NCERT Solutions for Class 11 Maths Maths Chapter 8

Binomial Theorem Class 11

Chapter 8 Binomial Theorem Exercise 8.1, 8.2, miscellaneous Solutions

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Exercise 8.1 : Solutions of Questions on Page Number : 166

Q1 :  

Expand the expression (1- 2x)5


Answer :

By using Binomial Theorem, the expression (1– 2x)5 can be expanded as

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Q2 :  

Expand the expression


Answer :

By using Binomial Theorem, the expression can be expanded as

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Q3 :  

Expand the expression (2x - 3)6


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Q4 :  

Expand the expression


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Q5 :  

Expand


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Q6 :  

Using Binomial Theorem, evaluate (96)3


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Q7 :  

Using Binomial Theorem, evaluate (102)5


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Q8 :  

Using Binomial Theorem, evaluate (101)4


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Q9 :  

Using Binomial Theorem, evaluate (99)5


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Q10 :  

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


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Q11 :  

Find (a + b)4– (a– b)4. Hence, evaluate.


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Q12 :  

Find (x+ 1)6+ (x – 1)6. Hence or otherwise evaluate.


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Q13 :  

Show that is divisible by 64, whenever nis a positive integer.


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Q14 :  

Prove that.


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<< Previous Chapter 7 : Permutations and Combinations Next Chapter 9 : Sequences and Series >>

Exercise 8.2 : Solutions of Questions on Page Number : 171

Q1 :  

Find the coefficient of x5in (x + 3)8


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Q2 :  

Find the coefficient of a5b7in (a - 2b)12


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Q3 :  

Write the general term in the expansion of (x2- y)6


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Q4 :  

Write the general term in the expansion of (x2- yx)12, x 0


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Q5 :  

Find the 4thterm in the expansion of (x- 2y)12 .


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Q6 :  

Find the 13thterm in the expansion of.


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Q7 :  

Find the middle terms in the expansions of


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Q8 :  

Find the middle terms in the expansions of


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Q9 :  

In the expansion of (1 + a)m + n, prove that coefficients of amand anare equal.


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Q10 :  

The coefficients of the (r- 1)th, rthand (r + 1)thterms in the expansion of

(x+ 1)nare in the ratio 1:3:5. Find nand r.


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Q11 :  

Prove that the coefficient of xnin the expansion of (1 + x)2nis twice the coefficient of xnin the expansion of (1 + x)2n-1 .


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Q12 :  

Find a positive value of mfor which the coefficient of x2in the expansion

(1 + x)mis 6.


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<< Previous Chapter 7 : Permutations and Combinations Next Chapter 9 : Sequences and Series >>

Exercise Miscellaneous : Solutions of Questions on Page Number : 175

Q1 :  

Find a, band n in the expansion of (a+ b)nif the first three terms of the expansion are 729, 7290 and 30375, respectively.


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Q2 :  

Find aif the coefficients of x2and x3in the expansion of (3 + ax)9are equal.


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Q3 :  

Find the coefficient of x5in the product (1 + 2x)6(1 - x)7using binomial theorem.


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Q4 :  

If a and b are distinct integers, prove that a - b is a factor of an - bn, whenever n is a positive integer.

[Hint: write an = (a - b + b)n and expand]


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Q5 :  

Evaluate.


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Q6 :  

Find the value of.


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Q7 :  

Find an approximation of (0.99)5using the first three terms of its expansion.


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Q8 :  

Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of


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Q9 :  

Expand using Binomial Theorem.


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Q10 :  

Find the expansion of using binomial theorem.


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<< Previous Chapter 7 : Permutations and Combinations Next Chapter 9 : Sequences and Series >>

Maths - Maths : CBSE NCERT Exercise Solutions for Class 11th for Binomial Theorem ( Exercise 8.1, 8.2, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

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