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

    $\left( { - \infty \,,\,\sec \,4} \right]\, \cup \,\left[ {\sec \,2\,,\,\infty } \right)$

Similar Questions

If the quadratic equation ${x^2} + \left( {2 - \tan \theta } \right)x - \left( {1 + \tan \theta } \right) = 0$ has $2$ integral roots, then sum of all possible values of $\theta $ in interval $(0, 2\pi )$ is $k\pi $, then $k$ equals 

If the product of roots of the equation ${x^2} - 3kx + 2{e^{2\log k}} - 1 = 0$ is $7$, then its roots will real when

  • [IIT 1984]

The number of ordered pairs $(x, y)$ of real numbers that satisfy the simultaneous equations $x+y^2=x^2+y=12$ is

  • [KVPY 2015]

If $\alpha,\beta,\gamma, \delta$ are the roots of $x^4-100x^3+2x^2+4x+10 = 0$ then $\frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma}+\frac{1}{\delta}$ is equal to :-

Let $\alpha$ and $\beta$ be the two disinct roots of the equation $x^3 + 3x^2 -1 = 0.$ The equation which has $(\alpha \beta )$ as its root is equal to