This set of Distillation Design Quiz focuses on “Numerical Method – Newton Raphson Method”.
1. In matrix language, The Newton Raphson equation is
a) Ji Yif = -Fk
b) Ji Xif = -Fk
c) Ji Kif = -Fk
d) Ji Tif = -Fk
View Answer
Explanation: In matrix language, The Newton Raphson equation is Ji Xif = -Fk,, here i represents the number of gas rows and j similarly columns of liquid.
2. What is Fk?
a) Vector
b) Matrix
c) Factor
d) Correction
View Answer
Explanation: As Fk= (f1 f2 f3 ……fn)T, Fk is Vector , Matrix and Factor are correlated by an empirical correlation of total functions and temperature.
3. A square nXn matrix is called
a) Jacobin Matrix
b) Raphson Matrix
c) Newton Matrix
d) 2N Matrix
View Answer
Explanation: A square n X n matrix is called Jacobin Matrix, where the number of row properties are equal to number of column properties.
4. For any instance, XK+1 is
a) Xk + h
b) Xk + t
c) Xk + X
d) Xk + X1
View Answer
Explanation: For any instance XK+1 is Xk + h, where h is the common difference and Xk is the previous calculated value of series.
5. Independent variable are in the range of
a) Tmin< Tj > Tmax
b) Tmin> Tj > Tmax
c) Tmin< Tj > Tmax
d) Tj < Tmax
View Answer
Explanation: Independent variable are in the range of Tmin < Tj < Tmax, i.e. the maximum temperature should be less than initial and greater than the final temperature.
6. In quasi Newton Method, Sk represents the
a) Vector factor
b) Scalar factor
c) Separation factor
d) Correction factor
View Answer
Explanation: In quasi Newton Method, Sk represents the Scalar factor, while function quantiles such as temperature and pressure relations are called as vector ones.
7. Solve cos x = 2x?
a) 0.6780
b) 0.3456
c) 0.45018
d) 0.998
View Answer
Explanation: Solving f(x) = 0 then f(x) = cos x − 2x, x0 = 0.5, x1 = 0.45063, x2 = 0.45018, x3 = 0.45018, the root is x = 0.45018.
8. Find XK+1? If Xk = 0.5, consider a difference of 5 stages
a) 4.5
b) 5.5
c) 3.5
d) Can’t be calculated
View Answer
Explanation: For XK+1 = Xk + h = 0.5+ 5 = 5.5.
9. The first assumption of the NR Method is
a) Assume K=0
b) Assume Xi = 0
c) Assume F(x) = 0
d) Assume F’(x) = 0
View Answer
Explanation: The first assumption of the NR Method is assume K=0, as we assume k=0, then we calculate F(x) = 0 and then F’(x) = 0.
10. Jacobin equation is solved using the
a) Matrix Multiplication
b) LU Factorization
c) Elimination Method
d) Follow up method
View Answer
Explanation: Jacobin equation is solved using the LU Factorization method, where we eliminate the lower and upper triangle matrix resulting in a singular matrix.
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