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Byju's Answer
Standard XII
Mathematics
Definition of a Determinant
If a1,a2,a3...
Question
If
a
1
,
a
2
,
a
3
,
5
,
4
,
a
6
,
a
7
,
a
8
,
a
9
are H.P and
D
=
∣
∣ ∣
∣
a
1
a
2
a
3
5
4
a
6
a
7
a
8
a
9
∣
∣ ∣
∣
, then the value of
21
D
.
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Solution
∴
a
n
=
20
n
and
d
=
1
20
∣
∣ ∣
∣
a
1
a
2
a
3
5
4
a
6
a
7
a
8
a
9
∣
∣ ∣
∣
∵
D
=
∣
∣ ∣ ∣ ∣ ∣ ∣
∣
20
20
2
20
3
20
4
20
5
20
6
20
7
20
8
20
9
∣
∣ ∣ ∣ ∣ ∣ ∣
∣
=
(
20
)
3
4
×
7
∣
∣ ∣ ∣ ∣ ∣ ∣
∣
1
1
2
1
3
1
4
5
2
3
1
7
8
7
9
∣
∣ ∣ ∣ ∣ ∣ ∣
∣
Applying
R
1
→
R
1
−
R
2
and
R
2
→
R
2
−
R
3
=
(
20
)
3
4
×
7
∣
∣ ∣ ∣ ∣ ∣ ∣
∣
0
−
3
10
−
1
3
0
−
3
40
−
1
9
1
7
8
7
9
∣
∣ ∣ ∣ ∣ ∣ ∣
∣
=
20
3
4
×
7
(
3
90
−
3
120
)
=
20
3
4
×
7
(
1
30
−
1
40
)
=
20
3
4
×
7
(
40
−
30
1200
)
=
20
3
4
×
7
×
1
120
=
20
×
20
×
20
4
×
7
×
1
120
=
5
×
10
7
×
1
3
=
50
21
∴
21
D
=
21
×
50
21
=
50
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Similar questions
Q.
If
a
1
,
a
2
,
a
3
,
5
,
4
,
a
6
,
a
7
,
a
8
,
a
9
are in H.P., and
D
=
∣
∣ ∣
∣
a
1
a
2
a
3
5
4
a
6
a
7
a
8
a
9
∣
∣ ∣
∣
, then the value of
[
D
]
is (where [.] represents the greatest integer function)
Q.
For an A.P.,
a
1
,
a
2
,
a
3
,
…
…
, if
a
3
+
a
5
+
a
8
=
11
and
a
4
+
a
2
=
−
2
, then the value of
a
1
+
a
6
+
a
7
is
Q.
For
A
P
a
1
,
a
2
,
a
3
,
..., if
a
4
a
7
=
2
3
, find
a
6
a
8
Q.
If
(
1
+
x
)
10
=
a
0
+
a
1
x
+
a
2
x
2
+
.
.
.
.
.
.
a
10
x
10
, then value of
(
a
0
−
a
2
+
a
4
−
a
6
+
a
8
−
a
10
)
2
+
(
a
1
−
a
3
+
a
5
−
a
7
+
a
9
)
2
is
Q.
If
(
1
+
x
)
10
=
a
0
+
a
1
x
+
a
2
x
2
+
.
.
.
.
.
+
a
10
x
10
, then value
(
a
0
−
a
2
+
a
4
−
a
6
+
a
8
−
a
10
)
2
+
(
a
1
−
a
3
+
a
5
−
a
7
+
a
9
)
2
is
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