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Previous year question hub

Numerical Methods - Engineering Mathematics - Mechanical Engineering Previous Year Questions

Practice Numerical Methods - Engineering Mathematics - Mechanical Engineering previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

20Papers
14Years
23Questions
1Topics

Numerical Methods question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Numerical Methods. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Easy 20 87%
Medium 3 13%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

MCQ 11 47.8%
Numerical Answer Type (NAT) 11 47.8%
Fill in the blanks 1 4.3%

Subject weightage

Top subjects by unique question coverage.

Mechanical Engineering
23 Qs

Most asked topics

Top topics across the included previous year papers.

Engineering Mathematics
23 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Numerical Methods
23 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

Mechanical Engineering (ME) 2026
2 Qs
Mechanical Engineering (ME) 2025
1 Qs
Mechanical Engineering (ME) 2024
1 Qs
Mechanical Engineering (ME) 2023
1 Qs
Mechanical Engineering (ME) 2021 [Session 1]
1 Qs
Mechanical Engineering (ME) 2020 [Session 1]
1 Qs
Mechanical Engineering (ME) 2020 [Session 2]
1 Qs
Mechanical Engineering (ME) 2019 [Session 1]
1 Qs
Mechanical Engineering (ME) 2019 [Session 2]
1 Qs
Mechanical Engineering (ME) 2018 [Session 1]
1 Qs
Mechanical Engineering (ME) 2016 [Session 2]
2 Qs
Mechanical Engineering (ME) 2016 [Session 3]
1 Qs
Mechanical Engineering (ME) 2014 [Session 3]
2 Qs
Mechanical Engineering (ME) 2014 [Session 1]
1 Qs
Mechanical Engineering (ME) 2014 [Session 2]
1 Qs
Mechanical Engineering (ME) 2014 [Session 4]
1 Qs
Mechanical Engineering (ME) 2013 [Session 3]
1 Qs
Mechanical Engineering (ME) 2011
1 Qs
Mechanical Engineering (ME) 2010
1 Qs
Mechanical Engineering (ME) 2007
1 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
Mechanical Engineering (ME) 202620262View paper
Mechanical Engineering (ME) 202520251View paper
Mechanical Engineering (ME) 202420241View paper
Mechanical Engineering (ME) 202320231View paper
Mechanical Engineering (ME) 2021 [Session 1]20211View paper
Mechanical Engineering (ME) 2020 [Session 1]20201View paper
Mechanical Engineering (ME) 2020 [Session 2]20201View paper
Mechanical Engineering (ME) 2019 [Session 1]20191View paper
Mechanical Engineering (ME) 2019 [Session 2]20191View paper
Mechanical Engineering (ME) 2018 [Session 1]20181View paper
Mechanical Engineering (ME) 2016 [Session 2]20162View paper
Mechanical Engineering (ME) 2016 [Session 3]20161View paper
Mechanical Engineering (ME) 2014 [Session 1]20141View paper
Mechanical Engineering (ME) 2014 [Session 2]20141View paper
Mechanical Engineering (ME) 2014 [Session 3]20142View paper
Mechanical Engineering (ME) 2014 [Session 4]20141View paper
Mechanical Engineering (ME) 2013 [Session 3]20131View paper
Mechanical Engineering (ME) 201120111View paper
Mechanical Engineering (ME) 201020101View paper
Mechanical Engineering (ME) 200720071View paper

All Numerical Methods previous year questions

Practice every matching question in batches of 20, with every available option.

1
2007 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2007
A calculator has accuracy up to 8 digits after decimal place. The value of \( \int_{0}^{2\pi} \sin x dx \) when evaluated using this calculator by trapezoidal method with 8 equal intervals, to 5 significant digits is
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2
2010 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2010

5 skilled workers can build a wall in 20 days; 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30 days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?

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3
2011 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2011
The integral \( \int_{1}^{3} \frac{1}{x} dx \), when evaluated by using Simpson’s 1/3 rule on two equal subintervals each of length 1, equals
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4
2013 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2013 [Session 3]
Match the CORRECT pairs.

