Cube root of 217 is

3^{2n + 2} - 8n - 9 is divisible by

If , then 121ⁿ- 25ⁿ +1900ⁿ - (-4)ⁿ is divisible by

If p and q be positive , then the coefficient of x^p and x^q in the expansion of ( 1 + x ) ^p+q will be

The constant term in the expansion of    is

The number of terms in the expansion of (1 + 6 x + 9 x²)²³ is

The number of terms in the expansion (√3 + √5)⁷ + (√3 - √5)⁷ is 

The sum of binomial coefficient is

ⁿc₀ - 1/2 ⁿc₁ + 1/3 ⁿc₂ - ........ + (-1)ⁿ  is equal to

The remainder when 2²⁰⁰⁶ + 2007 is divided by 17 is