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E M B I B E
Higher Algebra
>
Chapter 2 - Proportion
>
Examples. II .
>
Q 11
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EASY
JEE Main
IMPORTANT
Earn 100
If
b
is a mean proportional between
a
and
c
, prove that
a
2
-
b
2
+
c
2
a
-
2
-
b
-
2
+
c
-
2
=
b
4
.
Important Questions on Proportion
EASY
JEE Main
IMPORTANT
Higher Algebra
>
Chapter 2 - Proportion
>
Examples. II .
>
Q 12
If
a
:
b
=
c
:
d
and
e
:
f
=
g
:
h
, prove that
a
e
+
b
f
:
a
e
-
b
f
=
c
g
+
d
h
:
c
g
-
d
h
.
EASY
JEE Main
IMPORTANT
Higher Algebra
>
Chapter 2 - Proportion
>
Examples. II .
>
Q 13
Solve the equations
2
x
3
-
3
x
2
+
x
+
1
2
x
3
-
3
x
2
-
x
-
1
=
3
x
3
-
x
2
+
5
x
-
13
3
x
3
-
x
2
-
5
x
+
13
.
EASY
JEE Main
IMPORTANT
Higher Algebra
>
Chapter 2 - Proportion
>
Examples. II .
>
Q 14
Solve the equations
3
x
4
+
x
2
-
2
x
-
3
3
x
4
-
x
2
+
2
x
+
3
=
5
x
4
+
2
x
2
-
7
x
+
3
5
x
4
-
2
x
2
+
7
x
-
3
.
EASY
JEE Main
IMPORTANT
Higher Algebra
>
Chapter 2 - Proportion
>
Examples. II .
>
Q 15
Solve the equations
(
m
+
n
)
x
-
(
a
-
b
)
(
m
-
n
)
x
-
(
a
+
b
)
=
(
m
+
n
)
x
+
a
+
c
(
m
-
n
)
x
+
a
-
c
.
EASY
JEE Main
IMPORTANT
Higher Algebra
>
Chapter 2 - Proportion
>
Examples. II .
>
Q 16
If
a
,
b
,
c
,
d
are proportional, prove that
a
+
d
=
b
+
c
+
(
a
-
b
)
(
a
-
c
)
a
.
EASY
JEE Main
IMPORTANT
Higher Algebra
>
Chapter 2 - Proportion
>
Examples. II .
>
Q 17
If
a
,
b
,
c
,
d
,
e
are in continued proportion, prove that
(
a
b
+
b
c
+
c
d
+
d
e
)
2
=
a
2
+
b
2
+
c
2
+
d
2
b
2
+
c
2
+
d
2
+
e
2
.
EASY
JEE Main
IMPORTANT
Higher Algebra
>
Chapter 2 - Proportion
>
Examples. II .
>
Q 18
If the work done by
(
x
-
1
)
men in
(
x
+
1
)
days is to the work done by
(
x
+
2
)
men in
(
x
-
1
)
days in the ratio of
9
:
10
, find
x
.
MEDIUM
JEE Main
IMPORTANT
Higher Algebra
>
Chapter 2 - Proportion
>
Examples. II .
>
Q 19
Find four proportionals such that the sum of the extremes is
21
, the sum of the means
19
, and sum of the squares of all the four numbers is
442
.
