Binomial Theorem-I
Binomial Theorem-I
Binomial Theorem-I
( )
6
1. Write the general term in expansion of x 2 − y .
12
1
Find the 10th term in binomial expansion of 2x 2 +
x
2.
9
4x 5
3. th
Find the 6 term in expansion of −
5 2x
12
x 3a
4. Find the 9th term in expansion of − 2
a x
7
3 x3
5. Find the 4 term from end in expansion of 2 −
th
x 6
25
1
6. Find the 11 term from end in expansion of 2x − 2
th
x
20
2 2 3
Find the middle term in expansion of x −
2x
7.
3
7
x3
8. Find the middle term in expansion of 3x −
6
Prove that the coefficient of the middle term in expansion of (1 + x ) is equal to the sum of
2n
10.
15
−17 1
11. Find the coefficient of x 32
and x in the expansion of x 4 − 3 .
x
10
1
13. Find the term independent of x in expansion of 3x 2 − 3 .
2x
FIITJEE Ltd., Punjabi Bagh Centre, 31, 32, 33, Central Market, West Avenue Road, Punjabi Bagh, New Delhi - 26, Ph: 011-45634000.
The coefficient of 3 consecutive terms in expansion of (1 + x ) are in the ratio 1 : 7 : 42, then
n
14.
find n
If the coefficients of ar −1, ar , ar +1 in binomial expansion of (1 + a ) are in A.P. then prove that
n
15.
n2 − ( 4r + 1) n + 4r 2 − 2 = 0 .
If the third, fourth, fifth and sixth terms in the expansion of ( x + y ) are a, b, c, d
n
16.
b2 − ac 5a
respectively, then prove that =
c 2 − bd 3c
m
log (10−3n ) n − 2 log3
17. For m,n N , let the 6 term in expansion of the binomial 2
th
+ 2( ) be
equal to 21. Further if binomial coefficients and 2nd, 3rd and 4th terms in expansion represent
respectively the 1st, 3rd and 5th term of an A.P. Find (m + n).
18. ( )( )
Given 1 − 2x + 5x 2 − 10x 3 1 + x 3 (1 + x ) = 1 + a1x + a 2 x 2 + a3 x 3 + .... and that a12 = 2a2 ,
n
(1+ x )(1+ y )( x + y )
n
19. Show that n
Cr 3 is equal to coefficient of x n y n in expansion of .
r =0
( )
n
20. Find number of distinct terms in expansion of 1 + 2x + 3x 2 + 10x 3
1
Find the numerically greatest term in the expansion of ( 3 − 5x )
15
21. when x = .
5
2
Find the numerically greatest term in the expansion of ( 7 − 5x )
11
22. when x = .
3
FIITJEE Ltd., Punjabi Bagh Centre, 31, 32, 33, Central Market, West Avenue Road, Punjabi Bagh, New Delhi - 26, Ph: 011-45634000.