CBSE Class class-12 Applied Mathematics — Very Short Answer Questions

Calculate 3-yearly moving averages for the following data : Years (t): 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020 Variables (x): 3, 5, 7, 10, 12, 14, 15, 16

A man in a boat goes 12 km downstream and comes back to the starting point by rowing non-stop in a total time of 3 hours. If the speed of the stream is 3 km/h, find the speed with which the man can row the boat in still water.

(a) For a Poisson distribution, if mean (m) = 1, then find $P(r = 1)$. OR (b) Find the mean and standard deviation of the Binomial distribution $B\left(4, \frac{1}{3}\right)$.

A man takes a personal loan of Rs 2,00,000 at an interest rate of 15% p.a. compounded monthly, to be repaid by equal monthly instalments in 4 years. Calculate the EMI, using reducing balance method. [Given : $(1.0125)^{-48} = 0.55$]

(a) Solve the following differential equation : $\frac{dy}{dx} = \frac{2 - y}{x + 1}$ OR (b) If $\int_{a}^{b} x^3 dx = 0$ and $\int_{a}^{b} x^2 dx = \frac{2}{3}$, then find the values of 'a' and 'b'.