The number of solutions for the equation $x^2 - 5|x| + 6 = 0$ is

Let $\overline{a}, \overline{b}$ and $\overline{c}$ be three non-zero vectors such that no two of them are collinear and $(\overline{a} \times \overline{b}) \times \overline{c}=\frac{1}{3}|\overline{b}||\overline{c}| \overline{a}$. If $\theta$ is the angle between the vectors $\overline{b}$ and $\overline{c}$,then the value of $\sin \theta$ is

The solution of the differential equation $\frac{dy}{dx} = \sin(x+y) \tan(x+y) - 1$ is

If the radius of a nucleus with mass number $125$ is $1.5 \text{ fermi}$,then the radius of a nucleus with mass number $64$ is: (in $text{ fermi}$)

$A$ calcite crystal is placed over a dot on a piece of paper and rotated. On seeing through the calcite,one will see:

What is the final product obtained by the reduction of glycerol with hydriodic acid $(HI)$?