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)10000 or 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 n is a positive integer.

Provethat.

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

Find the coefficient of a5b7 in (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 4th term in the expansion of (x – 2y)12 .

Find the 13th term 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 am and an are equal.

The coefficients of the (r – 1)^th, r^th and (r + 1)^th terms in the expansion of (x + 1)ⁿare in the ratio 1:3:5. Find n and 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 m for which the coefficient of x² in the expansion (1 + x)^mis 6.

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

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

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.

Find thevalueof.

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

Expand using Binomial Theorem .

Find the expansion of using binomial theorem.