NCERT Solutions class-11 Maths Miscellaneous

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Miscellaneous Exercise

1. Find and in the expansion of if the first three terms of the expansion are 729, 7290 and 30375 respectively.

Ans. Given:

…..(i)

…..(ii)

And

…..(iii)

Multiplying eq. (i) and eq. (iii),

…..(iv)

Squaring both sides in eq. (ii),

…..(v)

Dividing eq. (iv) by eq. (v),

From eq. (i),

And From eq. (ii),

Therefore, , and


2. Find if the coefficient of and in the expansion of are equal.

Ans. Here

Coefficient of = and Coefficient of =

According to question,

=


3. Find the coefficient of in the product using binomial theorem.

Ans. Using Binomial Theorem,

=

Coefficient of in the product

=

=


4. If and are distinct integers, prove that is a factor of whenever is a positive integer.

Ans. We have,

which shows that is a factor of


5. Evaluate:

Ans. Given:

Using Binomial Theorem,

=

=

=

=


6. Find the value of

Ans. Putting and we have

=

=

= =

= =

= =


7. Find an approximation of using the first three terms of its expansion.

Ans. Here =

= = = 0.951


8. Find if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of is

Ans. Here

5th term from the beginning =

5th term from the end = term from beginning = term from the beginning

=

Now,


9. Expand using binomial theorem

Ans. We have

=

=

=

=


10. Find the expansion of using binomial theorem.

Ans. Here

=

=

=

=

=


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