NCERT Solutions for Class 11 Maths Maths Chapter 8

Expand the expression (1- 2x)⁵

Expand the expression

Expand the expression (2x - 3)⁶

Expand the expression

Expand

Using Binomial Theorem, evaluate (96)³

Using Binomial Theorem, evaluate (102)⁵

Using Binomial Theorem, evaluate (101)⁴

Using Binomial Theorem, evaluate (99)⁵

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

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

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

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

Prove that.

Find the coefficient of x⁵in (x + 3)⁸

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

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

Find the 13^thterm in the expansion of.

Find the middle terms in the expansions of

Find the middle terms in the expansions of

In the expansion of (1 + a)^{m + n}, prove that coefficients of a^mand aⁿare equal.

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

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

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

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

(1 + x)^mis 6.

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

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

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

Find the value of.

Find an approximation of (0.99)⁵using 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

Expand using Binomial Theorem.

Find the expansion of using binomial theorem.