Advanced Engineering Mathematics

What is the difference between linear and non-linear programming problem.

What is optimization Technique? Give example.

What is mean, variance and standard Deviation of Uniform Distribution and Exponential Distribution.

Fit a straight line of following set of observation:

What is spearman rank correlation?

Write the dual of:

What is difference between skewness and kurtosis.

Find the optimal assignment for the problem with minimum cost:

Define Poisson Distribution. Derive it a limiting case of Binomial distribution Find the mean and Variance also.

Old hens can be bought at Rs 2.00 with young ones at Rs 5.00 each. An old hen lays 3 eggs a young one 5 eggs a week. Each egg is sold for 30P. If the expenses incurred on their feeding be Rs 1.00 per hen per week, find how many hens of each kind a person having Rs.80 for investment can purchase to earn maximum profit, if he has accomodation only for 20 hens in his house.

Obtain the optimal transportation plan from the following table:

Calculate the coefficient of correlation and obtain lines of regression for the following data:

If $\theta$ be the acute angle between the two lines of regression of variables $x$ and $y$, show that:

where $r$, ${\sigma }_x$, ${\sigma }_y$ have their usual meaning. Explain the significance where $r=0$ and $r=\pm 1$.

A random variable x has the following probability distribution:

What are the engineering Application of optimization also give various classification of optimization problems.

Write the formulae of Trapezoidal rule and simpson 1/3 rule.

Find the inverse Laplace transform of:

Write the formulae of Fourier sine transform and inverse Fourier sine transform.

State convolution theorem for Z - transform.

The distance covered by an athlete for the 50 meter race is given in the following table. Determine the speed of the athlete at t = 5 sec.

From the following table find f'(6):

Prove that:

and hence deduce the integral ${\int }_0^{\infty }\frac{{\sin }^{2}t}{t^2}dt$.