Q.1
14 Marks(a)
Explain False position method.
(b)
Explain intermediate value property theorem.
(c)
Find the relative error if the number X = 0.004997 is
i)truncated to three decimal digits
ii)rounded off to three decimal digits.
Gujarat Technological UniversitySummer 2025 examination
GTU 3140510 Numerical Methods in Chemical Engineering Summer 2025 Question Paper & PDF
B.E. · Chemical Engineering · Semester 4 · Subject code 3140510
- Total
- 70 marks
- To pass
- 23 marks (33%)
- Duration
- 2.5 Hours 10:30 AM – 1:00 PM
- Questions
- 5 with internal choice
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Q.2
14 Marks(a)
Enlist various methods for solving linear algebraic equations.
(b)
Explain various types of errors in computations.
(c)
Find a root of the equation 𝑥³ − 4𝑥 − 9 = 0, using the bisection method correct to three decimal places.
OR
(c)
Find the root of the equation 𝑥𝑒𝑥 = cos 𝑥, using the secant method correct to four decimal places.
Q.3
14 Marks(a)
Explain Descarte’s rule of sign with example.
(b)
Find 𝑥2 of 𝑥⁴ − 𝑥 = 10, correct to three decimal places, using the Newton-Raphson method, where 𝑥0 = 2.
(c)
Solve the following equations using Gauss-Jacobi’s method. 27𝑥 + 6𝑦 − 𝑧 = 85; 𝑥 + 𝑦 + 54𝑧 = 110; 6𝑥 + 15𝑦 + 2𝑧 = 72
OR
(a)
Enlist Limitations of Newton-Raphson’s Method.
(b)
Solve the following equations by the Gauss elimination method:
𝑥 + 𝑦 + 𝑧 = 9; 2𝑥 − 3𝑦 + 4𝑧 = 13; 3𝑥 + 4𝑦 + 5𝑧 = 40
(c)
Fit a curve of the form 𝑦 = 𝑎𝑒𝑏𝑥, to the following data:
x: 0 1 2 3 y: 1.05 2.10 3.85 8.30
Q.4
14 Marks(a)
Find the iterative formula for finding √𝑁 where is N is real number, using Newton Raphson formula.
(b)
Explain working procedure of method of least square.
(c)
Find the missing values in the following data:
x: 45 50 55 60 65 y: 3.0 …… 2.0 ….. -2.4
OR
(a)
Write down normal equations to fit the straight line 𝑦 = 𝑎 + 𝑏𝑥.
(b)
Evaluate
i)∆ tan⁻¹ 𝑥,
ii)∆(𝑒𝑥𝑙𝑜𝑔2𝑥)
(c)
Find the cubic polynomial which takes the following values:
x: 0 1 2 y: 1 2 1 10 Hence evaluate 𝑓(4).
Q.5
14 Marks(a)
Write an algorithm for Newton’s Forward interpolation method.
(b)
Use the Trapezoidal rule to estimate the integral ∫ 𝑒𝑥²𝑑𝑥 2 0 taking the number 10 intervals.
(c)
Solve 𝑦′ = 𝑥 + 𝑦, 𝑦(0) = 1 by Taylor’s series method. Hence find the values of y at 𝑥 = 0.1 𝑎𝑛𝑑 𝑥 = 0.2.
OR
(a)
Write an algorithm for Trapezoidal Rule.
(b)
Discuss in brief about boundary problems.
(c)
Using Euler’s method, find an approximate value of y corresponding to 𝑥 = 1, given that 𝑑𝑦 𝑑𝑥 ⁄ = 𝑥 + 𝑦 𝑎𝑛𝑑 𝑦 = 1 𝑤ℎ𝑒𝑛 𝑥 = 0.
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About this paper
Official Gujarat Technological University (GTU) examination paper for Numerical Methods in Chemical Engineering (Summer 2025, B.E. · Chemical Engineering, Sem 4). Features complete 70-mark regular & remedial examination pattern, official marking distribution across all 5 questions, and direct 1-click official PDF download.
Transcribed for student exam preparation from Gujarat Technological University official examination archives. Questions, syllabus guidelines, and curriculum marking schemes remain the intellectual property of Gujarat Technological University.