Arts (English Medium) इयत्ता ११ - CBSE Question Bank Solutions

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

Expand the expression: (2x – 3)⁶

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

Expand the expression: `(x + 1/x)^6`

Using Binomial Theorem, evaluate the following:

(96)³

Using binomial theorem, evaluate f the following:

(101)⁴

Using binomial theorem, evaluate the following:

(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 (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 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`