Data Science for Engineers Week 5 NPTEL Assignment Answers 2025

Need help with this week’s assignment? Get detailed and trusted solutions for Data Science for Engineers Week 5 NPTEL Assignment Answers. Our expert-curated answers help you solve your assignments faster while deepening your conceptual clarity.

✅ Subject: Data Science for Engineers
📅 Week: 5
🎯 Session: NPTEL 2025 July-October
🔗 Course Link: Click Here
🔍 Reliability: Verified and expert-reviewed answers
📌 Trusted By: 5000+ Students

For complete and in-depth solutions to all weekly assignments, check out 👉 NPTEL Data Science for Engineers Week 5 NPTEL Assignment Answers

🚀 Stay ahead in your NPTEL journey with fresh, updated solutions every week!

NPTEL Data Science for Engineers Week 5 Assignment Answers 2025

1. The values of μ₁, μ₂ and μ₃ while evaluating the Karush-Kuhn-Tucker (KKT) condition with all the constraints being inactive are

• μ₁=μ₂=μ₃=1
• μ₁=μ₂=μ₃=0
• μ₁=μ₃=0,μ₂=1
• μ₁=μ₂=0,μ₃=1

Answer : See Answers

2. Gradient based algorithm methods compute

• only step length at each iteration
• both direction and step length at each iteration
• only direction at each iteration
• none of the above

Answer :

3. The point on the plane x+y−2z=6 that is closest to the origin is

• (0, 0, 0)
• (1, 1, 1)
• (−1, 1, 2)
• (1, 1, −2)

Answer :

4. Find the maximum value of f(x,y)=49−x²−y² subject to the constraints x+3y=10.

• 49
• 46
• 59
• 39

Answer :

5. The minimum value of f(x,y)=x²+4y²−2x+8y subject to the constraint x+2y=7 occurs at the below point:

• (5, 5)
• (−5, 5)
• (1, 5)
• (5, 1)

Answer :

6. Which of the following statements is/are NOT TRUE with respect to the multi variate optimization?

I – The gradient of a function at a point is parallel to the contours
II – Gradient points in the direction of greatest increase of the function
III – Negative gradients points in the direction of the greatest decrease of the function
IV – Hessian is a non-symmetric matrix

• I
• II and III
• I and IV
• III and IV

Answer : See Answers

7. The solution to an unconstrained optimization problem is always the same as the solution to the constrained one.

• True
• False

Answer :

8. A manufacturer incurs a monthly fixed cost of $7350 and a variable cost, C(m)=0.001m3−2m2+324m dollars. The revenue generated by selling these units is, R(m)=−6m2+1065m. How many units produced every month (m) will generate maximum profit?

• m=46
• m=90
• m=231
• m=125

Answer :

9.

Answer : See Answers

NPTEL Data Science for Engineers Week 5 Assignment Answers 2024

1. Which of the following statements is/are not TRUE with respect to the multi variate optimization?

I – The gradient of a function at a point is parallel to the contours
II – Gradient points in the direction of greatest increase of the function
III – Negative gradients points in the direction of the greatest decrease of the function
IV – Hessian is a non-symmetric matrix

• I
• II and III
• I and IV
• III and IV

Answer :- c

2. The solution to an unconstrained optimization problem is always the same as the solution to the constrained one.

• True
• False

Answer :- b

3. Gradient based algorithm methods compute

• only step length at each iteration
• both direction and step length at each iteration
• only direction at each iteration
• none of the above

Answer :- b

5. Which among the following is the stationary point for f(x₁,x₂)?

• (0, 0)
• (1, −1)
• (−1, −1)
• (−1, 1)

Answer :- b

6. Find the eighen values corresponding to Hessian matrix of f.

• 1, −1
• 1, 1
• 2, 8
• 0, 2

Answer :- c

7. Find the minimum value of f.

• 0
• −5
• −1
• 1

Answer :- b

9. What is the minimum value of f(x₁,x₂) subject to the above mentioned constrained?

• −5
• −1
• 27
• 0

Answer :- c

10. Find the maximum value of f(x,y)=49−x²−y² subject to the constraints x+3y=10.

• 49
• 46
• 59
• 39

Answer :- d