1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Term Independent of x
Find the term...
Question
Find the term independent of x in the expansion of
(
√
x
3
+
√
3
2
x
2
)
10
.
Open in App
Solution
The
(
r
+
1
)
t
h
term is
T
r
+
1
=
10
C
r
(
√
x
3
)
10
−
r
(
√
3
2
x
2
)
r
=
10
C
r
x
10
−
r
2
3
10
−
r
2
.
(
√
3
)
r
2
r
x
2
r
∴
T
r
+
1
=
10
C
r
√
3
3
10
−
r
2
×
2
r
x
10
−
r
2
−
2
r
........(i)
The term becomes independent when exponent of x is zero.
⇒
10
−
r
2
−
2
r
=
0
⇒
10
−
r
2
=
2
r
⇒
10
−
r
=
4
r
⇒
10
=
5
r
⇒
r
=
2
Now, substitute
r
=
2
in equation (i), we get
T
3
=
10
C
2
(
√
3
)
2
3
4
.2
2
=
10
!
8
!
2
!
×
3
3
4
2
2
T
3
=
10
×
9
2
×
3
×
3
×
3
×
4
Hence, Independent term,
T
3
=
5
12
Suggest Corrections
0
Similar questions
Q.
Find the term independent of
x
in the expansion of
(
√
x
3
+
3
2
x
2
)
10
Q.
Find the term independent of x in the expansion of
a)
(
√
x
3
+
√
3
2
x
2
)
10
b)
(
2
x
2
−
3
x
3
)
25
Q.
The perm independent of
x
in the expansion of
(
√
x
3
+
√
3
2
x
2
)
10
is
Q.
The term independent of x in the expansion of
(
√
(
x
3
)
+
√
(
3
2
x
2
)
)
10
is
Q.
The term independent of
x
in the expansion
(
√
x
√
3
+
√
3
2
x
2
)
10
is equal to:
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
Visualising the Coefficients
MATHEMATICS
Watch in App
Explore more
Term Independent of x
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
AI Tutor
Textbooks
Question Papers
Install app