Complete solution set of the inequality $\left( {{{\sec }^{ - 1}}\,x - 4} \right)\left( {{{\sec }^{ 1}}\,x - 1} \right)\left( {{{\sec }^{ - 1}}\,x - 2} \right) \ge 0$ is
$\left[ {\sec 2\,,\,\sec \,1} \right]$
$\left[ {\sec 1\,,\,\sec \,2} \right]\, \cup \,\left[ {\sec \,4\,,\,\infty } \right)$
$\left( { - \infty \,,\,\sec \,2} \right]\, \cup \,\left[ {\sec \,1\,,\,\infty } \right)$
$\left( { - \infty \,,\,\sec \,4} \right]\, \cup \,\left[ {\sec \,2\,,\,\infty } \right)$
The number of real solutions of the equation $|{x^2} + 4x + 3| + 2x + 5 = 0 $are
The number of distinct real roots of $x^4-4 x^3+12 x^2+x-1=0$ is
The number of ordered pairs $(x, y)$ of positive integers satisfying $2^x+3^y=5^{x y}$ is
If the sum of the two roots of the equation $4{x^3} + 16{x^2} - 9x - 36 = 0$ is zero, then the roots are
If $2 + i$ is a root of the equation ${x^3} - 5{x^2} + 9x - 5 = 0$, then the other roots are