250+ TOP MCQs on Numerical Method – Newton Raphson Method and Answers

Distillation Design Quiz on “Numerical Method – Newton Raphson Method”.

1. In matrix language, The Newton Raphson equation is
a) J_i Y_if = -F_k
b) J_i X_if = -F_k
c) J_i K_if = -F_k
d) J_i T_if = -F_k
Answer: b
Clarification: In matrix language, The Newton Raphson equation is J_i X_if = -F_k,, here i represents the number of gas rows and j similarly columns of liquid.

2. What is F_k?
a) Vector
b) Matrix
c) Factor
d) Correction
Answer: d
Clarification: As F_k= (f1 f2 f3 ……fn)^T, F_k 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
Answer: a
Clarification: 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, X_K+1 is
a) X_k + h
b) X_k + t
c) X_k + X
d) X_k + X1
Answer: a
Clarification: For any instance X_K+1 is X_k + h, where h is the common difference and X_k is the previous calculated value of series.

5. Independent variable are in the range of
a) T_min< T_j > T_max
b) T_min> T_j > T_max
c) T_min< T_j > T_max
d) T_j < T_max
Answer: c
Clarification: Independent variable are in the range of T_min < T_j < T_max, 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
Answer: b
Clarification: 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
Answer: c
Clarification: 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 X_K+1? If X_k = 0.5, consider a difference of 5 stages
a) 4.5
b) 5.5
c) 3.5
d) Can’t be calculated
Answer: b
Clarification: For X_K+1 = X_k + h = 0.5+ 5 = 5.5.

9. The first assumption of the NR Method is
a) Assume K=0
b) Assume X_i = 0
c) Assume F(x) = 0
d) Assume F’(x) = 0
Answer: a
Clarification: 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
Answer: b
Clarification: 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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