NCERT Solutions class-11 Maths Exercise 8.1

Exercise 8.1

Expand each of the expression in Exercises 1 to 5.

1.

Ans. Using Binomial Theorem,

=

=

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2.

Ans. Using Binomial Theorem,

=

=

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3.

Ans. Using Binomial Theorem,

=

=

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4.

Ans. Using Binomial Theorem,

=

=

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5.

Ans. Using Binomial Theorem,

=

=

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Using binomial theorem evaluate each of the following:

6.

Ans. Given:

Using Binomial Theorem,

=

= 1000000 – 120000 + 4800 – 64

= 1004800 – 120064 = 884736

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7.

Ans. Given:

Using Binomial Theorem,

=

= 10000000000 + 1000000000 + 40000000 + 800000 + 8000 + 32

= 11040808032

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8.

Ans. Given:

Using Binomial Theorem,

=

= 100000000 + 4000000 + 60000 + 400 + 1

= 104060401

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9.

Ans. Given:

Using Binomial Theorem,

=

= 10000000000 – 500000000 + 10000000 – 100000 + 500 – 1

= 9509900499

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10. Using binomial theorem, indicate which number is larger or 1000.

Ans. Given:

Using Binomial Theorem,

= 1 + 10000 (0.1) + other positive numbers

= 1 + 1000 + other positive numbers

which is greater than 1000

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11. Find Hence evaluate:

Ans. Given:

Using Binomial Theorem,

=

=

=

Putting and

=

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12. Find Hence or otherwise evaluate

Ans. Given:

Using Binomial Theorem,

=

= =

Putting

=

= 2 [ 8 + 60 + 30 + 1] = = 198

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13. Show that is divisible by 64 whenever is a positive integer.

Ans. Given:

Using Binomial Theorem,

=

=

which shows that is divisible by 64.

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14. Prove that

Ans. L.H.S. =

=

= = R.H.S.