
Appeared in:2082 Shrawan2080 Baishakh2078 Bhadra
#4Repeated 3 Times[5 Marks]Derivatives and its Applications
State and prove Lagrange's Mean Value theorem. Verify it for the function $f(x) = \log x$ in the interval $[1, e]$.
Appeared in:2081 Bhadra2081 Baishakh2076 Ashwin
#5Repeated 3 Times[5 Marks]Derivatives and its Applications
Find the radius of curvature at the origin for the curve $x^3 + y^3 = 3axy$.
Appeared in:2081 Bhadra2079 Baishakh2075 Ashwin
#6Repeated 3 Times[5 Marks]Derivatives and its Applications
Find the radius of curvature of the cycloid $x = a(\theta + \sin\theta), y = a(1 - \cos\theta)$ at any point $\theta$.
Appeared in:2082 Shrawan2080 Bhadra2078 Kartik
#7Repeated 2 Times[5 Marks]Derivatives and its Applications
Define asymptotes and explain their types. Find the asymptotes of the curve $x^2 y^2 - x^2 y - x y^2 + x + y + 1 = 0$.
Appeared in:2083 Baishakh2081 Bhadra
#8Repeated 2 Times[5 Marks]Derivatives and its Applications
State Rolle's theorem and verify the theorem for the function $f(x) = e^{-x} \sin x, x \in [0, \pi]$.
Appeared in:2083 Baishakh2081 Bhadra
#9Repeated 1 Times[5 Marks]Derivatives and its Applications
Find the pedal equation of the curve $y^2 = 4a(x + a)$.
Appeared in:2083 Baishakh
Antiderivatives and its Applications
8 Questions#1Repeated 3 Times[5 Marks]Antiderivatives and its Applications
Show that $\int_0^1 \cot^{-1}(1 - x + x^2)\,dx = \frac{\pi}{2} - \log 2$.
Appeared in:2082 Shrawan2079 Bhadra2076 Chaitra
#2Repeated 3 Times[5 Marks]Antiderivatives and its Applications
Using the rule of differentiation under the integral sign, evaluate $\int_0^{\pi/2} \frac{\log(1 + \cos\alpha \cos x)}{\cos x}\,dx$.
Appeared in:2081 Bhadra2078 Bhadra2075 Chaitra
#3Repeated 3 Times[5 Marks]Antiderivatives and its Applications
Find the area enclosed by the curve $y^2(2a - x) = x^3$ (cissoid of Diocles) and its asymptote.
Appeared in:2081 Bhadra2079 Baishakh2074 Chaitra
#4Repeated 3 Times[5 Marks]Antiderivatives and its Applications
Find the volume of the solid generated by the revolution of the cardioid $r = a(1 - \cos\theta)$ about the initial line.
Appeared in:2082 Baishakh2081 Baishakh2078 Bhadra
#5Repeated 2 Times[5 Marks]Antiderivatives and its Applications
Apply differentiation under the integral sign to evaluate $\int_0^\infty e^{-ax}\frac{\sin x}{x}\,dx$ and then show that $\int_0^\infty \frac{\sin x}{x}\,dx = \frac{\pi}{2}$.
Appeared in:2083 Baishakh2082 Baishakh
#6Repeated 2 Times[5 Marks]Antiderivatives and its Applications
Define Gamma function and use it to show that $\int_0^{\pi/2} \cos^4\theta \sin^2\theta\, d\theta = \frac{\pi}{32}$.
Appeared in:2083 Baishakh2082 Shrawan
#7Repeated 2 Times[5 Marks]Antiderivatives and its Applications
Find the surface area of solid generated by revolving the cycloid $x = a(\theta + \sin\theta), y = a(1 - \cos\theta)$ about its base.
Appeared in:2083 Baishakh2082 Shrawan
#8Repeated 1 Times[5 Marks]Antiderivatives and its Applications
Show that $\int_0^\pi \frac{x \sin x}{1 + \cos^2 x}\,dx = \frac{\pi^2}{4}$.
Appeared in:2083 Baishakh
Ordinary Differential Equations and its Applications
7 Questions#1Repeated 3 Times[5 Marks]Ordinary Differential Equations and its Applications
Solve the differential equation: $\frac{dy}{dx} + x \sin 2y = x^3 \cos^2 y$.
Appeared in:2083 Baishakh2082 Shrawan2081 Bhadra
#2Repeated 3 Times[5 Marks]Ordinary Differential Equations and its Applications
Solve the differential equation $x^2 \frac{d^2y}{dx^2} + x \frac{dy}{dx} + y = \log x$.
Appeared in:2083 Baishakh2082 Shrawan2081 Bhadra
#3Repeated 3 Times[5 Marks]Ordinary Differential Equations and its Applications
Find the general and singular solutions of the differential equation $y = px + \frac{a}{p}$, where $p = \frac{dy}{dx}$.
Appeared in:2081 Bhadra2082 Baishakh2076 Ashwin
#4Repeated 3 Times[5 Marks]Ordinary Differential Equations and its Applications
Solve the differential equation: $\frac{dy}{dx} + y \log y = x y e^x$.
Appeared in:2082 Baishakh2079 Baishakh2076 Chaitra
#5Repeated 3 Times[5 Marks]Ordinary Differential Equations and its Applications
Solve the differential equation: $(D^2 - 4D + 4)y = 8x^2 e^{2x}$.
