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# Distillation Design MCQ’s – Numerical Method – Newton Raphson Method

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}

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Answer: b

Explanation: 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.

What is F_{k}?

a) Vector

b) Matrix

c) Factor

d) Correction

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Answer: d

Explanation: 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.

A square nXn matrix is called

a) Jacobin Matrix

b) Raphson Matrix

c) Newton Matrix

d) 2N Matrix

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Explanation: A square n X n matrix is called Jacobin Matrix, where the number of row properties are equal to number of column properties.

For any instance, X_{K+1} is

a) X_{k} + h

b) X_{k} + t

c) X_{k} + X

d) X_{k} + X1

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Answer: a

Explanation: 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.

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}

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Answer: c

Explanation: 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.

In quasi Newton Method, Sk represents the

a) Vector factor

b) Scalar factor

c) Separation factor

d) Correction factor

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Answer: b

Explanation: In quasi Newton Method, Sk represents the Scalar factor, while function quantiles such as temperature and pressure relations are called as vector ones.

Solve cos x = 2x?

a) 0.6780

b) 0.3456

c) 0.45018

d) 0.998

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Answer: c

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.

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

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Answer: b

Explanation: For X_{K+1} = X_{k} + h = 0.5+ 5 = 5.5.

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

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Answer: a

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.

Jacobin equation is solved using the

a) Matrix Multiplication

b) LU Factorization

c) Elimination Method

d) Follow up method

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Answer: b

Explanation: Jacobin equation is solved using the LU Factorization method, where we eliminate the lower and upper triangle matrix resulting in a singular matrix.