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Four cards are drawn from a pack of cards. Find the probability that there are two spades and two hearts.
Evaluate ∫ (1 + 𝑥) 2 0 𝑑𝑥 by Gaussian two point quadrature formula.
Solve 𝑦′ = 3𝑥 + 𝑦 2 using 4th order Runge – Kutta method with y (0) = 1 and h = 0.05.
Construct the difference table for 𝑓(𝑥) = (𝑥 + 2)² for x = 1, 2, 3, 4 and find ∇2𝑓(3).
Apply Gauss-Seidel iteration method correct to four decimal places to solve the system 20𝑥 + 𝑦 − 2𝑧 = 17 3𝑥 + 20𝑦 − 𝑧 = −18 2𝑥 − 3𝑦 + 20𝑧 = 25
x 20 30 40 50 y 512 439 346 243
Calculate the median from the following frequency distribution of marks obtained by 22 students: Marks Below 10 Below 20 Below 30 Below 40 Below 50 No. of students 3 8 17 20 22
Find the value of 1 31 by using Newton-Raphson method corrected up to four decimal places.
In a company, the coefficient of variation of wages of male and female workers were 55% and 70% respectively. The standard deviations were Rs. 22 and Rs. 15.40 respectively. Calculate the combined average wages for all workers if 80% of the workers were male.
Let 𝑋 be a random variable with probability density function 𝑓(𝑥) = 6𝑥(1 − 𝑥), 0 ≤ 𝑥 ≤ 1 Determine a number 𝑏 such that 𝑃(𝑋 < 𝑏) = 𝑃(𝑋 > 𝑏)
Using the method of least squares, find the best fitting straight line to the given data: x 1 2 3 4 5 y 1 3 5 6
Find a real root of the equation 𝑥log10𝑥 = 1.2 using Regula-Falsi method, correct up to four decimal places.
x : 11 14 14 17 17 21 25 y : 15 27 27 30 34 38 46
Two Math tests are taken in a class. 25% passed both tests and 42% passed the first test. What percent of those who passed the first test also passed the second?
Compute f(0.4) from the data presented in the table using Lagrange’s interpolation: x 0.3 0.5 0.6 f (x) 0.61 0.69 0.72
Solve using partial pivoting by Gaussian elimination method 8𝑦 + 2𝑧 = −7 3𝑥 + 5𝑦 + 2𝑧 = 8 6𝑥 + 2𝑦 + 8𝑧 = 26
Estimate f (0.5) using Newton’s forward interpolation formula from the given data: x 0 1 2 3 4 f (x) 1 7 23 55 109
Let 𝑝(𝑥) be the probability mass function of the discrete random variable 𝑋 which assumes the values 𝑥1, 𝑥2, 𝑥3, 𝑥4 such that 2𝑝(𝑥1) = 3𝑝(𝑥2) = 𝑝(𝑥3) = 5𝑝(𝑥4). Construct a table for the mass function and the distribution function of the random variable 𝑋.
Find a real root of 𝑥³ + 2𝑥² − 3𝑥 − 1 = 0 correct up to two decimal places by Secant method starting from 𝑥0 = 2 and 𝑥1 = 1.
Evaluate ∫ 1 1+𝑥 3 0 𝑑𝑥 with n = 6 using Simpson’s 3/8th rule.
The overall percentage of failures in a certain examination is 40. What is the probability that out of a group of 6 candidates, at least 4 passed the examination?
Using Taylor’s series method, evaluate y (0.1) correct to four decimal places for the differential equation 𝑦′ = 𝑥 − 𝑦² with y (0) = 1.
BE Civil
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Official Gujarat Technological University (GTU) examination paper for Numerical And Statistical Methods for Civil Engineering (Summer 2025, B.E. · Civil Engineering, Sem 4). 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.
2140606 Numerical And Statistical Methods for Civil Engineering
Official GTU PDF · Summer 2025
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