If $v = \frac{4}{3} \pi r^3$, at what rate is cubic / unit sec is increasing when $r = 10$, and $\frac{dr}{dt} = 0.01$ ?

The value of the integral $\int_{-3}^{3} (x^3 - x) dx$ is :

If $x = \log t$ and $y = \frac{1}{t^2}$, then $\frac{d^2 y}{d x^2}$ is equal to

The area bounded by the curve $y = x^2$ between $x = 0$ and $x = \pi$ in the first quadrant is :

The supply function of a commodity is P = $x^3+2x+18$. When 4 units of commodity are sold , then producer surplus is:

If $C(x) = ax^2 - bx - c$ represents the total cost function then the slope of the tangent to the marginal cost curve at the point $(x, y)$ is :

The total cost function for $x$ units of a commodity is given by $C(x) = \frac{25x^3}{3} - 75x^2 + 48x + 34$. The output $x$ at which the marginal cost is minimum is :