In which of the following is incomplete double circulation observed?

Let $\overline{a}=\hat{i}+\hat{j}+\hat{k}$,$\overline{b}=\hat{i}-\hat{j}+\hat{k}$ and $\overline{c}=\hat{i}-\hat{j}-\hat{k}$ be three vectors. $A$ vector $\overline{v}$ in the plane of $\overline{a}$ and $\overline{b}$,whose projection on $\overline{c}$ is $\frac{1}{\sqrt{3}}$,is given by

One line of the pair of lines $x^2+xy-2y^2=0$ is perpendicular to one line of the pair of lines $3y^2-5xy-2x^2=0$. If the combined equation of the two lines other than those two perpendicular lines is $ax^2+2hxy+by^2=0$,then $a+2h+b=$

$A$ fire hydrant delivers water of density $\rho$ at a volume rate $L$. The water travels vertically upward through the hydrant and then makes a $90^o$ turn to emerge horizontally at speed $V$. The pipe and nozzle have a uniform cross-section throughout. The force exerted by the water on the corner of the hydrant is

Which of the following acts as both an oxidizing agent and a reducing agent?

The number of circles that touch all the straight lines $x+y=4$,$x-y=-2$,and $y=2$ is