1
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1 The relation between root mean square speed (vrms) and most probable sped (vp) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be :

A
$${v_{rms}} = \sqrt {{2 \over 3}} {v_p}$$
B
$${v_{rms}} = \sqrt {{3 \over 2}} {v_p}$$
C
$${v_{rms}} = {v_p}$$
D
$${v_{rms}} = \sqrt {{1 \over 3}} {v_p}$$
2
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1
Out of Syllabus A Carnot engine takes 5000 kcal of heat from a reservoir at 727$$^\circ$$C and gives heat to a sink at 127$$^\circ$$C. The work done by the engine is

A
3 $$\times$$ 106 J
B
Zero
C
12.6 $$\times$$ 106 J
D
8.4 $$\times$$ 106 J
3
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1 A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of 60 ms$$-$$1. What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail?

[Specific heat capacity of iron = 0.42 Jg$$-$$1 $$^\circ$$C$$-$$1]

A
675$$^\circ$$C
B
1600$$^\circ$$C
C
16.07$$^\circ$$C
D
6.75$$^\circ$$C
4
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1
Out of Syllabus A Carnot engine whose heat sinks at 27$$^\circ$$C, has an efficiency of 25%. By how many degrees should the temperature of the source be changed to increase the efficiency by 100% of the original efficiency?

A
Increases by 18$$^\circ$$C
B
Increases by 200$$^\circ$$C
C
Increases by 120$$^\circ$$C
D
Increases by 73$$^\circ$$C
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