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Joint Entrance Examination
Mathematics
Sets, Relations and Functions
Question 118
Question 118 of 161
Medium
NUMERICAL
Set
A
A
A
has
m
m
m
elements and set
B
B
B
has
n
n
n
elements. If the total number of subsets of
A
A
A
is 112 more than the total number of subsets of
B
B
B
, then the value of
m
⋅
n
m\cdot n
m
⋅
n
is: Answer: 28
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Official solution
\[2^m-2^n=112 = 16\times7 = 2^4(2^3-1)\] Matching forms:
n
=
4
n=4
n
=
4
,
2
m
−
4
−
1
=
7
⇒
2
m
−
4
=
8
⇒
m
−
4
=
3
⇒
m
=
7
2^{m-4}-1=7 \Rightarrow 2^{m-4}=8 \Rightarrow m-4=3 \Rightarrow m=7
2
m
−
4
−
1
=
7
⇒
2
m
−
4
=
8
⇒
m
−
4
=
3
⇒
m
=
7
. \[mn = 7\times4 = 28\]
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