Applied Mathematics for Electrical Engineering — Winter 2025

Find a positive root of the equation x3−4x−9=0using bisection method in four steps.

Find a real root of the equation1 x 3 − x − 1 = 0 by using false position method.

Derive a formula to find reciprocal of a positive number Nusing Newton- Raphson method. Hence, find1 correct to three decimal places using Newton-Raphson method.

Given the following table of values of f ( x ) , find the values of  f ( 7 ) ,  2 f ( 9 ) ,  3 f ( 9 ) . x 1 3 5 7 9 f ( x )03

Find the Newton’s forward interpolation polynomial which takes the following values: y ( 0 ) = 1 , y (1 ) = 0 , y ( 2 ) = 1 a n d y ( 3 ) = 1 0 .04 Also, find y(4).

Write Lagrange’s interpolation formula for unequal intervals. Compute f ( 9 . 2 ) using it and the following data. x 9 9.5 11 f ( x )07 2.1972 2.2513 2.3979

Write Newton’s divided interpolation formula. Compute f(10.5)using it and the following data. x 10 11 13 17 f ( x )07 2.3026 2.3979 2.5649 2.8332

Fit a straight line to the following data. x 1 2 3 4 y03 3 dx

Evaluate  with n =6by using Simpson’s 3/8 rule. x+10 dy 2x

Using Euler’s method, find = y− ,y(0)=1(take h=0.1). dx y

Fit a parabola to the following data. x 1 2 3 y03

Using Taylor series method, find y ( 0 .1 ) correct to four decimal places, if y ( x ) satisfies y  = x − y 2 and y ( 0 ) = 104 .

Apply Runge-Kutta method of fourth order to calculate y(0.2)given that y  = x + y , y ( 0 ) = 1 taking h = 0 .107

Four balls are to be drawn without replacement from a box containing 8 red and white balls. If Xdenotes the number of red ball drawn, find the probability distribution of X.

x Is f(x)= ;x=0,1,2,3,4define probability distribution? Justify your answer.6

Three bags contain 3 red, 7 black; 8 red, 2 black, and 4 red and 6 black balls respectively. One of the bags is selected at random and a ball is drawn from it. If the ball drawn is red, find the probability that it is drawn from the third bag.

Aproblem of Mathematics is given to three students A, Band Cwhose chances of solving it are 1/3, 1/4 and 1/2, respectively. What is the probability that the problem will be solved?

Check whether the function defined by f ( x ) = = 0 x6 ; ; − O1 t h  e r x w  i s1 e04 is a probability density function?

Define Conditional Probability. In a certain assembly plant, three machines B1 , B2 and B3 produces 30%, 45% and 25% of the products, respectively. It is known from past experience that 2%, 3% and 2% of the products made by each machine, respectively, are defective. Suppose that a finished product is randomly selected. What is the probability that it is defective?

Find the arithmetic mean by short-cut method for the following data. x03 f 2 8 43 133 207 260 213 120 54 9 1

The probability distribution is given as below. Find expectation and variance. x 5 6 7 8 9 i p i04 0.05 0.10 0.30 0.40 0.10 0.05

Find median for the following data. x 0-10 10-20 20-30 30-40 40-50 50-60 f07

Calculate the average marks of the students by step deviation method for the following data. Marks 0-10 10-20 20-30 30-40 40-50 40-60 No. of Students 40 41 55 30 21 16

Determine the smallest value of k in the Chebyshev’s inequality for which the probability is at least 0.95.

Calculate mode for the following data. x 0-100 100-200 200-300 300-400 400-500 500-600 600-700 f 10 20 25 25 37 19 19