Given in the figure are two blocks $A$ and $B$ of weight $20 \, N$ and $100 \, N$,respectively. These are being pressed against a wall by a force $F$ such that the system does not slide as shown. If the coefficient of friction between the blocks is $0.1$ and between block $B$ and the wall is $0.15$,the frictional force applied by the wall on block $B$ is ........ $N$.

$A$ car $P$ approaching a crossing at a speed of $10\, m/s$ sounds a horn of frequency $700\, Hz$ when $40\, m$ in front of the crossing. The speed of sound in air is $340\, m/s$. Another car $Q$ is at rest on a road which is perpendicular to the road on which car $P$ is reaching the crossing (see figure). The driver of car $Q$ hears the sound of the horn of car $P$ when he is $30\, m$ in front of the crossing. The apparent frequency heard by the driver of car $Q$ is .... $Hz$.

$A$ road is $10\,m$ wide. Its radius of curvature is $50\,m$. The outer edge is raised above the inner edge by a distance of $1.5\,m$. This road is most suited for a velocity of ......... $m/s$. (in $.5$)

For any integer $n \geq 2$,let $I_n = \int \tan^n x \, dx$. If $I_n = \frac{1}{a} \tan^{n-1} x - b I_{n-2}$ for $n \geq 2$,then the ordered pair $(a, b)$ equals to

Name the blood cells,whose reduction in number can cause clotting disorder,leading to excessive loss of blood from the body.

$\int_0^{\pi / 2} \sin ^8 x \cos ^2 x \, dx$ is equal to