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JEE Mains Previous Years Questions with Solutions

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1

JEE Main 2014 (Offline)

MCQ (Single Correct Answer)
If Z is a compressibility factor, van der Waals equation at low pressure can be written as:
A
Z = 1 + $$RT \over Pb$$
B
Z = 1 - $$a \over VRT$$
C
Z = 1 - $$Pb \over RT$$
D
Z = 1 + $$Pb \over RT$$

Explanation

Compressibility factor $$\left( Z \right) = {{PV} \over {RT}}$$

(For one mole of real gas)

van der Waals equation

$$\left( {P + {a \over {{V^2}}}} \right)\left( {V - b} \right) = RT$$

At low pressure, volume is very large and hence correction term $$b$$ can be neglected in comparison to very large volume of $$V.$$

i.e.$$\,\,\,V - b \approx V$$

$$\left( {P + {a \over {{V^2}}}} \right)V = RT;$$

$$PV + {a \over V} = RT$$

$$PV = RT - {a \over V};$$

$${{PV} \over {RT}} = 1 - {a \over {VRT}}$$

Hence, $$\,\,\,z = 1 - {a \over {VRT}}$$
2

JEE Main 2013 (Offline)

MCQ (Single Correct Answer)
For gaseous state, if most probable speed is denoted by C*, average speed by $$\mathop C\limits^{\_\_} $$ and mean square speed by C, then for a large number of molecules the ratios of these speeds are:
A
C*: $$\mathop C\limits^{\_\_} $$ : C = 1.128 : 1.225 : 1
B
C*: $$\mathop C\limits^{\_\_} $$ : C = 1.225 : 1.128 : 1
C
C*: $$\mathop C\limits^{\_\_} $$ : C = 1 : 1.225 : 1.128
D
C*: $$\mathop C\limits^{\_\_} $$ : C = 1 : 1.128 : 1.225

Explanation

Most probable speed $$\left( {{C^ * }} \right) = \sqrt {{{2RT} \over M}} $$

Average Speed $$\left( {\overline C } \right) = \sqrt {{{8RT} \over {\pi M}}} $$

Root mean square velocity $$\left( c \right) = \sqrt {{{3RT} \over M}} $$

$${C^ * }:\overline C :C = \sqrt {{{2RT} \over M}} :\sqrt {{{8RT} \over {\pi M}}} :\sqrt {{{3RT} \over M}} $$

$$ = 1:\sqrt {{4 \over \pi }} :\sqrt {{3 \over 2}} $$

$$ = 1:1.128:1.225$$
3

AIEEE 2012

MCQ (Single Correct Answer)
The compressibility factor for a real gas at high pressure is :
A
1 + RT/pb
B
1
C
1 + pb/RT
D
1–pb/RT

Explanation

$$\left( {P + {a \over {{V^2}}}} \right)\left( {V - b} \right) = RT\,\,$$

at high pressure $${a \over {{V^2}}}$$ can be neglected

$$PV - Pb = RT\,\,\,$$

and $$\,\,\,PV = RT + Pb$$

$${{PV} \over {RT}} = 1 + {{Pb} \over {RT}}$$

$$z = 1 + {{Pb} \over {RT}};Z > 1\,\,\,$$ at high pressure
4

AIEEE 2011

MCQ (Single Correct Answer)
'a’ and `b’ are van der Waals’ constants for gases. Chlorine is more easily liquefied than ethane because
A
a and b for Cl2 < a and b for C2H6
B
a and b for Cl2 > a and b for C2H6
C
a for Cl2 > a for C2H6 and b Cl2 < b for C2H6
D
a for Cl2 < a for C2H6 and b Cl2 > b for C2H6

Explanation

The value of $$a$$ is a measure of the magnitude of the attractive forces between the molecules of the gas. Greater the value of $$'a',$$ larger is the attractive inter-molecular force between the gas molecules.

The value of $$b$$ related to the effective size of the gas molecules. It is also termed as excluded volume.

The gases with higher value of $$a$$ and lower value of $$b$$ are more liquefiable, hence for $$C{{\rm l}_2}$$ $$''a'''$$ should be greater than for $${C_2}{H_6}$$ but for it $$b$$ should be less than for $${C_2}{H_6}.$$

Questions Asked from Gaseous State

On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Indicates No. of Questions
JEE Main 2021 (Online) 31st August Morning Shift (1)
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JEE Main 2021 (Online) 27th August Morning Shift (1)
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JEE Main 2021 (Online) 26th August Evening Shift (1)
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JEE Main 2020 (Online) 3rd September Evening Slot (1)
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JEE Main 2020 (Online) 2nd September Morning Slot (1)
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JEE Main 2019 (Online) 10th April Evening Slot (1)
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JEE Main 2019 (Online) 10th April Morning Slot (1)
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JEE Main 2019 (Online) 9th April Evening Slot (1)
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JEE Main 2019 (Online) 9th April Morning Slot (1)
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JEE Main 2019 (Online) 12th January Evening Slot (1)
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JEE Main 2019 (Online) 12th January Morning Slot (1)
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JEE Main 2019 (Online) 9th January Morning Slot (1)
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JEE Main 2018 (Online) 16th April Morning Slot (1)
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JEE Main 2017 (Online) 9th April Morning Slot (1)
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JEE Main 2017 (Online) 8th April Morning Slot (1)
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JEE Main 2016 (Online) 10th April Morning Slot (1)
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JEE Main 2016 (Online) 9th April Morning Slot (1)
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JEE Main 2016 (Offline) (1)
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JEE Main 2014 (Offline) (1)
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JEE Main 2013 (Offline) (1)
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AIEEE 2012 (1)
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AIEEE 2011 (1)
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AIEEE 2010 (1)
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AIEEE 2007 (1)
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AIEEE 2005 (1)
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AIEEE 2004 (2)
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AIEEE 2003 (1)
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AIEEE 2002 (3)
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