In $\triangle ABC$,$(a+b+c)\left(\tan \frac{A}{2}+\tan \frac{B}{2}\right)$ is equal to

$A$ cylinder of height $h$ is filled with water and is kept on a block of height $h / 2$. The level of water in the cylinder is kept constant. Four holes numbered $1, 2, 3$ and $4$ are at the side of the cylinder and at heights $0, h / 4, h / 2$ and $3h / 4$ respectively from the base of the cylinder. When all four holes are opened together,the hole from which water will reach the farthest distance on the plane $PQ$ is the hole number

$A$ fish looking up through the water sees the outside world,contained in a circular horizon. If the refractive index of water is $\frac{4}{3}$ and the fish is $12 \ cm$ below the water surface,the radius of this circle in $cm$ is

The coordinate axes are rotated through an angle of $135^o$. If the coordinates of a point $P$ in the new system are $(4, -3)$,then the coordinates of $P$ in the original system are:

The value of $\cos \frac{2 \pi}{15} \cos \frac{4 \pi}{15} \cos \frac{8 \pi}{15} \cos \frac{14 \pi}{15}$ is :

$A$ particle is performing $U.C.M.$ along the circumference of a circle of diameter $50 \ cm$ with frequency $2 \ Hz$. The acceleration of the particle in $m/s^2$ is