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NDA Math Determinants
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© examsnet.com
Question : 55
Total: 68
If the value of the determinant
|
a
1
1
1
b
1
1
1
c
|
is positive,where,
a
≠
b
≠
c
,then the value of abc
[NDA II 2015]
cannot be less than 1
is greater than -8
is less than -8
must be greater than 8
Validate
Solution:
|
a
1
1
1
b
1
1
1
c
|
>
0
⇒
a
(
b
c
−
1
)
−
1
(
c
−
1
)
+
1
(
1
−
b
)
>
0
⇒
a
b
c
−
a
−
c
+
1
+
1
−
b
>
0
⇒
a
b
c
+
2
−
(
a
+
b
+
c
)
>
0
⇒
a
b
c
>
(
a
+
b
+
c
)
−
2
Let;
a
=
−
1
;
b
=
0
&
c
=
1
Then;
0
>
−
2
[which is correct]
Hence,
abc
=
0
∴ After considering all the option; (b) is correct option,
© examsnet.com
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