NCERT Solutions class-11 Maths Exercise 8.2

Exercise 8.2

Find the coefficient of:

1. in

Ans. General form of the expansion is ………(i)

Putting in eq. (i),

Therefore, coefficient of on the expansion is = 1512.

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2. in

Ans. General form of the expansion is ………(i)

Putting in eq. (i),

Therefore, coefficient of on the expansion is =

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Write the general term in the expansion of

3.

Ans. General form of the expansion is

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4.

Ans. General form of the expansion is

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5. Find the 4^th term in the expansion of

Ans. General form of the expansion is

Putting

= =

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6. Find the 13^th term in the expansion of

Ans. General form of the expansion is …..(i)

Putting

= = = 18564

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Find the middle terms in the expansion of:

7.

Ans. Here which is an odd number.

Therefore, the middle terms are and are 4^th and 5^th terms.

General form of the expansion is …..(i)

Putting and in eq. (i),

=

= =

=

= =

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8.

Ans. Here which is an even number.

Therefore, the middle terms are is 6^th term.

General form of the expansion is …..(i)

Putting in eq. (i),

=

=

=

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9. In the expansion of prove that coefficients of and are equal.

Ans. Coefficient of in the expansion of

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10. The coefficients of the and terms in the expansion of are in the ratio 1 : 3 : 5. Find and

Ans. Given:

and

and

and

Solving both equations, we have and

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11. Prove that the coefficient of in the expansion of is twice the coefficient of in the expansion of

Ans. Since, Coefficient of in the expansion of is

=

= ……….(i)

Also Coefficient of in the expansion of is ……….(ii)

From eq. (i) and eq. (ii), it is clear that Coefficient of in the expansion of is twice the Coefficient of in the expansion of .