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Evaluate ∫ 𝑑𝑥 1+𝑥3 𝑑𝑥 9 0 correct to four decimal places by Simpson’s³ 8 rule. Take ℎ = 1.
Find a real root of the equation 𝑥³ − 2𝑥 − 5 = 0 by the method of false position correct to three decimal places.
A bag contains 8 white and 6 red balls. Find the probability of drawing two balls of the same colour.
Using the method of least squares, find the straight line 𝑦 = 𝑎𝑥 + 𝑏, that fits the following data: 𝑥: 0.5 1.0 1.5 2.0 2.5 3.0 𝑦: 15 17 19 14 10
Using Runge-Kutta method of fourth order compute 𝑦(0.2) from 10 𝑑𝑦 𝑑𝑥 = 𝑥² + 𝑦², 𝑦(0) = 1, take ℎ = 0.1.
Find by Taylor’s series method the value of 𝑦 at 𝑥 = 0.1 and 𝑥 = 0.2 from 𝑑𝑦 𝑑𝑥 = 𝑥²𝑦 − 1, 𝑦(0) = 1.
𝑋 is continuous random variable with probability density function given by 𝑓(𝑥) = { 𝑘𝑥; 0 ≤ 𝑥 < 2 2𝑘; 2 ≤ 𝑥 < 4 −𝑘𝑥 + 6𝑘; 4 ≤ 𝑥 < 6 . Find 𝑘.
Find the cubic polynomial which takes the following values by Newton forward interpolation: 𝑥: 0 1 2 3 𝑓(𝑥): 1 2 1 10 Hence evaluate 𝑓(4).
Size of item: 6 7 8 9 10 11 12 Frequency: 3 6 9 13 8 5
𝑥: 0 1 2 4 𝑦: 1 1 2
Evaluate ∫ 𝑒𝑥+𝑒−𝑥 2 𝑑𝑥 1.8 1.0 using Simpson’s¹ 3 rule by taking ℎ = 0.2.
The probability density function of a variate 𝑋 is 𝑋: 0 1 2 3 4 5 6 𝑃(𝑋): 𝑘 3𝑘 5𝑘 7𝑘 9𝑘 11𝑘 13𝑘
The probability that a pen manufactured by a company will be defective is
Given 𝑃(𝐴) = 1 4 , 𝑃(𝐵) = 1 3 and 𝑃(𝐴 ∪ 𝐵) = 1 2 , evaluate 𝑃(𝐴/𝐵), 𝑃(𝐴 ∩ 𝐵′) and 𝑃(𝐴/𝐵′).
A factory has three machines, X, Y and Z, producing 1000, 2000 and 3000 bolts per day respectively. The machine X produces 1% defective bolts, Y produces 1.5% and Z produces 2% defective bolts. At the end of the day, a bolt is drawn at random and it is found to be defective. What is the probability that this defective bolt has been produced by the machine X?
Two cards are drawn in succession from a pack of 52 cards. Find the chance that the first is a king and the second a queen if the first card is
Class interval: 0-10 10-20 20-30 30-40 Frequency: 1 4 3
A pair of dice is tossed twice. Find the probability of sum of scoring 7 points
employees: 8 16 20 17
BE Electrical
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Official Gujarat Technological University (GTU) examination paper for Applied Mathematics for Electrical Engineering (Summer 2026, B.E. · Electrical Engineering, Sem 3). Features complete 70-mark regular & remedial examination pattern, official marking distribution across all 5 questions, and direct 1-click official PDF download.
Transcribed for student exam preparation from Gujarat Technological University official examination archives. Questions, syllabus guidelines, and curriculum marking schemes remain the intellectual property of Gujarat Technological University.
3130908 Applied Mathematics for Electrical Engineering
Official GTU PDF · Summer 2026
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