NCERT Class 11-Math՚s: Chapter – 8 Binomial Theorem Part 6 (For CBSE, ICSE, IAS, NET, NRA 2023)

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Question 21:

The ratio of the coefficient of to the term independent of in is

(A)

(B)

(C)

(D)

Answer:

(B) Is the correct choice.

Let be the general term of , so

Now, for the coefficient of term containing ,

Therefore, is the coefficient of (from (1) )

To find the term independent of , put

Thus is the term independent of (from (1) )

Now the ratio is

Question 22:

If , then

(A)

(B)

(C)

(D)

Answer:

B is the correct choice. On simplification, we get

Since and , will not contain any i and hence .

8.3 EXERCISE

Short Answer Type

Question 1:

Find the term independent of , , in the expansion of

Answer:

Question 2:

If the term free from in the expansion of is , find the value of k.

Answer:

Question 3:

Find the coefficient of x in the expansion of .

Answer:

Question 4:

Find the term independent of x in the expansion of,

Answer:

Question 5:

Find the middle term (terms) in the expansion of

(i) (ii)

Answer:

(i) (ii)

Question 6:

Find the coefficient of in the expansion of .

Answer:

Question 7:

Find the coefficient of in the expansion of

Answer:

Question 8:

Find the sixth term of the expansion , if the binomial coefficient of the third term from the end is 45.

[Hint: Binomial coefficient of third term from the end Binomial coefficient of third term from beginning .]

Answer:

Question 9:

Find the value of , if the coefficients of and terms in the expansion of are equal.

Answer: