INDIAN SCHOOL MUSCAT SENIOR SECTION DEPARTMENT OF MATHEMATICS CLASS XI BINOMIAL THEOREM Q
Ans 6 𝑎
𝑏
1.
Expand using binomial theorem (√ − √ ) 𝑏 𝑎
2.
Find the value of 1.018 − 0.998 till five decimal places.
3.
The fourth term in the expansion of (𝑎𝑥 + ) is . find value of n and a.
1 𝑛
5
𝑥
2
0.16011
4.
Using binomial theorem prove that 23𝑛 − 7𝑛 − 1 is divisible by 49 ∀ 𝑛 ∈ 𝑁.
5.
Find the term containing 𝑥 −15 in the expansion of (3𝑥 2 −
6.
The sum of coefficients of the first three terms of (𝑥 − 𝑁, is 559. Find the term containing 𝑥 3 .
7.
The coefficient of 𝑥 7 in the expansion of (𝑎𝑥 2 + expansion of (𝑎𝑥 −
8.
1 𝑏𝑥 2
11
1
) 𝑏𝑥
11
10.
11.
) 3𝑥 3
3 𝑥2
10
𝑚
) , x≠ 0, m ∈
and 𝑥 −7 in the
𝟏 𝟐
−𝟒𝟎 𝒂𝟕 𝟐𝟕 -5940𝒙𝟑
ab = 1
) are equal. Find the relation between a and b.
Find the ratio of the coefficients of eleventh term from the starting and 1
eleventh term from the end in the expansion of (2𝑥 −
9.
𝑎
6,
Find the middle terms in the expansion of (
2𝑥 2 3
−
3 2𝑥
25
) . 𝑥2
-32
9 2)
1 2𝑛
If 𝑥 𝑝 occurs in the expansion of (𝑥 2 + 𝑥 ) , then prove that its coefficient is (2𝑛)! 4𝑛 − 𝑝 2𝑛 + 𝑝 ( 3 )! ( 3 )! In the expansion of (1 + 𝑥 )𝑛, the coefficients of the three consecutive terms are 220, 495 and 792 respectively. Find n and the position of these terms.
n = 12