Question diagram

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5
2014 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2014 [Session 1]
Using the trapezoidal rule, and dividing the interval of integration into three equal subintervals, the definite integral \(\int_{-1}^{1} |x| dx\) is ______
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6
2014 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2014 [Session 2]
The value of \(\int_{2.5}^{4} \ln(x)dx\) calculated using the Trapezoidal rule with five subintervals is ______
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7
2014 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2014 [Session 3]
The real root of the equation \(5x = 2\cos x - 1 = 0\) (up to two decimal accuracy) is ________
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8
2014 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2014 [Session 3]
The definite integral ∫₁³ (1/x) dx is evaluated using Trapezoidal rule with a step size of 1. The correct answer is ______
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9
2014 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2014 [Session 4]
Consider an ordinary differential equation dx/dt = 4t + 4. If x = x₀ at t = 0, the increment in x calculated using Runge-Kutta fourth order multi-step method with a step size of Δt = 0.2 is
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10
2016 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2016 [Session 2]
The error in numerically computing the integral \(\int_{0}^{\pi}(\sin x + \cos x) dx\) using the trapezoidal rule with three intervals of equal length between 0 and \(\pi\) is __________
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11
2016 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2016 [Session 2]
Numerical integration using trapezoidal rule gives the best result for a single variable function, which is
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12
2016 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2016 [Session 3]
The root of the function \( f(x) = x^3 + x - 1 \) obtained after first iteration on application of Newton-Raphson scheme using an initial guess of \( x_0 = 1 \) is
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13
2018 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2018 [Session 1]
An explicit forward Euler method is used to numerically integrate the differential equation \[ \frac{dy}{dt} = y \] using a time step of 0.1. With the initial condition \( y(0) = 1 \), the value of \( y(1) \) computed by this method is __________ (correct to two decimal places).
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14
2019 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2019 [Session 1]
Evaluation of \(\int_{2}^{4} x^{3} dx\) using a 2-equal-segment trapezoidal rule gives a value of ______
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15
2019 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2019 [Session 2]
The derivative of \(f(x) = \cos(x)\) can be estimated using the approximation \(f'(x) = \frac{f(x+h) - f(x-h)}{2h}\). The percentage error is calculated as \(\left(\frac{\text{Exact value} - \text{Approximate value}}{\text{Exact value}}\right) \times 100\). The percentage error in the derivative of \(f(x)\) at \(x = \pi/6\) radian, choosing \(h = 0.1\) radian, is
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16
2020 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2020 [Session 1]
The evaluation of the definite integral \(\int_{-1}^{1.4} x|x| dx\) by using Simpson's 1/3rd (one-third) rule with step size \(h = 0.6\) yields
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17
2020 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2020 [Session 2]
For the integral ∫₀^{π/3} (8 + 4 cos x) dx, the absolute percentage error in numerical evaluation with the Trapezoidal rule, using only the end points, is ______________ (round off to one decimal place).
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18
2021 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2021 [Session 1]
The ordinary differential equation \(\frac{dy}{dt} = -\pi y\) subject to an initial condition \(y(0) = 1\) is solved numerically using the following scheme:
\[\frac{y(t_{n+1}) - y(t_n)}{h} = -\pi y(t_n)\]
where \(h\) is the time step, \(t_n = nh\), and \(n = 0, 1, 2, ...\). This numerical scheme is stable for all values of \(h\) in the interval ________.
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19
2023 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2023
The initial value problem \[ \frac{dy}{dt} + 2y = 0, \quad y(0) = 1 \] is solved numerically using the forward Euler’s method with a constant and positive time step of \( \Delta t \).
Let \( y_n \) represent the numerical solution obtained after \( n \) steps. The condition \( |y_{n+1}| \leq |y_n| \) is satisfied if and only if \( \Delta t \) does not exceed ______.
(Answer in integer)
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20
2024 · Mechanical Engineering · Engineering Mathematics · Numerical Methods
Mechanical Engineering (ME) 2024
In order to numerically solve the ordinary differential equation \(\frac{dy}{dt} = -y\) for \(t > 0\), with an initial condition \(y(0) = 1\), the following scheme is employed \[\frac{y_{n+1} - y_n}{\Delta t} = -\frac{1}{2}(y_{n+1} + y_n).\] Here, \(\Delta t\) is the time step and \(y_n = y(n\Delta t)\) for \(n = 0, 1, 2, ...\). This numerical scheme will yield a solution with non-physical oscillations for \(\Delta t > h\). The value of \(h\) is
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Showing 20 of 23 questions