If $x$ is a solution of the equation, $\sqrt {2x + 1}  – \sqrt {2x – 1}  = 1, \left( {x \ge \frac{1}{2}} \right)$ , then $\sqrt {4{x^2} – 1} $ is equal to 

If $3$ distinct real number $a$,$b$,$c$ satisfy $a^2(a + p) = b^2 (b + p) = c^2 (c + p)$ where $p \in R$, then value of $bc + ca + ab$ is

Let $\alpha ,\beta $ be the roots of ${x^2} + (3 – \lambda )x – \lambda = 0.$ The value of $\lambda $ for which ${\alpha ^2} + {\beta ^2}$ is minimum, is

Let $y = \sqrt {\frac{{(x + 1)(x – 3)}}{{(x – 2)}}} $, then all real values of $x$ for which $y$ takes real values, are

If $x$ is real, then the maximum and minimum values of the expression $\frac{{{x^2} – 3x + 4}}{{{x^2} + 3x + 4}}$ will be