# NPTEL Data Science for Engineers Assignment 5 Answers 2022

NPTEL Data Science for Engineers Assignment 5 Answers 2022:- All the Answers provided below to help the students as a reference, You must submit your assignment at your own knowledge.

## What is Data Science for Engineers?

Data Science for Engineers is a fun-filled course where Domain Certification helps learners to gain expertise in a specific Area/Domain. This can be helpful for learners who wish to work in a particular area as part of their job or research or for those appearing for some competitive exam or becoming job-ready or specialising in an area of study.

Every domain will comprise Core courses and Elective courses. Once a learner completes the requisite courses per the mentioned criteria, you will receive a Domain Certificate showcasing your scores and the domain of expertise.

## CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of the average of best 6 assignments out of the total 8 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF THE AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

## NPTEL Data Science for Engineers Assignment 5 Answers 2022:-

Q1. An optimization problem, solved for N variables, with one equality constraint will have

a. N equations in N variables
b. N + 1 equations in N + 1 variables
c. N equations in N + 1 variables
d. none of these

Answer:- b. N + 1 equations in N + 1 variable

Q2. While minimizing a function f(x,y)=6x2+4y2 with a constraint 3x+2y≤12, the unconstrained minimum solution is __________ the constrained minimum solution

a. Equal to
b. Less than
c. Greater than
d. both (b) and (c)

Q3. The function min f(x,y)=3x+y subject to the given constraints x2+y2<10 is an example of

a. Unconstrained multivariate optimisation
b. Multivariate optimisation with equality constraint
c. Multivariate optimisation with inequality constraint
d. None of the above

Answer: c. Multivariate optimisation with inequality constraint

Q4. What is the global minimum value for the function f(x,y)=(x+y)2+5?

a. 0
b. -∞
c. 5
d. global minimum does not exist

Consider the function f(x,y)=5x2+3y2;+8xy+12x+6y as the function to be optimized and answer questions 5 and 6.

Q5. The saddle point of the function f(x,y) exists in which of the following coordinates (x,y)

a. (6,-9)
b. (5,3)
c. (2,-3)
d. There is no saddle point

Q6. The Hessian matrix obtained for the function f(x,y) is

a.\begin{bmatrix} 5 & 3 \\ 12 & 6 \end{bmatrix}
b.\begin{bmatrix} 12 & 6 \\ 5 & 3 \end{bmatrix}
c.\begin{bmatrix} 10 & 8 \\ 8 & 6 \end{bmatrix}
d.\begin{bmatrix} 5 & 8 \\ 8 & 3 \end{bmatrix}

Answer: c.\begin{bmatrix} 10 & 8 \\ 8 & 6 \end{bmatrix}

Q7. The eigenvalues for the Hessian matrix obtained in Q6 are

a. -2.5, 2.5
b. 8.3584, -3.46
c. 4.5046, -5.3654
d. 16.2462, -0.2462

Q8. Geometrically, finding the minimum of the function f(x,y)=x2+4y2 subject to the constraint 3x+7y=4 implies that

a. The minimum value exist in the the gradient of the tangent 3x + 7y = 4
b. The minimum value is present in the contour of the ellipse x² + 4y² = k such that it’s tangent is 3x + 7y = 4
c. The minimum value is present at the point (0,0)
d. The minimum value is not dependent on the constraint

Answer: b. The minimum value is present in the contour of the ellipse x² + 4y² = k such that it’s tangent is 3x + 7y = 4

Q9. State whether the following statements are True or False.

i) The decision variables of the optimization function need not be independent of each other
ii) An optimization problem with linear objective function and linear constraints is said to be a linear optimization problem

a. i) – TRUE; ii) – FALSE
b. i) – FALSE; ii) – FALSE
c. i) – TRUE; ii) – TRUE
d. i) – FALSE; ii) – TRUE

Answer: d. i) – FALSE; ii) – TRUE