Carnot engine efficiency to be raised with the same sink: new source temperature

The same question, asked 4 times: 4 May 2023 S1, 10 May 2024 S1*, 16 Apr 2026 S2*, 17 Apr 2026 S1. Every wording below, oldest first.

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Question 1
4 May 2023 S1
23 $A Carnot engine, whose efficiency is 40% takes heat from a source maintained at temperature 600 K. It is desired to have an efficiency 60%, then the intake temperature for the same exhaust (sink) temperature should be$
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Question 2
10 May 2024 S1
37 $50\%$
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Question 3
16 Apr 2026 S2
113 $A Carnot engine with efficiency 50% takes heat from a source at 600 K. To increase the efficiency by 20%, keeping temperature of the sink same, the new temperature of the source will be$
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Question 4
17 Apr 2026 S1
115 $A Carnot engine, whose efficiency is 40% takes heat from a source maintained at temperature 600K. To have an efficiency 60%, the intake temperature for the same exhaust temperature should be$
Tap an option to check your answer.

Question 1