Appeared in:2081 Bhadra2080 Bhadra2078 Bhadra
#6Repeated 2 Times[5 Marks]Ordinary Differential Equations and its Applications
Solve the differential equation $(D^2 + 2D + 5)y = e^{-x} \sin x$.
Appeared in:2083 Baishakh2082 Baishakh
#7Repeated 1 Times[5 Marks]Ordinary Differential Equations and its Applications
Find the general solution of $y = 2px + y^2 p^3$, where $p = \frac{dy}{dx}$.
Appeared in:2083 Baishakh
Plane Analytic Geometry
6 Questions#1Repeated 3 Times[5 Marks]Plane Analytic Geometry
Transform the equation $72x^2 - 120xy + 32y^2 + 74x - 50y + 2 = 0$ by translating the axes into an equation with linear terms missing.
Appeared in:2082 Shrawan2079 Bhadra2075 Ashwin
#2Repeated 3 Times[5 Marks]Plane Analytic Geometry
Derive the equation of a hyperbola in standard form $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$.
Appeared in:2081 Bhadra2078 Bhadra2074 Chaitra
#3Repeated 3 Times[5 Marks]Plane Analytic Geometry
Describe and sketch the graph of the polar equation of the conic $r = \frac{12}{3 + 2\cos\theta}$. Identify its eccentricity, directrix, and vertices.
Appeared in:2082 Baishakh2081 Baishakh2078 Kartik
#4Repeated 2 Times[5 Marks]Plane Analytic Geometry
Identify the conic $x^2 + 6xy + y^2 - 4x + 4y + 12 = 0$, and hence find its center and the length of axes.
Appeared in:2083 Baishakh2082 Baishakh
#5Repeated 2 Times[5 Marks]Plane Analytic Geometry
Find the angle through which the axes must be turned so that the equation $x + 2y + 5 = 0$ may be reduced to the form $x = c$ and determine the value of $c$.
Appeared in:2083 Baishakh2082 Baishakh
#6Repeated 2 Times[5 Marks]Plane Analytic Geometry
Derive the standard equation of an ellipse.
Appeared in:2082 Shrawan2082 Baishakh
Curriculum Syllabus & Course Topics
Sourced from TU curriculum portalChapter-wise Units & Micro-Syllabus Topics (5 Units)
1. Derivatives and its Applications
- 1.1Review of derivative and differentiability, mean value theorems with interpretations
- 1.2Indeterminate forms, types and their real life examples, L-Hospital's rule
- 1.3Power series of single valued functions
- 1.3.1Taylor's series
- 1.3.2Maclaurin's series
- 1.4Asymptotes to C artesian and Polar curves
- 1.5Pedal equation to Cartesian and Polar curves
- 1.6Curvature and radius of curvature for Cartesian curves
2. Antiderivatives and its Applications
- 2.1Review of definite and indefinite integrals
- 2.2Differentiation under integral sign
- 2.3Improper integrals
- 2.4Application of Beta and Gamma functions
- 2.5Area, arc length, volume and surface of revolution in plane for Cartesian curves
- 2.6Centroid and moment of inertia under area of curve
3. Ordinary Differential Equations and its Applications
- 3.1Review of order, degree, solution of first order first degree differential equations by variable separation method and solution of homogeneous equations
- 3.2Linear differential equation and equations reducible to linear differential equation of first order Bernoulli’s equation, modeling electric circuit
- 3.3First order and higher degree differential equations; Clairaut’s form
- 3.4Linear second order differential equations with constant coefficient and variable coefficients reducible to constant coefficients, Cauchy’s equations and modeling mass spring system
- 3.5Application in physical sciences and engineering
4. Plane Analytic Geometry
- 4.1Transformation of coordinates: Translation and rotation
- 4.2Equation of conic in Cartesian and Polar form, identification of conics
5. Three dimensional geometry
- 5.1The straight line: Symmetrical and general form
- 5.2Coplanar lines
- 5.3Shortest distance
- 5.4Sphere: General equation, plane section by planes, tangent planes
- 5.5Introduction to right circular cone and right circular cylinder
Examination Scheme & Marks Distribution
Evaluation Structure
- Final Board Theory Exam: 60 Marks (Pass mark: 24)
- Internal Assessment: 40 Marks (Pass mark: 16)
- Practical / Lab Exam: 25 or 50 Marks (Continuous lab evaluation + viva, where applicable)
* This is the general current IOE 60/40 scheme; verify course-specific details in the syllabus above.
Exam Preparation Guidelines
- Review the 2 available past examination papers to identify recurring patterns, core problem types, and chapter weightage.
- Practice numerical problems step-by-step with clean formula derivations, clear units, and standard assumptions.
- Structure answers with labeled diagrams, concise bullet points, and highlight final answers in numerical solutions.
Frequently Asked Questions (Engineering Mathematics I)
Q: How can I download Engineering Mathematics I past question papers?
You can preview or download the Engineering Mathematics I question papers (PDF) directly using the built-in viewer on this page with zero redirects or paywalls.
Q: What is the pass mark for Engineering Mathematics I?
The general current scheme is a 60-mark final theory exam and a 40-mark internal assessment, with pass marks of 24 and 16. Verify the course-specific syllabus above.
Q: Where can I find the complete syllabus for this subject?
The available chapter-wise syllabus and topic breakdown is indexed in the Syllabus section above, with links to the curriculum PDF source.
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Curriculum Syllabus & Marking Scheme