NCERT solutions for Class 11 Mathematics chapter 8 - Binomial Theorem [Latest edition]

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

Expand the expression (2x – 3)⁶

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

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

Using Binomial Theorem, evaluate (96)³

Using Binomial Theorem, evaluate (101)⁴

Using Binomial Theorem, evaluate (99)⁵

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 .

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

(1 + x)^m is 6

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

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

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]

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

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

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

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`

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

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