Applied Mathematics for Electrical Engineering — Summer 2022

Use false position method to find the root of f(x) x2 x20 in the range 1 x3, correct to three decimal places.

Fit a straight line to the following data: x 6 7 7 8 8 8 9 9 y 5 5 4 5 4 3 4 3

The velocity v of a particle at distance s from point on its path is given by the following table: s (meter) 0 10 20 30 40 50 60 v (meter/second) 47 58 64 65 61 52 38 Find the time taken to travel 60 meter using Simpson’s 1/3 rule.

There are 3 statistician, 2 economists and 4 engineers. Acommittee of 4 is to be formed in such a way that there are 2 statisticians and engineers. Find the probability.

Find coefficient of variation for the following distribution. x 5 10 15 20 25 i f 7 4 6 3 i

Discuss bisection method. Find a root of x3 x110 correct to four decimal places using bisection method.

Discuss Newton-Raphson method. Find a real root of f(x)  x1.2sin x0.5 0, correct to four decimal places, which lies between 1.5 and 2 by using Newton-Raphson method.

1 State Trapezoidal rule with n=10 and using it evaluate exdx.0

Fit a second degree parabola y ax2 bxcin least square sense for the following data: x 1 2 3 4 y 10 12 13 16 19

Compute the values of f (x)at x=0.02 and x=0.38 using Newton’s forward and backward interpolation formula respectively for: x 0.0 0.1 0.2 0.3 0.4 f(x) 1.0000 1.1052 1.2214 1.3499 1.4918 OR1

1 dx Evaluate the integral  by Gaussian integration two point 1 x2 1 formula.

Find the third divided difference with arguments 2, 4, 9, 10 of the function f(x) x3 2x.

Determine the interpolating polynomial of degree three using Lagrange’s interpolation formula x 0 1 3 y -12 0 12 24

Define sample space, simple events and compound events.

Is the function  0,x0 f(x) a probability distribution? 8xe4x2 ,x 0

dy x2 Using Picard’s method find a solution of  ,y(0) 0upto dx y2 1 second approximation.

Aperson hits a target with rifle shot in 4 out of 5 times. Another person can hit the same target with the same rifle in 3 out of 4 times. Find the probability of the target being hit when both try or by at least one hits the target.

An equipment will function only if three components A, Band Care all working. The probability of A’s failure during one year is 5% that of B’s failure is 15% and that of C’s failure is 10%. What is the probability that the equipment will fail before the end of that year?

Use fourth order Runge-Kutta method to find the value of y when x=0.2, given that y' x y2, and y=1 when x=0.

Find the skewness when the second and third central moments are 16 and 42 respectively.

The following distribution shows the selling of cars in a week by a dealer. No. of cars 0 1 2 3 4 Probability 0.2 0.25 0.35 .05 0.08 0.07 What is the average number of cars he sells?

Find the Karl Pearson’s coefficient of skewness for: Class 50-55 55-60 60-65 65-70 70-75 Frequency 8 10 15 17 Also show that the distribution is platykurtic.

Find S.D. of the marks obtained by students: 65, 58, 67, 34, 48, 45, 70, 62, 60, 50.

There are 5 black balls and 4 red balls. Find the number of ways in which 6 balls can be selected so that there are at least 2 red balls in that selection.

Three machines A, Band Cproduce 50%, 30% and 20% of the total number of items. The production of defective item is 3%, 4%, 5% respectively on each machine. If an item selected at random and is found to be defective, find the probability that the item was produced by machine A.