Let $$\alpha$$ and $$\beta$$ be the distinct roots of $$a{x^2} + bx + c = 0$$, then

$$\mathop {\lim }\limits_{x \to \alpha } {{1 - \cos \left( {a{x^2} + bx + c} \right)} \over {{{\left( {x - \alpha } \right)}^2}}}$$ is equal to

If $$f$$ is a real valued differentiable function satisfying

$$\left| {f\left( x \right) - f\left( y \right)} \right|$$ $$ \le {\left( {x - y} \right)^2}$$, $$x, y$$ $$ \in R$$
and $$f(0)$$ = 0, then $$f(1)$$ equals

If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately :

Let x₁, x₂,...........,x_n be n observations such that

$$\sum {x_i^2} = 400$$ and $$\sum {{x_i}} = 80$$. Then a possible value of n among the following is