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Standard XII
Mathematics
Arithmetic Progression
Question
If
a
2
,
b
2
,
c
2
are in A.P. then the following are also in A.P. True or False? If true write 1 otherwise write 0
1
b
+
c
,
1
c
+
a
,
1
a
+
b
.
Open in App
Solution
Verified by Toppr
Assume
1
b
+
c
,
1
c
+
a
,
1
a
+
b
.
are in A.P
⇒
1
c
+
a
−
1
b
+
c
=
1
a
+
b
−
1
c
+
a
⇒
b
−
a
b
+
c
=
c
−
b
a
+
b
⇒
b
2
−
a
2
=
c
2
−
b
2
⇒
2
b
2
=
a
2
+
c
2
Hence our assumption it True.
Thus answer is 1.
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Similar Questions
Q1
If
a
2
,
b
2
,
c
2
are in A.P. then the following are also in A.P. True or False? If true write 1 otherwise write 0
1
b
+
c
,
1
c
+
a
,
1
a
+
b
.
View Solution
Q2
If
a
2
,
b
2
,
c
2
are in A.P., then the following are also in A.P.
1
b
+
c
,
1
c
+
a
,
1
a
+
b
.
View Solution
Q3
Given a,b,c,d are in G.P then
(
a
−
d
)
2
=
(
b
−
c
)
2
+
(
c
−
a
)
2
+
(
d
−
b
)
2
.If you think this is true then write 1 otherwise write 0 ?
View Solution
Q4
If
a
2
,
b
2
,
c
2
are in A.P. then show that
1
b
+
c
,
1
c
+
a
,
1
a
+
b
are also in A.P.
View Solution
Q5
1
a
,
1
b
,
1
c
are in
H
.
P
,
then the following are also in A.P.
b
+
c
,
c
+
a
,
a
+
b
If it is true, then answer will be 1 otherwise 0.
View Solution