Important Questions for CBSE Class 11 Maths Chapter 8 - Binomial Theorem
CBSE Class 11 Maths Chapter-8 Important Questions - Free PDF Download
1 Marks Questions
1. What is The middle term in the expansion of 
Ans. Since 
is odd there is two middle term
and 
2. When 
is a positive integer, the no. of terms in the expansion of 
is
Ans. The no. of terms in the expansion of is one more than the index 
3. Write the general term 
Ans. 
4. In the expansion of 
find the 3rd term from the end
Ans. 3rd term form end 
term from beginning
i.e 
5. Expand 
Ans. 
6. The middle term in the expansion of 
is
Ans. 
7. Find the no. of terms in the expansions of 
Ans.
No. of term is 15
8. Find the coeff of 
in 
Ans. 
Put 
Coeff of is 
9. Find the term independent of 
Ans.
Put 
Independent term is 
10. Expand 
Ans. 
4 Marks Questions
1. Which is larger 
or 
Ans.
2. Prove that 
Ans.
3. Using binomial theorem, prove that 
always leaves remainder 1 when divided by 25.
Ans. Let 
4.Find the 13th term in the expansion of 
, 
Ans.The general term in the expansion of
For 13th term, 
5. Find the term independent of 
in the expansion of 
Ans.
For independent term 
The req. term is 
6. Find the coefficient of 
in the expansion of the product 
Ans.
Coeff of is
7. Compute 
Ans.
8. Expand 
Ans.
9. Find the fourth term from the end in the expansion of 
Ans.Fourth term from the end would be equal to 
term from the beginning
10. Find the middle term of 
Ans.
so there are two middle term
i.e 
term and 
term
11. Find the coefficient of 
in 
Ans.
Put 
s
coeff. Of 
is
12. Find a positive value of m for which the coefficient of 
in the expansion 
is 6.
Ans. 
Put 
ATQ 
13. Show that the coefficient of the middle term in the expansion of
is equal to the sum of the coefficients of two middle terms in the expansion of 
Ans.As 
is even so the expansion has only one middle term which is 
Coeff. of 
is 
And 
is odd so two middle term
and 
i.e 
and 
term
The coefficients of these terms are 
and 
Now ATQ
14. Find a if the coeff. of and
in the expansion of
are equal
Ans.
ATQ
15. Find 
Hence evaluate 
Ans.
Put 
16. Show that 
is divisible by 64, whenever n is positive integer.
Ans. 
17. Find the general term in the expansion of 
Ans. 
18. In the expansion of 
prove that coefficients of 
and 
are equal.
Ans. 
Put 
and 
respectively
Coeff of is 
Coeff of is 
H.P
19. Expand 
Ans. 
20. Find the sixth term of the expansion 
if the binomial coefficient of the third term from the end is 45.
Ans. The binomial coeff of the third term from end = binomial coeff of the third term from beginning = 
21. Find a if the 17th and 18th terms of the expansion 
are equal.
Ans. 
ATQ put 
and 17
22. Find the term independent of in the expansion of 
Ans. 
Put 
23. If the coeff of 
and 
terms in the expansion of 
are equal find 
Ans.
Coeff are
and 
ATQ 
24. Show that the coeff of the middle term in the expansion of is equal to the sum of the coeff of two middle terms in the expansion of 
Ans. As 
is even so the expansion has only one middle term which is 
term
Coeff of is 
Similarly being odd the other expansion has two middle term i.e
and term
i.e and
The coeff are and
25. Find the value of 
if the coeff of 
and 
terms in the expansion of 
are equal.
Ans. 
Put 
And 
ATQ 
26. Find the 13th term in the expansion of 
Ans. 
Put
6 Marks Questions
1.Find 
, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of 
is 
Ans.Fifth term from the beginning in the expansion of is
How fifth term from the end would be equal to 
in term from the beginning
ATQ 
2.The coefficients of three consecutive terms in the expansion of 
are in the ratio 1:7:42. Find
Ans.Let three consecutive terms in the expansion of are 
term
Coefficients are
and 
respectively
ATQ 
On solving eq. 
and 
we get 
3. The second, third and fourth terms in the binomial expansion
are 240, 720 and 1080 respectively. Find 
, a and n.
Ans.
Divide by and 
by
We get
and 
On solving we get
4.If a and b are distinct integers, prove that a-b is a factor of 
whenever is positive.
Ans.Let 
Where
5. The sum of the coeff. 0f the first three terms in the expansion of 
being natural no. is 559. Find the term of expansion containing 
Ans.The coeff. Of the first three terms of are 
and 
Therefore, by the given condition
On solving we get 
6.Show that the middle term in the expansion of 
is 
Ans.As 
is even, the middle term of the expansion 
term
7. In the expansion of 
the ratio of 7th term from the beginning to the 7th term the end is 1:6 find
Ans.
7th term from end 
term from beginning
ATQ
8.If the coeff. Of 5th 6th and 7th terms in the expansion of 
are in A.P, then find the value of .
Ans.
Coeff of 5th , 6th, 7th terms in the expansion of are 
and 
ATQ 
9. If P be the sum of odd terms and Q that of even terms in the expansion of prove that
Ans.
Sq. and and subt.
Sq. and adding we get
10.If three successive coeff. In the expansion of are 220,495 and 792 then find
Ans. Let coeff are 
ATQ 
Dividing by
Dividing by
On solving 
and 
we get 
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