This kind of cheap question paper was made by Gujarat Technological University (GTU).

1. Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
ME – SEMESTER –I-(New) EXAMINATION – SUMMER- 2019
Subject Code: 3713007 Date: 08/05/2019
Subject Name: Mathematical and Statistical Methods in Chemical Engineering
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 [a] Write derivation of formula of weighted linear least square estimation. [7]
[b] The table below gives the temperature T in C0
and length l (in mm) of a heated
rod. If l = a0 + a1T , find the best values for a0 and a1.
T ( in C0
) 20 30 40 50 60 70
l (in mm) 800.3 800.4 800.6 800.7 800.9 801.0
[7]
Q.2 [a] Using Gauss Seidel Method solve the system of equations.
10𝑥1 − 2𝑥2 − 𝑥3 − 𝑥4 = 3
−2𝑥1 − 10𝑥2 − 𝑥3 − 𝑥4 = 15
−𝑥1 − 𝑥2 + 10𝑥3 − 2𝑥4 = 27
−𝑥1 − 𝑥2 − 2𝑥3 + 10𝑥4 = −9
[7]
[b] Using Gauss Elimination Method solve the system of equations.
2𝑥 + 𝑦 + 𝑧 = 10
3𝑥 + 2𝑦 + 3𝑧 = 18
𝑥 + 4𝑦 + 9𝑧 = 16
[7]
OR
[b] write short note on Iterative methods to solve Linear Algebraic Equations [7]
Q.3 [a] Design Newton iteration for cube roots and Compute 3
7 . [7]
[b] Find root of the equation x2
– logex – 12 = 0 correct to three decimal places
using bisection method.
[7]
OR

2. Q.3 [a] Solve the following system of nonlinear equations by Newton Raphson
method.
𝑥2
− 𝑦2
= 4 , 𝑥2
+ 𝑦2
= 16
[7]
[b] Find the root of 𝑓(𝑥) = 𝐶𝑜𝑠𝑥 − 𝑥 𝑒𝑥
correct upto three place of decimal by
using secant method.
[7]
Q.4 [a] Solve
𝑑𝑦
𝑑𝑥
= 𝑦𝑧 + 𝑥 ,
𝑑𝑧
𝑑𝑥
= 𝑥𝑧 + 𝑦 given that 𝑦(0) = 1 , 𝑧(0) = −1 find
𝑦(0.1) , 𝑧(0.1)
[7]
[b] Discussed the Predictor-corrector method for solving ordinary differential
equation and obtain 𝑦(0.8) for the equation 𝑦′
= 1 + 𝑦2
with 𝑦(0) =
0 , 𝑦(0.2) = 0.2027, 𝑦(0.4) = 0.4228 , 𝑦(0.6) = 0.6841.
[7]
OR
Q.4 [a] Explain Explicit Admas-Bashforth techniques. [7]
[b] Explain Leverberg-Marquardt method. [7]
Q.5 [a] Using finite defference method solve the equation
𝜕𝑢
𝜕𝑡
=
𝜕2𝑢
𝜕𝑥2 subject to the finite
defference method solve the equation
𝜕𝑢
𝜕𝑡
=
𝜕2𝑢
𝜕𝑥2condition 𝑢(𝑥, 0) = 𝑠𝑖𝑛𝜋𝑥, 0 ≤
𝑥 ≤ 1; 𝑢(0, 𝑡) = 𝑢(1, 𝑡) = 0, ,take h= 1/3 and k = 1/36
[7]
[b] Apply Runge-Kutta fourth order method, to find an approximate value of
y(0.2) given that
𝑑𝑦
𝑑𝑥
= 3 x +
𝑦
2
, y(0) = 1.
[7]
OR
Q.5 [a] Explain procedure to solve following heat conduction equation
𝐾
𝜕2𝑇
𝜕 𝑥2
=
𝜕𝑇
𝜕𝑡
Using finite difference technique.
[7]
[b] Write a short note on Finite Difference Approximations to partial derivatives. [7]