CBSE Class 12 Applied Mathematics — Long Answer Questions

Solve the following inequation : $\frac{2x - 1}{12} - \frac{x - 11}{3} < \frac{3x + 1}{4}, x \in R$

(a) Find the consumer's surplus for the demand function $p = 25 - x - x^2$, where the prevailing market price $p_0 = 19$. OR (b) Solve the following initial value differential equation : $(x - 1) \frac{dy}{dx} = 2xy$, when $y(2) = 1$.

Mr. Arya wants to know the amount he should pay for a gold mine expected to yield an annual return of Rs 4 lakh for the next 10 years, after which it will be worthless. Find the amount he should pay for the mine, if he wants to yield 18% annual return on his investment and also set up a sinking fund to replace the purchase price. Assume that the sinking fund earns 10% annually. [Use $(1.1)^{10} = 2.5937$]

(a) Two cards are drawn at random and one by one with replacement from a well-shuffled pack of 52 playing cards. Find the probability distribution of the number of aces. Also, find its mean and variance. OR (b) It is given that 2% of the screws manufactured by a company are defective. Use Poisson distribution to find the probability that a packet of 100 screws contains (i) no defective screw, (ii) one defective screw.