For a chemical reaction,$A + 2B \to C + D,$ the rate of reaction increases $3$ times when the concentration of $A$ only is increased $9$ times. While when the concentration of $B$ only is increased $2$ times,the rate of reaction also increases $2$ times. The order of this reaction is:

$A$ man wants to reach a certain destination. One-sixth of the total distance is muddy while half the distance is tar road. For the remaining distance,he takes a boat. His speed of travelling in mud,in water,and on tar road is in the ratio $3:4:5$. The ratio of the durations he requires to cross the patch of mud,stream,and tar road is

Match the following columns and select the correct option:

Column-$I$	Column-$II$
$(a)$ Floating ribs	$(i)$ Located between $2^{nd}$ and $7^{th}$ ribs
$(b)$ Acromion process	$(ii)$ Head of humerus
$(c)$ Scapula	$(iii)$ Clavicle articulation
$(d)$ Glenoid cavity	$(iv)$ Do not connect with the sternum

$(a)\quad(b)\quad(c)\quad(d)$

The equations of the perpendicular bisectors of sides $AB$ and $AC$ of a $\triangle ABC$ are $x-y+5=0$ and $x+2y=0$ respectively. If the coordinates of vertex $A$ are $(1, -2)$,then the equation of $BC$ is

The image of the point $(3, 8)$ in the line $x + 3y = 7$ is

$A$ class has $15$ boys and $5$ girls. Suppose $3$ students are selected at random from the class. The probability that there are $2$ boys and $1$ girl is