Chemical Engineering
GATE CH topic:numerical-methods PYQs
Build your understanding with focused practice from past exam papers.
How to practice topic:numerical-methods
Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.
Questions 1–10 of 16. Imported answers require independent review unless marked reviewed.
Question 35
Open questionCHNAT1 markNeeds review
Using single step trapezoid rule, the value of
is ______ (rounded off to two decimal places).Log in to check the answer
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Open questionCHNAT2 marksNeeds review
The data given in the table are fitted to the equation
using the method of least squares. The value of m is _____ (rounded off to one decimal place). | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| 2 | 6 | 7 | 10 |
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Open questionCHNAT2 marksNeeds review
The Newton-Raphson method is used to find the root of
Starting with an initial guess
, the second iterate
is ____ (rounded off to 2 decimal places).Log in to check the answer
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Open questionCHNAT2 marksNeeds review
The Newton-Raphson method is used to solve
, where
. If the initial guess
, the value of the next iterate,
, rounded off to 2 decimal places, is ______Log in to check the answer
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Open questionCHMCQ2 marksNeeds review
Simpson’s one-third rule is used to estimate the definite integral
with an interval length of 0.5. Which one of the following is the CORRECT estimate of
obtained using this rule?Your answerChoose one option.
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Open questionCHNAT1 markNeeds review
The area of a circular field is 25 m
. The radius,
, is to be determined using the Newton-Raphson iterative method. For an initial guess of
m, the revised estimate of
after one iteration is ________ m (rounded off to three decimal places).Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 46
Open questionCHNAT2 marksNeeds review
The equation
with the initial condition
is to be solved using a predictor-corrector approach. Use a predictor based on the implicit Euler’s method and a corrector based on the trapezoidal rule of integration, each with a full-step size of 0.5. Considering only positive values of
, the value of
at
is __________ (rounded off to three decimal places).Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 1
Open questionCHMCQ1 markNeeds review
An ordinary differential equation (ODE),
, with an initial condition
, has the analytical solution
. Using Runge-Kutta second order method, numerically integrate the ODE to calculate
at
using a step size of
. If the relative percentage error is defined as,
then the value of
at
is ________.Your answerChoose one option.
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To solve an algebraic equation
, an iterative scheme of the type
is proposed, where
. At the solution
,
and
. The order of convergence for this iterative scheme near the solution is ________.Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 1
Open questionCHMCQ1 markNeeds review
Which one of the following methods requires specifying an initial interval containing the root (i.e., bracketing) to obtain the solution of
, where
is a continuous non-linear algebraic function?Your answerChoose one option.
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