$A$ sample of a radioactive element has a mass of $10 \, g$ at an instant $t=0$. The approximate mass of this element in the sample after two mean lives is ........ $g$.

If the cold junction is held at $0^{\circ} C$,the thermo emf $V$ of a thermocouple varies as $V = 10 \times 10^{-6} t - \frac{1}{40} \times 10^{-6} t^2$,where $t$ is the temperature of the hot junction in $^{\circ} C$. The neutral temperature and the maximum value of thermo emf are respectively:

Potato and tomato are native of

The equations of the perpendicular bisectors of sides $AB$ and $AC$ of a $\triangle ABC$ are $x-y+5=0$ and $x+2y=0$ respectively. If the coordinates of vertex $A$ are $(1, -2)$,then the equation of $BC$ is

The equation $x^2 - 2\sqrt{3}xy + 2y^2 = 0$ represents two sides of a triangle. If the angle between them is $\frac{\pi}{3}$,then the perimeter of that triangle is

Assertion $A$: An astronaut inside a massive spaceship orbiting around the Earth will experience a finite but small gravitational force.
Reason $R$: The centripetal force necessary to keep the spaceship in orbit around the Earth is provided by the gravitational force between the Earth and the spaceship.