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Exercise 8.1 - Chapter 8 Binomial Theorem class 11 ncert solutions Maths - SaraNextGen [2024]


 

Question 1:

Expand the expression (1– 2x)5

Answer:

By using Binomial Theorem, the expression (1– 2x)can be expanded as

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5568/Chapter%208_html_1efb1de7.gif

Question 2:

Expand the expressionhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5569/Chapter%208_html_m254b627e.gif

Answer:

By using Binomial Theorem, the expression https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5569/Chapter%208_html_m254b627e.gif  can be expanded as

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5569/Chapter%208_html_m7d8846ba.gif

Question 3:

Expand the expression (2x – 3)6

Answer:

By using Binomial Theorem, the expression (2x – 3)can be expanded as

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/4236/chapter%208_html_m2ebe63d3.gif

Question 4:

Expand the expressionhttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5570/Chapter%208_html_m7b30e533.gif

Answer:

By using Binomial Theorem, the expression https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5570/Chapter%208_html_m7b30e533.gif  can be expanded as

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5570/Chapter%208_html_m375bf0f1.gif

Question 5:

Expand https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5659/Ch-8_html_50d8591.gif

Answer:

By using Binomial Theorem, the expression https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5659/Ch-8_html_50d8591.gif  can be expanded as

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5659/Ch-8_html_4e98296.gif

Question 6:

Using Binomial Theorem, evaluate (96)3

Answer:

96 can be expressed as the sum or difference of two numbers whose powers are easier to calculate and then, binomial theorem can be applied.

It can be written that, 96 = 100 – 4

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/4239/chapter%208_html_2a4e7d12.gif

Question 7:

Using Binomial Theorem, evaluate (102)5

Answer:

102 can be expressed as the sum or difference of two numbers whose powers are easier to calculate and then, Binomial Theorem can be applied.

It can be written that, 102 = 100 + 2

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/4240/chapter%208_html_41ec6427.gif

Question 8:

Using Binomial Theorem, evaluate (101)4

Answer:

101 can be expressed as the sum or difference of two numbers whose powers are easier to calculate and then, Binomial Theorem can be applied.

It can be written that, 101 = 100 + 1

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/4241/chapter%208_html_m32c7b2e7.gif

Question 9:

Using Binomial Theorem, evaluate (99)5

Answer:

99 can be written as the sum or difference of two numbers whose powers are easier to calculate and then, Binomial Theorem can be applied.

It can be written that, 99 = 100 – 1

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/4242/chapter%208_html_m64b11caa.gif

Question 10:

Using Binomial Theorem, indicate which number is larger (1.1)10000 or 1000.

Answer:

By splitting 1.1 and then applying Binomial Theorem, the first few terms of (1.1)10000 can be obtained as

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/4243/chapter%208_html_m49002564.gif

Question 11:

Find (a + b)4 – (a – b)4. Hence, evaluatehttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5571/Chapter%208_html_m5828f0d6.gif .

Answer:

Using Binomial Theorem, the expressions, (a + b)4 and (a – b)4, can be expanded as

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5571/Chapter%208_html_m36a879ff.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5571/Chapter%208_html_644b00be.gif

Question 12:

Find (x + 1)6 + (x – 1)6. Hence or otherwise evaluatehttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5572/Chapter%208_html_114a06d3.gif .

Answer:

Using Binomial Theorem, the expressions, (x + 1)6 and (x – 1)6, can be expanded as

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5572/Chapter%208_html_3ddca4d6.gif

By puttinghttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5572/Chapter%208_html_m6349be68.gif , we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5572/Chapter%208_html_451accb3.gif

Question 13:

Show that https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5573/Chapter%208_html_m12be085a.gif is divisible by 64, whenever n is a positive integer.

Answer:

In order to show that https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5573/Chapter%208_html_m12be085a.gif is divisible by 64, it has to be proved that,

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5573/Chapter%208_html_737047ca.gif , where k is some natural number

By Binomial Theorem,

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5573/Chapter%208_html_m4d274ce5.gif

For a = 8 and m = n + 1, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5573/Chapter%208_html_m67e2b52.gif

Thus,

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5573/Chapter%208_html_m12be085a.gif is divisible by 64, whenever n is a positive integer.

Question 14:

Prove thathttps://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5574/Chapter%208_html_m4e5eff9.gif .

Answer:

By Binomial Theorem,

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5574/Chapter%208_html_53729de4.gif

By putting b = 3 and a = 1 in the above equation, we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/168/5574/Chapter%208_html_28f6f472.gif

Hence, proved.

Also Read : Exercise-8.2-Chapter-8-Binomial-Theorem-class-11-ncert-solutions-Maths

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