What is the exam pattern and passing mark for GTU Numerical Methods in Chemical Engineering (BE03005041)?

The GTU theory examination carries 70 total marks with a duration of 2.5 Hours. Minimum passing criteria is 23 marks (33%). The paper consists of 5 main questions with official marking breakdown and internal choices.

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Gujarat Technological UniversityWinter 2025 examination

GTU BE03005041 Numerical Methods in Chemical Engineering Winter 2025 Question Paper & PDF

B.E. · Chemical Engineering · Semester 3 · Subject code BE03005041

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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.1

14 Marks

(a)

3 marks

Explain following terms: 1) Significant figures, 2) Truncation Error.

(b)

4 marks

Explain sources of arising errors in numerical computation.

(c)

7 marks

Round off the numbers 865250 and 37.46235 to four significant figures and compute

E_a

E_r

E_p

in each case.

Q.2

14 Marks

(a)

3 marks

Describe intermediate value properties theorem.

(b)

4 marks

Find a root of the equation

x^3 - x - 1 = 0

, using the bisection method correct to three decimal places.

(c)

7 marks

Find by Newton’s method, the real root of the equation

3x = \cos x + 1

,correct to four decimal places.

(c)

7 marks

Find the root of the equation

xe^x = \cos x

using the secant method correct to four decimal places.

Q.3

14 Marks

(a)

3 marks

Explain the Gauss Jordan method to solve the system of linear equations.

(b)

4 marks

Apply Gauss elimination method to solve the equations:

$x + 4y - z = -5; x + y - 6z = -12; 3x - y - z = 4$

(c)

7 marks

Apply the Gauss-Seidal iteration method to solve the equations. $20x + y - 2z = 17; 3x + 20y - z = -18; 2x - 3y + 20z = 25$

(a)

3 marks

Explain Eigen values and Eigen vectors.

(b)

4 marks

Find the eigenvalues and eigenvectors of the matrix

\begin{bmatrix} 5 & 4 \\ 1 & 2 \end{bmatrix}

(c)

7 marks

Solve by Jacobi’s iteration method, the equations correct to two decimal places. $10x + y - z = 11.19; x + 10y + z = 28.08; -x + y + 10z = 35.61$

Q.4

14 Marks

(a)

3 marks

Write down normal equations to fit the straight line

y = a + bx

(b)

4 marks

Fit a straight line to the following data:

x	6	7	7	8	8	8	9	9	10
y	5	5	4	5	4	3	4	3	3

(c)

7 marks

Find the missing term is the table:

x	2	3	4	5	6
y	45.0	49.2	54.1	....	67.4

(a)

3 marks

Establish the following identities:

\Delta = E - 1

\Delta = 1 - E^{-1}

(b)

4 marks

From the following table, estimate the number of students who obtained marks between 40 and 45:

Marks:	30-40	40-50	50-60	60-70	70-80
No. of Students:	31	42	51	35	31

(c)

7 marks

Find the distance moved by a particle and its acceleration at the end of 4 seconds, if the time verses velocity data is as follows:

t	0	1	3	4
v	21	15	12	10

Q.5

14 Marks

(a)

3 marks

Write the formula of Simpson’s one-third rule.

(b)

4 marks

Use the Trapezoidal rule to estimate the integral

\displaystyle\int_0^2 e^{x^2}\,dx

taking 10 intervals

(c)

7 marks

Using Euler’s method, find an approximate value of

y

corresponding to

x = 1

, given that

\dfrac{dy}{dx} = x + y

and

y = 1

when

x = 0

(a)

3 marks

Describe Milne’s predictor-corrector method.

(b)

4 marks

Solve

y' = x + y, y(0) = 1

by Taylor’s series method. Hence find the values of

y

x = 0.1

and

x = 0.2

(c)

7 marks

Apply the Runge-Kutta fourth order method to find an approximate value of

y

when

x = 0.2

given that

\dfrac{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 (Winter 2025, B.E. · Chemical Engineering, Sem 3). 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.

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