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Important Questions for CBSE Class 11 Maths Chapter 8 – Binomial Theorem

 



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 expansionare 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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