$A$ body is projected vertically upwards with a velocity $u$ from the top of a tower. The time taken by it to reach the ground is $n$ times the time taken by it to reach the highest point in its path. The height of the tower is:

The angle between the lines whose direction cosines are given by the equations $l^2+m^2-n^2=0$ and $l+m+n=0$ is

The parabola with directrix $x+2y-1=0$ and focus $(1,0)$ is

The length of the common chord of the circles of radii $15$ and $20$,whose centers are $25$ units of distance apart,is

If $p \rightarrow (p \wedge \sim q)$ is false,then the truth values of $p$ and $q$ are respectively

Two rigid boxes containing different ideal gases are placed on a table. Box $A$ contains one mole of nitrogen at temperature $T_0$,while box $B$ contains one mole of helium at temperature $\left( \frac{7}{3} \right) T_0$. The boxes are then put into thermal contact with each other,and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of the boxes). The final temperature of the gases,$T_f$,in terms of $T_0$ is: