GATE DA 2025 Set 1 — Question 48
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MSQ+2 / -0EasyActivation FunctionsNeural NetworksMachine LearningContinuityContinuity & DifferentiabilityCalculus & OptimizationDifferentiability
Calculus & Optimization → Continuity & Differentiability → Activation Functions
Last updated
Question
Which of the following statements is/are correct about the rectified linear unit (ReLU) activation function defined as , where ?
Correct answer
(A) ReLU is continuous everywhere; (C) ReLU is not differentiable at x = 0
Solution
The ReLU function is defined as if and if .(A) Correct. The function is continuous everywhere. and , so it is continuous at .(B) Incorrect. The derivative is for and for . At , the left-hand derivative is and the right-hand derivative is . Since they are not equal, it is not differentiable at .(C) Correct. As explained above, the derivative does not exist at .(D) Incorrect. Counterexample: Let and . , but . Thus in general.
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 DA 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 Continuity & Differentiability
2026 Set 1 Q11For a classification problem, Principal Component Analysis (PCA) has been used to reduce the…2026 Set 1 Q12Consider that you are training a classifier for a 10-class classification problem. Each input is…2026 Set 1 Q23In the following table, the
Task column lists a few tasks related to machine learning. The…2026 Set 1 Q27Let be a function defined on . Which of the following statements…2026 Set 1 Q29Consider that for a supervised learning task, the objective function being minimized is…