If one of the lines $2x^2 - xy + by^2 = 0$ passes through the point $(-4, -2)$,then $b^2 =$

The Test-tube Baby Programme employs which one of the following techniques?

The polar equation of the circle with centre $\left(2, \frac{\pi}{2}\right)$ and radius $3$ units is :

The mitral valve is supported by which of the following?

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:

$A$ mass $m$ moving horizontally (along the $x-$ axis) with velocity $v$ collides and sticks to a mass of $3m$ moving vertically upward (along the $y-$ axis) with velocity $2v$. The final velocity of the combination is