Consider the fourteen lines in the plane given by $y=x+r$ and $y=-x+r$,where $r \in \{0, 1, 2, 3, 4, 5, 6\}$. The number of squares formed by these lines,whose sides are of length $\sqrt{2}$,is:

The major product in the following reaction is:

The common bottle cork is a product of .......... .

If the angles of a triangle are in the ratio $4:1:1$,then the ratio of the longest side to the perimeter is

$A$ bus moving on a level road with a velocity $v$ can be stopped at a distance of $x$,by the application of a retarding force $F$. The load on the bus is increased by $25 \%$ by boarding the passengers. Now,if the bus is moving with the same speed and if the same retarding force is applied,the distance travelled by the bus before it stops is

When a wave traverses a medium,the displacement of a particle located at $x$ at a time $t$ is given by $y = a \sin (bt - cx)$,where $a, b,$ and $c$ are constants of the wave. Which of the following is a quantity with dimensions?