GATE EC 2016 Set 1 — 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 / -0.67EasyRatios, Percentages, Powers, Exponents & LogarithmsQuantitative AptitudeGeneral Aptitude
General Aptitude → Quantitative Aptitude → Ratios, Percentages, Powers, Exponents & Logarithms
Last updated
Question
If , and , the value of is ______
Correct answer
(C) 1
Solution
We are given three equations:
From equation (2):
From equation (3):
Now, substitute the expression for from the modified equation (1) into the modified equation (2):
Next, substitute this expression for into the modified equation (3):
Since the bases are the same (), the exponents must be equal:
The final answer is
1.
2.
3.
From equation (1):From equation (2):
From equation (3):
Now, substitute the expression for from the modified equation (1) into the modified equation (2):
Next, substitute this expression for into the modified equation (3):
Since the bases are the same (), the exponents must be equal:
The final answer is
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 Quantitative Aptitude
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…