Mathematics Iv (KAS-302) - AKTU Question Paper 2022-23
B.Tech · Semester 3 · Free PDF Download
This is the official AKTU Mathematics Iv Previous Year Question Paper for B.Tech Semester 3, academic session 2022-23. 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:2022-23
University:AKTU / UPTU
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Questions Asked in 2022-23
Mathematics Iv (KAS-302) — complete question paper
Section AAttempt all questions in brief. 2 x 10 = 20
- aFind partial differential equation (PDE) by eliminating 𝑎 and 𝑏 from
- cClassify the PDE, 𝑢௫௫ 𝑢 ௬௬ െ𝑢 ௫௬ ൌ0
- dWrite the wave equation in two dimensions
- eFind the arithmetic mean of the following frequency distributi on
- fWrite the formula of Karl Pearson correlation coefficient and write the range of correlation coefficient
- gIf 𝑃ሺ𝐴ሻ ൌ ଼ , then find the value of 𝑃ሺ𝐴 ∩𝐵 ሻ
- hWrite probability mass function of binomial distribution with mean and variance of the distribution. (i) Define “Null Hypothesis”. (j) Discuss (in brief) “Control Charts”
Section BAttempt any three of the following: 10x3=30
- aSolve ൫𝑥ଶ𝐷ଶ െ𝑦 ଶ𝐷ᇱଶ൯ ൌ𝑥 𝑦, where 𝐷ଶ ൌ
- bA string is stretched and fastened to two points 𝑙 meter apart. Motion is started by displacing the string in the form 𝑢ሺ𝑥, 0ሻ ൌ 𝐴 sin from which it is released at time 𝑡ൌ0 . Show that the displacement of any point at a distance 𝑥 from one end at time 𝑡 is given by 𝑢ሺ𝑥, 𝑡ሻ ൌ 𝐴 sin cos
- cFit a parabolic curve of second degree to the following data
- dA bag contains 10 white and 15 black balls. If two balls are d rawn in succession without replacement, then find the probability that the first b all is white and the second ball is black
- eThe score of 10 candidates obtained in tests before and after attending some coaching classes are given below: Before: 54 76 92 65 75 78 66 82 80 78 After: 60 80 86 72 80 72 66 88 82 73 Is the coaching for the test effective? Test at 5% level of significance
Section CAttempt any one part of the following: 10x1=10
- aSolve,ሺ𝑚𝑧 െ 𝑛𝑦ሻ𝑝 ሺ𝑛𝑥 െ 𝑙𝑧ሻ𝑞 ൌ 𝑙𝑦 െ 𝑚𝑥, where 𝑝ൌ
- bBy Charpit’s method, find the complete solution of PDE
- aSolve by the method of separation of variables, the heat equation 𝑢௧ ൌ𝑢 ௫௫,0 ൏ 𝑥൏1 , 𝑡0subject to the initial and boundary conditions 𝑢ሺ𝑥, 0ሻ ൌ𝑥െ
- bSolve the Laplace equation 𝑢௫௫ 𝑢 ௬௬ ൌ0 𝑥∈ሺ0,1ሻ, 𝑦 ∈ ሺ0,1ሻ w i t h t h e conditions 𝑢ሺ𝑥, 0ሻ ൌ𝑢 ሺ𝑥, 1ሻ ൌ0 and 𝑢ሺ0, 𝑦ሻ ൌ0 , 𝑢ሺ1, 𝑦ሻ ൌ 𝑓ሺ𝑦ሻ by using the method of separation of variables
- aCalculate the correlation coefficient for the following heights ( i n i n c h e s ) o f fathers(𝑋) and their sons (𝑌)
- bThe first four moments of a distribution about the value 4 of t he variables are െ1.5, 17, െ30 a n d 80. Find moments 𝜇ଵ,𝜇 ଶ,𝜇 ଷ,𝜇 ସ a b o u t m e a n . A l s o f i n d 𝛽ଵ and 𝛽ଶ
- aA random variable 𝑋 has the following probability distribution values of Then, evaluate 𝑃ሺ𝑋6 ሻ
- bFor continuous random variable 𝑋if then, (i) Verify that 𝑓ሺ𝑥ሻ is a probability distribution function. (ii) Find 𝜆 such that 𝑃ሺ𝑋𝜆 ሻ ൌ𝑃 ሺ 𝑋𝜆 ሻ
- aThe values in two random samples are given below: Sample1: 15 25 16 20 22 24 21 17 19 23 Sample2: 35 31 25 38 26 29 32 34 33 27 29 31 population? Test at 5% level of significance
- bDiscuss one way analysis of var iance (ANOVA) with mathematical model and assumptions in the model
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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