The Euclidean algorithm is used to calculate the _____.

If radius of a sphere is rational, then which of the following is/are correct ?

$1.$Its surface area is rational.

$2.$ Its volume is rational.

Select the correct answer using the code given below :

Consider the following statements:

$1. \sin a=x+\frac{1}{x}$ is possible for some real value of $x$.

$2. \cos a=x+\frac{1}{x}$ is possible for some real value of $x$.

Which of the above statements is/are correct?

Consider the following statements:

$1.$ The equation $2 {\sin }^2 \mathrm{\theta } - \cos \mathrm{\theta } + 4= 0$ is possible for all $\mathrm{\theta }$?

$2. \tan \mathrm{\theta } + \cot \mathrm{\theta }$ cannot be less than $2$, where $0 < \theta < \frac{\mathrm{\pi }}{2}$.

Which of the above statements is/are correct?