Q.1
14 Marks(a)
Define Beta and Gamma functions. Also prove that ∫ 𝑥𝑑𝑥 √1−𝑥⁵ 1 0 = 1 5 𝛽 (2 5 , 1
2.
Also asked in Winter 2025 Q1a
Gujarat Technological UniversitySummer 2025 examination
GTU 130001 Mathematics-III (Maths 3) Summer 2025 Question Paper & PDF
B.E. · Computer Engineering · Semester 3 · Subject code 130001
- Total
- 70 marks
- To pass
- 23 marks (33%)
- Duration
- 2.5 Hours 2:30 PM – 5:30 PM
- Questions
- 5 with internal choice
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14 of 17 questions are types of question GTU sets again with new data. Each is marked below with the years it appeared.See all 11 repeated 130001 questions, most asked first
Q.2
14 Marks(a)
Obtain the Fourier series of periodic function 𝑓(𝑥) = 2𝑥, −1 < 𝑥 < 1, 𝑝 = 2.
Also asked in Winter 2025 Q3b OR
(b)
Test for exactness and solve [(𝑥 + 1)𝑒𝑥 − 𝑒𝑦]𝑑𝑥 − 𝑥𝑒𝑦𝑑𝑦 = 0, 𝑦(1) = 0.
Also asked in Winter 2025 Q2b
OR
Q.3
14 Marks(a)
Solve the initial value problem 𝑦′′ + 𝑦′ − 2𝑦 = 0, 𝑦(0) = 4 𝑎𝑛𝑑 𝑦′(0) = −5.
(b)
Find the solution of differential equation 𝑦′′ + 4𝑦 = 2𝑠𝑖𝑛3𝑥 by the method of undetermined co-efficients.
Also asked in Winter 2025 Q2a
OR
Q.4
14 Marks(a)
OR
Q.5
14 Marks(a)
A rod of length L with insulated side is initially at uniform temperature 100. Its ends are suddenly cooled at 0𝑜𝑐 and kept at that temperature. Find the temperature function 𝑢(𝑥, 𝑡).
Also asked in Winter 2025 Q5b OR
(b)
Prove that ∫ 1−𝑐𝑜𝑠𝜋𝑤 𝑤 ∞ 0 𝑠𝑖𝑛𝑤𝑥𝑑𝑤 = { 𝜋 2 , 𝑖𝑓 0 < 𝑥 < 𝜋 0, 𝑖𝑓 𝑥 > 𝜋.
OR
(b)
Find Fourier cosine integral of 𝑓(𝑥) = 𝑒−𝑘𝑥, where 𝑥 > 0, 𝑘 > 0.
More Mathematics-III papers
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Other Semester 3 subjects
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About this paper
Official Gujarat Technological University (GTU) examination paper for Mathematics-III (Maths 3) (Summer 2025, B.E. · Computer 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.