List of top Applied Mathematics Questions on Miscellaneous

Determine the equation of the straight-line trend.
If \( R_1 \) is the feasible region, then find the maximum value of the objective function \( z = 5x + 2y \).
What are the two trivial constraints?
Write the system of linear equations, obtained in (i) above, in matrix form \( AX = B \).
A river near a small town floods and overflows twice in every 10 years on an average. Assuming that the Poisson distribution is appropriate, what is the mean expectation? Also, calculate the probability of 3 or less overflows and floods in a 10-year interval.
[Given \( e^{-2} = 0.13534 \)]
In a binomial distribution, \( n = 200 \) and \( p = 0.04 \). Taking Poisson distribution as an approximation to the binomial distribution:
Assertion (A): Mean of Poisson distribution = 8.
Reason (R): \( P(X = 4) = \frac{512}{3e^8} \).
For testing the significance of the difference between the means of two independent samples, the degree of freedom (\( v \)) is taken as:
What time will it be after 1275 hours, if the present time is 9:00 p.m.?