A point P(3a, -2b) lies in region 4x + 7y ≤ (-3) which of the following options is true ?

If $y = e^{\frac{1}{2}\log(1+ \tan^2 x)}$, then $\frac{d^2y}{dx^2}$ is equal to:

If the total cost and total revenue of a company that produces and sells $x$ units of a particular product are $C(x) = 5x + 350$ and $R(x) = 50x - x^2$ respectively, then which of the following is/are the breakeven values: (A) $x = 10$ (B) $x = 25$ (C) $x = 45$ (D) $x = 30$ Choose the correct answer from the options given below:

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

If the random variable X follows the Poisson distribution such that P[X = k] = P[X = k+1], then the mean value of X is:

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