GATE EE 2025 Set 1 — Question 53
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0MediumDirectional DerivativesVector CalculusEngineering Mathematics
Engineering Mathematics → Vector Calculus → Directional Derivatives
Last updated
Question
Let . The rate of change of the real valued function,at the origin in the direction of the point is ___________ (round off to the nearest integer).
Correct answer
0 to 1
Solution
To find the rate of change of the function at the origin in the direction of the point , we calculate the directional derivative.
The magnitude of is .
The unit vector is:
1.Find the gradient of :
2.Evaluate the gradient at the origin :
3.Determine the unit direction vector:
The direction is given by the vector from the origin to , which is .The magnitude of is .
The unit vector is:
4.Calculate the directional derivative:
The rate of change is the dot product of the gradient and the unit direction vector:5.Round to the nearest integer:
Rounding to the nearest integer gives . According to the official answer key, the accepted range is 0 to 1.Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE EE question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Vector Calculus
2026 Set 1 Q14Consider the following differential equation:…2026 Set 1 Q30Two matrices and have a common eigenvalue , and the same corresponding…2026 Set 1 Q32Given that , the integral…2026 Set 1 Q35 is an skew-symmetric matrix with real-valued entries, and is an…2026 Set 1 Q36A time-limited waveform is specified as follows:…