NCERT Solutions class-11 Maths Miscellaneous

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

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

Ans. Here

Coefficient of = and Coefficient of =

According to question,

=

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

Ans. Using Binomial Theorem,

=

Coefficient of in the product

=

=

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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

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5. Evaluate:

Ans. Given:

Using Binomial Theorem,

=

=

=

=

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6. Find the value of

Ans. Putting and we have

=

=

= =

= =

= =

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

Ans. Here =

= = = 0.951

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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

5^th term from the beginning =

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

=

Now,

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9. Expand using binomial theorem

Ans. We have

=

=

=

=

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10. Find the expansion of using binomial theorem.

Ans. Here

=

=

=

=

=

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