Chapter 8 – Binomial Theorem (Ex – 8.2)

Binomial Theorem (Ex – 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.

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 a^m and aⁿ are equal.

Solution.

Question 10.
The coefficients of the (r – 1)^th, r^th 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.