CBSE (Commerce) Class 11CBSE
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NCERT solutions Mathematics Class 11 chapter 8 Binomial Theorem

Chapters

NCERT Mathematics Class 11

Mathematics Textbook for Class 11

Chapter 8 - Binomial Theorem

Pages 166 - 167

Expand the expression (1– 2x)5

Q 1 | Page 166

Expand the expression (1– 2x)5

Q 1 | Page 166

Expand the expression `(2/x - x/2)^5`

Q 2 | Page 166

Expand the expression (2x – 3)6

Q 3 | Page 166

Expand the expression `(x/3 + 1/x)^5`

Q 4 | Page 167

Expand `(x + 1/x)^6`

Q 5 | Page 167

Using Binomial Theorem, evaluate (96)3

Q 6 | Page 167

Using Binomial Theorem, evaluate (102)5

Q 7 | Page 167

Using Binomial Theorem, evaluate (101)4

Q 8 | Page 167

Using Binomial Theorem, evaluate (99)5

Q 9 | Page 167

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

Q 10 | Page 167

Find (a + b)4 – (a – b)4. Hence, evaluate `(sqrt3 + sqrt2)^4 - (sqrt3 - sqrt2)^4`

Q 11 | Page 167

Find (a + b)4 – (a – b)4. Hence, evaluate `(sqrt3 + sqrt2)^4 - (sqrt3 - sqrt2)^4`

Q 11 | Page 167

Find (x + 1)6 + (x – 1)6. Hence or otherwise evaluate `(sqrt2 + 1)^6 + (sqrt2 -1)^6`

Q 12 | Page 167

Show that 9n+1 – 8n – 9 is divisible by 64, whenever n is a positive integer.

Q 13 | Page 167

Prove that `sum_(r-0)^n 3^r  ""^nC_r = 4^n`

Q 14 | Page 167

Page 171

Find the coefficient of x5 in (x + 3)8

Q 1 | Page 171

Find the coefficient of a5b7 in (a – 2b)12

Q 2 | Page 171

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

Q 3 | Page 171

Write the general term in the expansion of (x2 – yx)12x ≠ 0

Q 4 | Page 171

Find the 4th term in the expansion of (x – 2y)12 .

Q 5 | Page 171

Find the 13th term in the expansion of `(9x - 1/(3sqrtx))^18 , x != 0`

Q 6 | Page 171

Find the middle terms in the expansions of  `(3 - x^3/6)^7`

Q 7 | Page 171

Find the middle terms in the expansions of `(x/3 + 9y)^10`

Q 8 | Page 171

In the expansion of (1 + a)m + n, prove that coefficients of am and an are equal.

Q 9 | Page 171

The coefficients of the (r – 1)thrth and (r + 1)th terms in the expansion of (x + 1)n are in the ratio 1:3:5. Find n and r.

Q 10 | Page 171

Prove that the coefficient of xn in the expansion of (1 + x)2n is twice the coefficient of xn in the expansion of (1 + x)2n–1 .

Q 11 | Page 171

Find a positive value of m for which the coefficient of x2 in the expansion

(1 + x)m is 6

Q 12 | Page 171

Pages 175 - 176

Find a if the coefficients of x2 and x3 in the expansion of (3 + ax)9 are equal.

Q 1 | Page 175

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

Q 1 | Page 175

Find the coefficient of x5 in the product (1 + 2x)6 (1 – x)7 using binomial theorem.

Q 3 | Page 175

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]

Q 4 | Page 175

Evaluate `(sqrt3  +sqrt2)^6 - (sqrt3 - sqrt2)^6`

Q 5 | Page 175

Find the value of `(a^2 + sqrt(a^2 - 1))^4 + (a^2 - sqrt(a^2 -1))^4`

Q 6 | Page 175

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

Q 7 | Page 175

Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of `(root4 2 + 1/ root4 3)^n " is " sqrt6 : 1`

Q 8 | Page 175

Expand using Binomial Theorem `(1+ x/2 - 2/x)^4, x != 0`

Q 9 | Page 176

Find the expansion of (3x2 – 2ax + 3a2)3 using binomial theorem.

Q 10 | Page 176

NCERT Mathematics Class 11

Mathematics Textbook for Class 11
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