B.TechSemester 42022-23Engineering Mathematics IvKAS-402

Engineering Mathematics Iv (KAS-402) - AKTU Question Paper 2022-23

B.Tech · Semester 4 · Free PDF Download

This is the official AKTU Engineering Mathematics Iv Previous Year Question Paper for B.Tech Semester 4, 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 4

Session:2022-23

University:AKTU / UPTU

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Questions Asked in 2022-23

Engineering Mathematics Iv (KAS-402) — complete question paper

Section AAttempt all questions in brief. 2 x 10 = 20

a
Obtain a partial differential equation that governs the family of surfaces
b
Find the complete integral of the partial differential equation
c
Classify the partial differential equation
d
Write down the two dimensional heat equation
e
What is the relation between the regression coefficients and the coefficient of correlation?
f
The fourth central moment is 48. What must be its standard deviation in order that the distribution be mesokurtic
g
and are any two independent events such that ()=0.4, ( )=0.7. Find the (), where is the complementary event of event
h
The random variable X is said to follow the Normal distribution with mean 9 and standard deviation 3, find ∗ such that (" >∗) =0.16 . (i) Write down the definition of the null hypothesis. (j) What is Statistical Quality Control (SQC)? Define in brief

Section BAttempt any three of the following: 10x3=30

a
Find the general solution of the partial differential equation
b
Solve the partial differential equation by the method of separation of variables 4 given that + =5-.)−-./), when =0
c
Use the method of least squares to fit the curve =01( for the following data
d
In a normal distribution, 12% of the items are unde r 30 and 85% items are under 60. Find the mean and standard deviation
e
The annual rainfall in Lucknow city is normally dis tributed with mean 45 cm. The rainfall during the last five years are 48 cm, 42 cm, 40 cm, 44 cm and 43 cm respectively. Can we conclude that the average rainfall during the last five years is less than the normal rainfall? Test at 5% level of significance. [The tabulated value o f 2.2/ = 2.776 and 2.3 = 2.132 for 4 degree of freedom.]

Section CAttempt any one part of the following: 10x1=10

a
Find the solution of the partial differential equation
b
Find the complete integral of the partial differential equation
b
An insulated rod of length l has its ends A and B maintained at 0℃ and 100 ℃ respectively until steady state conditions prevail. If B is suddenly r educed at 0℃ and maintained at 0℃, find the temperature at a distance x from A at time t
a
If 4−5 +33 =0 and 20 −9 =107 are two lines of regression. Find the mean values of and , the coefficient of correlation and the standard deviation of if the variance of is 9
b
First four moments about 2 are 1, 2.5, 5.5 and 16 r espectively. Find the first four central moments, moments about origin and coefficient of skewness
a
A bag A contains 8 white and 4 black balls. A secon d bag B contains 5 white and 6 black balls. One ball is drawn at random from bag A and is placed in bag B. Now, a ball is drawn at random from bag B. It is found that this ball is white. Fi nd the probability that a black ball has been transferred from bag A
b
If " variable follow the Poisson distribution such that (" =2)=9 (" =4)+90 (" =6). Find mean, variance and distribution
b
The given table shows that the value of sample mean "B and the range R for 10 samples of size 5 each. Draw mean and range chart and also comment on the state of control of the process. (Given = 0.58,5: = 0,5C = 2.115). Sample

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 — KAS-402

Questions that appeared in more than one session, found by comparing 2 years of Engineering Mathematics Iv papers (2021-22, 2022-23)

Classify the partial differential equation

Appeared in: 2021-22 · 2022-23

Write down the two dimensional heat equation

Appeared in: 2021-22 · 2022-23

Find the general solution of the partial differential equation

Appeared in: 2021-22 · 2022-23

Find the solution of the partial differential equation

Appeared in: 2021-22 · 2022-23

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