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Byju's Answer
Standard XII
Mathematics
Derivative from First Principle
Let Δ = | a...
Question
Let
Δ
=
∣
∣ ∣
∣
a
11
a
12
a
13
a
21
a
22
a
23
a
31
a
32
a
33
∣
∣ ∣
∣
and
a
p
q
=
i
p
+
q
where
i
=
√
−
1
.
The value of
Δ
is
A
real and positive
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B
real and negative
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C
0
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D
imaginary
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Solution
The correct option is
A
0
△
=
∣
∣ ∣
∣
a
11
a
12
a
13
a
21
a
22
a
23
a
31
a
32
a
33
∣
∣ ∣
∣
&
a
p
q
=
i
p
+
q
⇒
△
=
∣
∣ ∣ ∣
∣
i
2
i
3
i
4
i
3
i
4
i
5
i
4
i
5
i
6
∣
∣ ∣ ∣
∣
=
i
2
+
3
+
4
∣
∣ ∣ ∣
∣
1
1
1
i
i
i
i
2
i
2
i
2
∣
∣ ∣ ∣
∣
=
i
∣
∣ ∣
∣
1
1
1
i
i
i
−
1
−
1
−
1
∣
∣ ∣
∣
=
−
i
∣
∣ ∣
∣
1
1
1
i
i
i
1
1
1
∣
∣ ∣
∣
∴
△
=
0
Hence, option 'C' is correct.
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0
Similar questions
Q.
Matrix
A
=
⎡
⎢
⎣
1
2
3
1
1
5
2
4
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⎤
⎥
⎦
then the value of
a
31
A
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+
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A
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33
A
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is
Q.
Let
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a
2
,
a
3
,
a
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be real numbers such that and
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2
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2
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(
a
1
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a
2
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2
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(
a
2
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a
2
)
2
+
(
a
3
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a
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Q.
Let
a
1
,
a
2
,
a
3
,
a
4
be real numbers such that
a
1
+
a
2
+
a
3
+
a
4
=
0
and
a
2
1
+
a
2
2
+
a
2
3
+
a
2
4
=
1
. Then the smallest possible value of the expression
(
a
1
–
a
2
)
2
+
(
a
2
–
a
3
)
2
+
(
a
3
–
a
4
)
2
+
(
a
4
–
a
1
)
2
lies in the interval
Q.
If
a
1
,
a
2
,
a
3
,
a
4
and
b
are real numbers such that
(
a
2
1
+
a
2
2
+
a
2
3
)
b
2
−
2
(
a
1
a
2
+
a
2
a
3
+
a
3
a
4
)
b
+
(
a
2
2
+
a
2
3
+
a
2
4
)
≤
0
then
a
1
,
a
2
,
a
3
,
a
4
are the terms of a/an
Q.
Let
a
n
denote the
n
th
term of a geometric progression with common ratio less than
1.
If
a
1
+
a
2
+
a
3
=
13
and
a
2
1
+
a
2
2
+
a
2
3
=
91
,
then the value of
a
10
is
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