B.TechSemester 42023-24Mathematics –IiiBAS402

Mathematics –Iii (BAS402) - AKTU Question Paper 2023-24

B.Tech · Semester 4 · Free PDF Download

This is the official AKTU Mathematics –Iii Previous Year Question Paper for B.Tech Semester 4, academic session 2023-24. 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:2023-24

University:AKTU / UPTU

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Questions Asked in 2023-24

Mathematics –Iii (BAS402) — complete question paper · 70 marks · 3 Hours

Section AAttempt all questions in brief. 2 x 7 = 14

a
Find the complimentary function of (D3-4D2D’+3DD’2)z = 0. 2 1
b
Write auxiliary equation of yq-xp = z. 2 1
c
Classify the equation
d
Write moment about mean. 2 3
e
What is mean, median and mode of a normal distribution? 2 3
f
What is nth divided difference of a polynomial of degree n? 2 4
g
Find the value of ∫ 𝒙𝟑𝟔 𝟐 dx by Simpson’s rule. 2 5

Section BAttempt any three of the following: 7 x 3 = 21

a
Solve (D2+DD’-6D’2)z = x2 sin (x+y). 7 1
b
A string is stretched and fastened to two points l a Part. Motion is started by displacing the string in form y= a sin 𝑙 from which it is released at a time t=0. show that, y(x,t) = a 𝑠𝑖𝑛
c
The probability that a bomb droped from a plane will strike the target is 1/5.If the six bombs are dropped , find the probability that i) Exactly two will strike the target. ii) At least two will strike the target
d
Develop the divided difference table from the data given below and obtain the interpolation polynomial
e
Test the following system of equations is diagonally dominant and hence solve this system using Gauss-Seidel method

Section CAttempt any one part of the following: 7 x 1 = 7

a
Solve (y+z)p-(x+z)q = x-y. 7 1 MATHEMATICS –III
b
Solve (D2-DD’)z = sin x cos 2y. 7 1
a
Solve by method of variation of variables 𝑦3
b
Find Fourier sine and cosine transform of xn-1. 7 2
a
A sample of 100 dry battery cells tested to find the length of life produced the following results 𝑥 ̅ = 12 hours, σ = 3 hours. Assuming the data to be normally distributed, what percentage of battery cells are expected to have life. (i) More than 15 hours (ii) less than 6 hours (iii) between 10 and 14 hours. (Given area at z = 1 is 0.3413 , z = 2 is 0.4772 and z=0.67 is 0.2485)
b
Out of 8000 graduates in a town, 800 are females, out of 1600 graduate employees, 120 are females. Use χ2 –test to determine if any distinction is made in appointment on the basis of sex. The value of χ2 for 1 degree of freedom at 5% level is 3.841
a
Using Lagrange’s interpolation formula, find the values of y corresponding to x=10 from the following table
b
Using Regula-Falsi method, compute the real root of the equation
a
Using Picard’s method find a solution of 𝑑𝑥 =1+xy, upto third approximation, when 𝑥0 =0, 𝑦0 =0
b
Use Runge-Kutta method of fourth order to approximate y when x = 0.1 given that y = 1 at x=0 and

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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