51.

The number of solutions of the equation tan(x) + sec(x) = 2cos(x) and cos(x) $\ne$ 0 lying in the interval ($0, \mathrm{\pi }$) is :

• 2

• 1

• 0

• 3

The angle between $\overrightarrow{\mathrm{a}} \mathrm{and} \overrightarrow{\mathrm{b}}$ is $\frac{5\mathrm{\pi }}{6}$ and the projection of $\overrightarrow{\mathrm{a}}$ in the direction of $\overrightarrow{\mathrm{b}}$ is $\frac{- 6}{\sqrt{3}}$, then $\left|\overrightarrow{\mathrm{a}}\right|$ is equal to :

• 6

• $\frac{\sqrt{3}}{2}$

• 12

• 4

If birth to a male child and birth to a female child are equal-probable, then what is the probability that at least one of the three children born to a couple is male ?

• $\frac{4}{5}$

• $\frac{7}{8}$

• $\frac{8}{7}$

• $\frac{1}{2}$