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An ideal gas consists of a large number of identical molecules. Absolute temperature of the gas is T (in kelvin), molecular weight of gas is M and R is gas constant. Match the statements given in column-I with column-II and Choose correct option
Column-I Column II
A Root mean square speed of molecules is greater than P $\sqrt{\frac{R T}{M}}$
B Most probable speed of molecues is smaller than Q $1.5 \sqrt{\frac{R T}{M}}$
C Average velocity of a molecule is smaller than R $2 \sqrt{\frac{R T}{M}}$
D Speed of a molecule may be greater than S $2.5 \sqrt{\frac{R T}{M}}$

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$A - P Q; B - Q R S; C - P Q R S; D - P Q R S$

$A - P Q; B - Q R S; C - R S; D - P Q R S$

$A - P Q; B - S; C - P Q R S; D - P Q R S$

$A - P Q; B - Q S; C - P Q; D - R S$

answer is D.

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Detailed Solution

$A - P Q; B - Q R S; C - P Q R S; D - P Q R S$

Root mean square speed of molecules $= \sqrt{\frac{3 R T}{M}} = 1.732 \sqrt{\frac{R T}{M}}$

Most probable speed of molecues $= \sqrt{\frac{2 R T}{M}} = 1.44 \sqrt{\frac{R T}{M}}$

Average velocity of a molecule is zero

Speed of any individual molecule may be anything

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