# NCERT Solutions for Class 11 Maths Maths Chapter 8

## Binomial Theorem Class 11

### Exercise 8.1 : Solutions of Questions on Page Number : 166

Q1 :

Expand the expression (1- 2x)5

By using Binomial Theorem, the expression (1â€“ 2x)5 can be expanded as Q2 :

Expand the expression By using Binomial Theorem, the expression can be expanded as Q3 :

Expand the expression (2x - 3)6

Q4 :

Expand the expression Q5 :

Expand Q6 :

Using Binomial Theorem, evaluate (96)3

Q7 :

Using Binomial Theorem, evaluate (102)5

Q8 :

Using Binomial Theorem, evaluate (101)4

Q9 :

Using Binomial Theorem, evaluate (99)5

Q10 :

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

Q11 :

Find (a + b)4â€“ (aâ€“ b)4. Hence, evaluate .

Q12 :

Find (x+ 1)6+ (x â€“ 1)6. Hence or otherwise evaluate .

Q13 :

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

Q14 :

Prove that .

### Exercise 8.2 : Solutions of Questions on Page Number : 171

Q1 :

Find the coefficient of x5in (x + 3)8

Q2 :

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

Q3 :

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

Q4 :

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

Q5 :

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

Q6 :

Find the 13thterm in the expansion of .

Q7 :

Find the middle terms in the expansions of Q8 :

Find the middle terms in the expansions of Q9 :

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

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.

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 .

Q12 :

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

(1 + x)mis 6.

### 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.

Q2 :

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

Q3 :

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

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]

Q5 :

Evaluate .

Q6 :

Find the value of .

Q7 :

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

Q8 :

Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of Q9 :

Expand using Binomial Theorem .

Q10 :

Find the expansion of using binomial theorem.