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4-2.Quadratic Equations and Inequations
normal
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
A
$\left[ {\sec 2\,,\,\sec \,1} \right]$
B
$\left[ {\sec 1\,,\,\sec \,2} \right]\, \cup \,\left[ {\sec \,4\,,\,\infty } \right)$
C
$\left( { - \infty \,,\,\sec \,2} \right]\, \cup \,\left[ {\sec \,1\,,\,\infty } \right)$
D
$\left( { - \infty \,,\,\sec \,4} \right]\, \cup \,\left[ {\sec \,2\,,\,\infty } \right)$
Solution
$sec^{-1}x – 4$ is always $-ve$
$ \Rightarrow \,\left( {{{\sec }^{ – 1}}\,x – 1} \right)\left( {{{\sec }^{ – 1}}\,x – 2} \right) \le 0$
Standard 11
Mathematics
