1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Least Integer Function
The greatest ...
Question
The greatest negative integer satisfying
x
2
−
4
x
−
77
<
0
and
x
2
>
4
is
A
−
6
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
−
7
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
−
8
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
−
17
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is
D
−
6
Since
x
2
−
4
x
−
77
<
0
⇒
x
2
−
11
x
+
7
x
−
77
<
0
⇒
(
x
−
11
)
(
x
+
7
)
<
0
∴
−
7
<
x
<
11
...(1)
Also,
x
2
>
4
⇒
x
2
−
4
>
0
∴
x
<
−
2
or
x
>
2
...(2)
Using (1) and (2), we have
∴
The gratest negative interger satisfying the above inequality is
−
6
.
Suggest Corrections
0
Similar questions
Q.
The greatest negative integer satisfying
x
2
−
4
x
−
77
<
0
and
x
2
>
4
is...
Q.
The greatest negative integer satisfying
x
2
+
4
x
−
77
<
0
and
x
2
>
4
is
Q.
If
x
∈
[
0
,
10
]
, then the number of integral value(s) of
x
satisfying the equation
x
2
+
4
x
+
[
x
]
+
6
=
0
(where [.] denotes the greatest integer function) is
Q.
Number of integral values of
x
satisfying
[
x
2
−
2
]
2
−
9
[
x
2
−
2
]
+
14
=
0
, where [.] is greatest integer function
Q.
If
I
=
∫
3
1
(
tan
−
1
(
x
2
−
5
x
+
6
x
3
−
6
x
2
+
12
x
−
7
)
+
tan
−
1
(
1
x
2
−
4
x
+
4
)
)
then the value of
[
I
]
is
(where [.] represents the greatest integer function)
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
MATHEMATICS
Watch in App
Explore more
Least Integer Function
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Solve
Textbooks
Question Papers
Install app