Binomial Theorem Exercise 8.2
Exercise 8.2
Find the coefficient of:
1. 
in 
Ans. General form of the expansion is 
………(i)
Putting in eq. (i), 
Therefore, coefficient of on the expansion is 
= 1512.
2. 
in 
Ans. General form of the expansion is 
………(i)
Putting in eq. (i), 
Therefore, coefficient of on the expansion is 
= 
Write the general term in the expansion of
3. 
Ans. General form of the expansion is 
4. 
Ans. General form of the expansion 
is 
5. Find the 4th term in the expansion of 
Ans. General form of the expansion 
is 
Putting 
= 
= 
6. Find the 13th term in the expansion of 
Ans. General form of the expansion 
is 
…..(i)
Putting 
= 
= 
= 18564
Find the middle terms in the expansion of:
7. 
Ans. Here 
which is an odd number.
Therefore, the middle terms are 
and 
are 4th and 5th terms.
General form of the expansion is 
…..(i)
Putting and 
in eq. (i),
= 
= 
= 
= 
= 
= 
8. 
Ans. Here 
which is an even number.
Therefore, the middle terms are 
is 6th term.
General form of the expansion is 
…..(i)
Putting 
in eq. (i),
= 
= 
= 
9. In the expansion of 
prove that coefficients of 
and 
are equal.
Ans. Coefficient of in the expansion of 
10. The coefficients of the 
and 
terms in the expansion of 
are in the ratio 1 : 3 : 5. Find 
and 
Ans. Given: 
and 
and 
and 
Solving both equations, we have
and
11. Prove that the coefficient of 
in the expansion of 
is twice the coefficient of in the expansion of 
Ans. Since, Coefficient of in the expansion of is
= 
= 
……….(i)
Also Coefficient of in the expansion of 
is 
……….(ii)
From eq. (i) and eq. (ii), it is clear that Coefficient of in the expansion of is twice the Coefficient of in the expansion of .