The equation of the parabola with focus $(0,0)$ and directrix $x+y=4$ is

Two blocks of masses $10\,kg$ and $4\,kg$ are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of $14\,m/s$ to the heavier block in the direction of the lighter block. The velocity of the centre of mass is ......... $m/s$.

If $\int \sqrt{\frac{x}{a^3-x^3}} \, dx = g(x) + c$, then $g(x)$ is equal to:

Let $A$ and $B$ be independent events with $P(A)=0.3$ and $P(B)=0.4$. Find $P(A | B)$.

The half-life of a radioactive substance is $20 \, min$. The approximate time interval $(t_2 - t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it has decayed and the time $t_1$ when $\frac{1}{3}$ of it has decayed is ......... $min$.