Solution of the equation $\sqrt {x + 3 - 4\sqrt {x - 1} } + \sqrt {x + 8 - 6\sqrt {x - 1} } = 1$ is
$x \in \left[ {4,9} \right]$
$x \in \left[ {3,8} \right]$
$x \in \left[ {5,10} \right]$
$x \in \left[ {4,7} \right]$
Number of natural solutions of the equation $x_1 + x_2 = 100$ , such that $x_1$ and $x_2$ are not multiple of $5$
The real roots of the equation ${x^2} + 5|x| + \,\,4 = 0$ are
Let $\alpha, \beta, \gamma$ be the three roots of the equation $x ^3+ bx + c =0$. If $\beta \gamma=1=-\alpha$, then $b^3+2 c^3-3 \alpha^3-6 \beta^3-8 \gamma^3$ is equal to $......$.
The number of distinct real roots of the equation $x ^{7}-7 x -2=0$ is
The number of ordered pairs $(x, y)$ of positive integers satisfying $2^x+3^y=5^{x y}$ is