$\mathrm{Assertion} A:$ If $A, B, C, D$ are four points on a semi-circular arc with a centre at $O$ such that $\left|\overrightarrow{AB}\right|=\left|\overrightarrow{BC}\right|=\left|\overrightarrow{CD}\right|.$ Then, $\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{AD}=4\overrightarrow{AO}+\overrightarrow{OB}+\overrightarrow{OC}$

$\mathrm{Reason} R:$ Polygon law of vector addition yields $\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD}+\overrightarrow{AD}=4\overrightarrow{AO}$

In the light of the above statements, choose the most appropriate answer from the options given below.

A swimmer wants to cross a river from point $A$ to point $B$. Line AB makes an angle of $30°$ with the flow of the river. The magnitude of the velocity of the swimmer is the same as that of the river. The angle $\theta$ with the line $AB$ should be _______$°$, so that the swimmer reaches point $B$.

The velocity-displacement graph describing the motion of a bicycle is shown in the figure.

The acceleration-displacement graph of the bicycle's motion is best described by :

Consider a frame that is made up of two thin massless rods $AB$ and $AC$ as shown in the figure. A vertical force $\overrightarrow{P}$ of magnitude $100 \mathrm{N}$ is applied at point $A$ of the frame.

Suppose the force is $\overrightarrow{P}$ resolved parallel to the arms $AB$ and $AC$ of the frame. The magnitude of the resolved component along the arm $AC$ is $xN$. The value of $x$, to the nearest integer, is ________.

[Given : $\sin \left(35°\right)=0.573,\cos \left(35°\right)=0.819, \sin \left(110°\right)=0.939,\cos \left(110°\right)=-0.342$]

A mosquito is moving with a velocity $\overrightarrow{v}=0.5t^2\hat{\mathrm{i}}+3t\hat{\mathrm{j}}+9\hat{\mathrm{k}} \mathrm{m} {\mathrm{s}}^{-1}$ and accelerating in uniform conditions. What will be the direction of mosquitoes after $2 \mathrm{s}$ ?

A force $\overrightarrow{F}=4\hat{\mathrm{i}}+3\hat{\mathrm{j}}+4\hat{\mathrm{k}}$ is applied on an intersection point of $x=2$ plane and $x$-axis. The magnitude of torque of this force about a point $\left(2,3,4\right)$ is ________.

(Round off to the Nearest Integer)