Class 11 Maths Chapter 8 Binomial Theorem

Exercise 8.1

Expand each of the expressions in Exercises 1 to 5.

 Question 1.

Solution.

Question 2.

Solution.

Question 3.

Solution.

Question 4.

Solution.

Question 5.

Solution.

Using binomial theorem, evaluate each of the following
Question 6.

Solution.

Question 7.

Solution.

Question 8.

Solution.

Question 9.

Solution.

Question 10.
Using Binomial Theorem, indicate which number is larger or 1000.
Solution.
Splitting 1.1 and using binomial theorem to write the first few terms we have

Question 11.
Find . Hence, evaluate .
Solution.
By binomial theorem, we have

Question 12.
Find . Hence or otherwise evaluate .
Solution.
By using binomial theorem, we have

Question 13.
Show that  is divisible by 64, whenever n is a positive integer.
Solution.
We have to prove that 

Question 14.
Prove that  8Cr = 4n
Solution.
We have,

Exercise 8.2

Question 1.
Find the coefficient of x5 in (x + 3)8
Solution.
Suppose x5 occurs in the (r + 1)th term of the expansion (x + 3)8

Question 2.
a5 b7in (a-2b)12
Solution.
Suppose a5 b7 occurs in the (r + 1)th term of the expansion (a – 2b)12.

Write the general term in the expansion of
Question 3.
(x2 – y)6
Solution.

Question 4.
(x2 – yx)12, x ≠ 0
Solution.
We have given, (x2 – yx)12 = (x2 + (- yx))12, x ≠ 0

Question 5.
Find the 4th term in the expansion of (x – 2y)12.
Solution.

Question 6.
Find the 13th term in the expansion of , x ≠ 0
Solution.

Find the middle terms in the expansions of
Question 7.

Solution.
As the exponent 7 is odd, so there will be two middle terms in the expansion

Question 8.

Solution.

Question 9.
In the expansion of (1 + a)m+n, prove that coefficients of am and an are equal.
Solution.

Question 10.
The coefficients of the (r – 1)th, rth and (r + 1)th terms in the expansion of (x + 1 )n are in the ratio 1: 3: 5. Find n and r.
Solution.

Question 11.
Prove that the coefficient of xn in the expansion of (1 + x)2n is twice the coefficient of xn in the expansion of (1 + x)2n-1.
Solution.

Question 12.
Find a positive value of m for which the coefficient of x2 in the expansion (1 + x)m is 6.
Solution.