The order and degree Of the differential equation $\frac{d^2 y}{dx^2} + 2 e^{-x} = 0$, respectively are

If $R(x)$ is the total revenue received and $C(x)$ is the total cost incurred in the production of x units of a commodity, then the profit function $P(x)$

If $x^3 + y^3 = xy$, then $\frac{dy}{dx}$ is equal to :

If x is real, the minimum value of $f(x) = x^2 - 8x + 20$ is :

If $x = 2t^2 + 3, y = 3t^2 + 6t + 5$, then the value of $\frac{d^2y}{dx^2}$ is :

$\int \frac{dx}{x^{n+1} - x}\,dx$

The demand function P for maximising a profit monopolist is given by P=274-x², while the marginal cost is 4+3x for x units of commodity. The consumer surplus is