$A$ piece of steel is heated to $100^{\circ}C$ and allowed to cool in a room. Which graph correctly represents the cooling process?

The rate of disintegration of a radioactive element at any time is proportional to its mass at that time, where $k (k > 0)$ is the constant of proportionality. The time during which an original mass of $1.5 \text{ gm}$ will disintegrate to a mass of $0.5 \text{ gm}$ is ...

The differential equation $y\frac{dy}{dx} + x = a$ ($a$ is any constant) represents:

The rate of disintegration of a radioactive element at time $t$ is proportional to its mass at that time. Then the time during which the original mass of $1.5 \text{ g}$ will disintegrate into its mass of $0.5 \text{ g}$ is proportional to

At any point $(x, y)$ of a curve,the slope of the tangent is twice the slope of the line segment joining the point of contact to the point $(-4, -3)$. Find the equation of the curve given that it passes through $(-2, 1)$.

The slope at any point of a curve $y=f(x)$ is given by $\frac{dy}{dx}=3x^2$ and it passes through $(-1,1)$. The equation of the curve is