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

How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if

Find the r^th term in the expansion of `(x + 1/x)^(2r)`

Expand the following (1 – x + x²)⁴ 

Find the 4^th term from the end in the expansion of `(x^3/2 - 2/x^2)^9`

Evaluate: `(x^2 - sqrt(1 - x^2))^4 + (x^2 + sqrt(1 - x^2))^4`

Find the coefficient of x¹¹ in the expansion of `(x^3 - 2/x^2)^12`

Determine whether the expansion of `(x^2 - 2/x)^18` will contain a term containing x¹⁰?

Find the term independent of x in the expansion of `(sqrt(x)/sqrt(3) + sqrt(3)/(2x^2))^10`.

Show that `2^(4n + 4) - 15n - 16`, where n ∈ N is divisible by 225.

If n is a positive integer, find the coefficient of x^–1 in the expansion of `(1 + x)^2 (1 + 1/x)^n`

Which of the following is larger? 99⁵⁰ + 100⁵⁰  or 101⁵⁰

Find the coefficient of x⁵⁰ after simplifying and collecting the like terms in the expansion of (1 + x)¹⁰⁰⁰ + x(1 + x)⁹⁹⁹ + x²(1 + x)⁹⁹⁸ + ... + x¹⁰⁰⁰ .

If a₁, a₂, a₃ and a₄ are the coefficient of any four consecutive terms in the expansion of (1 + x)ⁿ, prove that `(a_1)/(a_1 + a_2) + (a_3)/(a_3 + a_4) = (2a_2)/(a_2 + a_3)`

The total number of terms in the expansion of (x + a)⁵¹ – (x – a)⁵¹ after simplification is ______.

If the coefficients of x⁷ and x⁸ in `2 + x^n/3` are equal, then n is ______.

If (1 – x + x²)ⁿ = a₀ + a₁ x + a₂ x² + ... + a_2n x²ⁿ , then a₀ + a₂ + a₄ + ... + a_2n equals ______.

The coefficient of x^p and x^q (p and q are positive integers) in the expansion of (1 + x)^{p + q} are ______.

The number of terms in the expansion of (a + b + c)ⁿ, where n ∈ N is ______.

If z = `sqrt(3)/2 + i^5/2 + sqrt(3)/2 - i^5/2`, then ______.

Find the coefficient of x in the expansion of (1 – 3x + 7x²)(1 – x)¹⁶.