GATE EC 2016 Set 3 — Question 9
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumMensuration & GeometryQuantitative AptitudeGeneral AptitudeDefinite & Improper IntegralsCalculusEngineering Mathematics
Engineering Mathematics → Calculus → Definite & Improper Integrals
Last updated
Question
Find the area bounded by the lines , in the first quadrant.
Correct answer
(B) 15.25
Solution
The lines are and .Step 1: Find the intersection point.
Multiply by 3:
Multiply by 2:
Adding the equations: .
Substitute into : .
The intersection point is .Step 2: Identify the vertices of the region in the first quadrant.
Area
Area
Area .
Multiply by 3:
Multiply by 2:
Adding the equations: .
Substitute into : .
The intersection point is .Step 2: Identify the vertices of the region in the first quadrant.
- Origin:
- x-intercept of (): . Point:
- Intersection point:
- y-intercept of (): . Point:
Area
Area
Area .
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 EC 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 Calculus
2026 Set 1 Q1Among the following options, the antonym of the word ‘nocturnal’ is _________.2026 Set 1 Q2The statements (S1), (S2), and (S3) pertain to the scores obtained by students in an exam. The…2026 Set 1 Q3The figure below has exactly three intersecting line segments with a rectangular portion …2026 Set 1 Q4Real numbers , , and (all greater than 1) satisfy…2026 Set 1 Q5The following observation is made about the scores obtained by 100 students in an exam: 'For each…