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Byju's Answer
Standard XII
Mathematics
Properties of Inequalities
Number of int...
Question
Number of integral values of
x
satisfying the inequality
(
3
4
)
6
x
+
10
−
x
2
<
27
64
is
A
6
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B
7
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C
8
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D
infinite
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Solution
The correct option is
B
7
(
3
4
)
6
x
+
10
−
x
2
<
27
64
⇒
(
3
4
)
6
x
+
10
−
x
2
<
(
3
4
)
3
⇒
6
x
+
10
−
x
2
>
3
(
∵
3
4
<
1
)
⇒
x
2
−
6
x
−
7
<
0
⇒
(
x
+
1
)
(
x
−
7
)
<
0
⇒
x
∈
(
−
1
,
7
)
Hence,
x
=
0
,
1
,
2
,
3
,
4
,
5
,
6
Suggest Corrections
0
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