B.TechSemester 32025-26Mathematics VBAS304
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Mathematics V (BAS304) - AKTU Question Paper 2025-26

B.Tech · Semester 3 · Free PDF Download

This is the official AKTU Mathematics V Previous Year Question Paper for B.Tech Semester 3, academic session 2025-26. Published by Dr. A.P.J. Abdul Kalam Technical University (AKTU/UPTU), Lucknow. Free PDF download — no login required.

Course:B.Tech
Semester:Semester 3
Session:2025-26
University:AKTU / UPTU

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Questions Asked in 2025-26

Mathematics V (BAS304) — complete question paper · 70 marks · 3 Hours

Section AAttempt all questions in brief.
  • a
    Find the Fourier sine and cosine transforms of
  • b
    One type of aircraft is found to develop engine trouble in 5 flights out of a total of 100 and another type in 7 flights out of a total of 200 flights. Is there a significant difference in the two types of aircrafts so far as engine defects are concerned?
  • c
    Show that the equation has exactly one real root , and obtain its value correct up to two decimal places using the Bisection Method
  • d
    Write any 2 advantages and 2 disadvantages of Randomized complete block chain (RBD)
  • e
    Explain the rule of Regula Falsi
  • f
    Starting with 𝑥3 = 0, find a root of 𝑥3 − 3𝑥 − 5 = 0, correct to three decimal places. Use Newton-Raphson Method
  • g
    The overall percentage of failures in a certain examination is 20. If six candidates appear in the examination, what is the probability that at least five pass the examination?
Section BAttempt any three of the following: 7 x 3 = 21
  • b
    Prove that: Poisson distribution is a particular limiting form of the Binomial distribution when p (or q) is very small and n is large enough. Poisson Distribution 𝑟! , where m is the mean of the distribution
  • c
    Find the complex form of the Fourier series: iii. 𝑓(𝑥) = 𝐶𝑜𝑠𝑎𝑥, −𝜋 < 𝑥 < 𝜋
  • d
    In a Survey a random sample of 198 farms were classified into three classes according to tenure status as owned, rented and mixed. They were also classified according to the level of the soil fertility as highly fertile, moderately fertile and low fertile farms. The results are given in Table. Tenure Status Soil Fertility Owned No. Rented No. Mixed No Total No. (%) High 40(64.5) 12(19.4) 10(16.1) 62(100.0) Moderate 22(47.9) 10(21.7) 14(30.4) 46(100.0) Low 22(24.4) 26(28.9) 42(46.7) 90(100.0) Total 84(42.4) 48(24.3) 66(33.3) 198(100.0) Does tenure status depend on soil fertility?
  • e
    Find the solution of 𝜕𝑡 for which 𝑢(0, 𝑡) = 𝑢(1, 𝑡), 𝑢(𝑥, 0) = 𝑠𝑖𝑛 method of variable separable
Section CAttempt any one part of the following:
  • a
    Define Normal Distribution and also derive Mean, Median and Standard Deviation of Normal Distribution
  • b
    Using Fourier SINE & COSINE transform prove these: iii. 𝐹𝑠{𝑓′′(𝑥)} = −
  • a
    Form an experiment conducted in LSD with 5 treatments the following results were obtained: Row MS = 11.667, Column MS = 11.405, Treatment MS = 49.151 and Error MS = 2.337
  • b
    What is Sampling Distribution of the Proportion and also Solve “ .A group of scientific men reported 1705 sons and 1527 daughters. Do these figures conform to the hypothesis that the sex ratio is
  • a
    By using Newton-Raphson’s method find the root of 𝑥4 − 𝑥 − 10 = 0, which is near to 𝑥 = 2 correct to three places of decimal
  • b
    Given that 𝑓(𝑥) = 𝑥 + 𝑥2 for −𝜋 < 𝑥 < 𝜋, find the Fourier expression of 𝑓(𝑥). Deduce that
  • a
    Assuming a Binomial distribution, find the probability of obtaining at least two “six” in rolling a fair die 4 times
  • b
    The function 𝑓(𝑥) is known to be a cubic polynomial. The following data are given: Using Newton’s divided difference formula, determine the value of 𝑘 such that the interpolating polynomial satisfies 𝑓(3) = 17. Hence, obtain the explicit form
  • a
    A Varietal trial on greengram was conducted in a CRD (Completely Randomized design) with 5 varieties, 𝑉1, 𝑉2, 𝑉3, 𝑉4 𝑎𝑛𝑑 𝑉5, and 3,4,5,4 and 4 replications, respectively. The results are presented in Table. The net plot size was 5.0 × 3.5 square metres. Compare all varieties. Varieties Total: 4.3 9.0 5.1 6.5 4.3 Mean: 1.43 2.25 1.02 1.62 1.08 Variance
  • b
    An infinitely long string having one end at 𝑥 = 0 is initialy at rest along 𝑥-axis. The end 𝑥 = 0 is given a transverse displacement 𝑓(𝑡), when 𝑡 > 0. Find the displacement of any point of the string at any time

Question text is extracted from the official AKTU question paper PDF above. Hindi translations are omitted — every question is printed in English in the original paper. Last verified: 2026-08-23.

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