Data Science for Engineers Week 5 NPTEL Assignment Answers 2025

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