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 UniversitySummer 2026 examination

GTU BE03005041 Numerical Methods in Chemical Engineering Summer 2026 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 2:30 PM – 5:00 PM
Questions: 5 with internal choice

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Q.1

14 Marks

(a)

3 marks

Find the relative error if the number $X = 0.004997$ is

itruncated to three decimal digits

iirounded off to three decimal digits.

(b)

4 marks

The area of cross-section of a rod is desired up to 0.2% error. How accurately should the diameter be measured?

(c)

7 marks

Using the Runge-Kutta method of fourth order, solve for y at $x = 1.2$ and $x = 1.4$ , given $x_0 = 1, y_0 = 0$ .

\dfrac{dy}{dx} = \dfrac{2xy + e^x}{x^2 + xe^x}

Q.2

14 Marks

(a)

3 marks

Describe intermediate value properties.

(b)

4 marks

Explain algorithm for finding the root of an equation using Newton-Raphson method.

(c)

7 marks

Use the method of false position, to find the fourth root of 32 correct to three decimal places.

(c)

7 marks

Using the bisection method find a positive real root of, $x \log_{10} x = 1.2$

Q.3

14 Marks

(a)

3 marks

Explain in brief about ordinary differential equations - boundary value problems.

(b)

4 marks

The velocity v(km/min) of a moped which starts from rest, is given at fixed intervals of time t (min) as follows, Estimate approximately the distance covered in twenty minutes.

t:	2	4	6	8	10	12	14	16	18	20
v:	10	18	25	29	32	20	11	5	2	0

(c)

7 marks

Solve the equations using Gauss-Jordan method. $10x - 7y + 3z + 5u = 6$ $-6x + 8y - z - 4u = 5$ $3x + y + 4z + 11u = 2$ $5x - 9y - 2z + 4u = 7$

(a)

3 marks

List out the interpolation methods, which can be used when data points are available at unequal intervals.

(b)

4 marks

A solid of revolution is formed by rotating about the x-axis, the area between the x-axis, the lines

x = 0

and

x = 1

and a curve through the points with the following co-ordinates, Estimate the volume of the solid formed using Simpson’s rule.

x:	0.00	0.25	0.50	0.75	1.00
y:	1.0000	0.9896	0.9589	0.9089	0.8415

(c)

7 marks

Find the eigenvalues and eigenvectors of the matrix, $A = \begin{bmatrix} 8 & -6 & 3 \\ -6 & 7 & -4 \\ 2 & -4 & 3 \end{bmatrix}$

Q.4

14 Marks

(a)

3 marks

Write an algorithm for trapezoidal rule.

(b)

4 marks

An experiment gave the following values, It is known that v and t are connected by the relation

v = at^b

. Find the best possible values of a and b.

v (ft/min):	350	400	50	600
t (min):	61	26	7	2.6

(c)

7 marks

Find the maximum and minimum value of y from the following data:

x:	-2	-1	0	1	2	3	4
y:	2	-0.25	0	-0.25	2	15.75	56

(a)

3 marks

Describe Milne’s predictor-corrector method.

(b)

4 marks

Find the least squares fit of the form

y = a_0 + a_1 x^2

to the following data,

x:	-1	0	1	2
y:	2	5	3	0

(c)

7 marks

A slider in a machine moves along a fixed straight rod. Its distance x cm along the rod is given below for various values of the time t seconds. Find the velocity of the slider and its acceleration when

t = 0.3\text{ second}

t =	0	0.1	0.2	0.3	0.4	0.5	0.6
x =	30.13	31.62	32.87	33.64	33.95	33.81	33.24

Q.5

14 Marks

(a)

3 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

(b)

4 marks

Using Milne’s method find

y(4.5)

given

5xy' + y^2 - 2 = 0

given

y(4) = 1, y(4.1) = 1.0049, y(4.2) = 1.0097, y(4.3) = 1.0143, y(4.4) = 1.0187

(c)

7 marks

Solve

x^4 - 5x^3 + 20x^2 - 40x + 60 = 0

, by Newton’s method given that all the roots of the given equation are complex.

(a)

3 marks

Determine

f(x)

as a polynomial in x for the following data:

x:	-4	-1	0	2	5
y = f(x):	1245	33	5	9	1335

(b)

4 marks

Using Lagrange’s formula, express the given function, a sum of partial fractions. $\dfrac{3x^2 + x + 1}{(x - 1)(x - 2)(x - 3)}$

(c)

7 marks

Solve by Taylor’s series method, here $y(1.1)$ and $y(1.2)$ , given $y(1) = 2$ .

\dfrac{dy}{dx} = \log(xy)

More Numerical Methods in Chemical Engineering papers

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About this paper

Official Gujarat Technological University (GTU) examination paper for Numerical Methods in Chemical Engineering (Summer 2026, 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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