The number of the real roots of the equation $(x+1)^{2}+|x-5|=\frac{27}{4}$ is ....... .

Let $\lambda \in R$ and let the equation $E$ be $| x |^2-2| x |+|\lambda-3|=0$. Then the largest element in the set $S =$ $\{ x +\lambda: x$ is an integer solution of $E \}$ is $..........$

Below are four equations in $x$. Assume that $0 < r < 4$. Which of the following equations has the largest solution for $x$ ?

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

The value of $x$ in the given equation ${4^x} - {3^{x\,\; - \;\frac{1}{2}}} = {3^{x + \frac{1}{2}}} - {2^{2x - 1}}$is

The roots of the equation ${x^4} - 4{x^3} + 6{x^2} - 4x + 1 = 0$ are