B.TechSemester 42024-25Mathematics –IvBAS403

Mathematics –Iv (BAS403) - AKTU Question Paper 2024-25

B.Tech · Semester 4 · Free PDF Download

This is the official AKTU Mathematics –Iv Previous Year Question Paper for B.Tech Semester 4, academic session 2024-25. Published by Dr. A.P.J. Abdul Kalam Technical University (AKTU/UPTU), Lucknow. Free PDF download — no login required.

Course:B.Tech

Semester:Semester 4

Session:2024-25

University:AKTU / UPTU

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Questions Asked in 2024-25

Mathematics –Iv (BAS403) — complete question paper · 70 marks · 3 Hours

Section A

a
Form the partial differential equation by eliminating arbitrary function from the following: ).()( itxgitxfz −++=
b
Use the method of characteristics to solve the first order PDE .1),0(;0 ==− yuyuu x
c
Classify the following operator: uxtx
d
The first three moments of a distribution, about the value ‘2’ of the variable are 1,16 and
40
Find the mean and variance of the distribution
e
Find the regression coefficient of y on x for the following: .22,13,10 === yxn
f
If X and Y are two random variables having joint density function : otherwise yxyxyxf Find )31(  YXP . otherwise yxyxyxf )31(  YXP
g
Write the formula of Chi-square 2 test

Section B

a
Solve the following differential equation using Lagrange’s equation: xyzqzxypyzx −=−+− 222 )()( MATHEMATICS –IV
b
A tightly stretched flexible string has its ends fixed at 0=x and lx= . At time 0=t , the string is given a shape defi ned by )()( xlxxF −= ,  is a constant and then released. Find the displacement ),( txy of any point x of the string at any time
c
The first four moments about the working mean 28.5 of a distribution are 0.294, 7.144, 42.409 and 454.98. Calculate the moments about the mean. Also evaluate 21, and comment upon the skewness and kurtosis of the distribution
d
If the heights of 300 students are normally distributed with mean 64.5 inches and standard deviation 3.3 inches, find the height below which 99% of the students lie (P(z=2.327)=0.49)
e
The following table shows the distribution of digits in numbers chosen at random from a telephone directory: Digits 0 1 2 3 4 5 6 7 8 9 Frequency 1026 1107 997 966 1075 933 1107 972 964 853 Test whether the digits may be taken to occur equally frequently in the directory. ( 2 at 5% level of significance for 9 d.f. is 16.919). Digits 0 1 2 3 4 5 6 7 8 9 Frequency 1026 1107 997 966 1075 933 1107 972 964 853

Section C

a
Solve the partial differential equations: yxyx tantantantan −=
b
Solve: )32sin()2)(1( yxzDDDD +=−−−− MATHEMATICS –IV 4.Attempt any one part of the following: 07 x 1 = 07
a
A bar with insulated sides is initially at a temperature 00C throughout. The 0=x is kept at 00C, and heat is suddenly applied at the end lx= so that  for , where A is a constant. Find the temperature function ),( txu . Find the Fourier Cosine transform of 1)( 2xxf += 1)( 2xxf += 5.Attempt any one part of the following: 07 x 1 = 07
a
Obtain a relation of the form xaby= for the following data by the method of least squares
b
For 10 observations on price (x) and supply (y), the following data were obtained (in appropriate units): 5506,2288,220,130 22 ====  yxyx and Obtain the two lines of regression and estimate the supply when the price is 16 units. 5506,2288,220,130 22 ====  yxyx 6.Attempt any one part of the following: 07 x 1 = 07
a
A manufacturer knows that the condensers he makes contain on an average 1% of defectives. He packs them in boxes of 100. What is the probability that a box picked at random will contain 4 or more faulty condensers?
b
In a sample of 1000 cases, the mean of a certain test is 14 and S.D. is 2.5. Assuming the distribution to be normal, find (i) How many students score between 12 and 15? (ii) How many score above 18? MATHEMATICS –IV (iii)How many score below 8? (iv) How many core 16? ZPZPZP ZPZPZP . 7.Attempt any one part of the following: 07 x 1 = 07
a
The 9 items of a sample have the following values: Does the mean of these values differ significantly from the assumed mean 47.5? ( )831.205.0 == fort ( )831.205.0 == fort
b
In a blade manufacturing factory, 1000 blades are examined daily. Draw the np chart for the following table and examine whether the process is under control? Date 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 No. of Defective blades

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.

Repeated Questions — BAS403

Questions that appeared in more than one session, found by comparing 3 years of Mathematics –Iv papers (2023-24, 2024-25, 2025-26)

Form the partial differential equation by eliminating arbitrary function from the following: ).()( itxgitxfz −++=