If the inequality $kx^2 -2x + k \geq  0$ holds good for atleast one real $'x'$ , then the complete set of values of $'k'$ is

The sum of the solutions of the equation $\left| {\sqrt x  - 2} \right| + \sqrt x \left( {\sqrt x  - 4} \right) + 2 = 0\left( {x > 0} \right)$ is equal to

Let $\alpha, \beta$ be roots of $x^2+\sqrt{2} x-8=0$. If $\mathrm{U}_{\mathrm{n}}=\alpha^{\mathrm{n}}+\beta^{\mathrm{n}}$, then $\frac{\mathrm{U}_{10}+\sqrt{2} \mathrm{U}_9}{2 \mathrm{U}_8}$ is equal to ............

The number of real solutions of the equation $|x{|^2}$-$3|x| + 2 = 0$ are

Number of natural solutions of the equation $xyz = 2^5 \times 3^2 \times  5^2$ is equal to

Let $\mathrm{S}=\left\{x \in R:(\sqrt{3}+\sqrt{2})^x+(\sqrt{3}-\sqrt{2})^x=10\right\}$. Then the number of elements in $\mathrm{S}$ is :