B.TechSemester 52024-25Mathematical Foundation Ai Ml And Data ScienceBCAI051
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Mathematical Foundation Ai Ml And Data Science (BCAI051) - AKTU Question Paper 2024-25

B.Tech · Semester 5 · Free PDF Download

This is the official AKTU Mathematical Foundation Ai Ml And Data Science Previous Year Question Paper for B.Tech Semester 5, 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 5
Session:2024-25
University:AKTU / UPTU

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Questions Asked in 2024-25

Mathematical Foundation Ai Ml And Data Science (BCAI051) — complete question paper · 70 marks · 3 Hours

Section AAttempt all questions in brief. 2 x 07 = 14
  • a
    How is the mode defined in statistics?
  • b
    Define skewness? How does it af fect the distribution of data?
  • c
    Describe sampling in the contex t of inferential statistics?
  • d
    Define a pseudo-random number?
  • e
    Describe a subspace of a vector space
  • f
    Define the kernel of a linear transformation
  • g
    With example explain the process of diagonalization of a matri x?
Section BAttempt any three of the following: 07 x 3 = 21
  • a
    Explain the concept of dispers ion and describe the various m easures of dispersion such as range, variance, and standard deviation. How do these measures help in understanding the spread of data?
  • b
    Describe estimation and discus s the difference between point estimation and interval estimation. How doe s estimation help in making dec isions about population parameters based on sample data?
  • c
    Discuss about the Gibbs sampling? How does it work in Markov Chain Monte Carlo?
  • d
    Explain the Cauchy-Schwarz in equality in inner product spaces? Explain its significance and how it can be used to bound the inner prod uct of two vectors. Provide an example illustrating the Cauchy-Schwarz inequality
  • e
    Define a linear transformation. Explain the conditions that a function T:V→W must satisfy to be considered a linear transformation, where V and W are vector spaces. Provide examples of linear transformations and non-linear transformations
Section CAttempt any one part of the following: 07 x 1 = 07
  • a
    Explain probability theory and its importance in statistical a n a l y s i s . Define measures of probability such as probability mass functio ns and probability density functions
  • b
    Discuss Chebyshev’s inequality and explain how it can be use d to estimate the probability that a random variable lies within a c ertain number of standard deviations from its mean
  • a
    Discuss the difference between a t-test and a z-test. What a re the assumptions underlying each test, and in what situations should each be used?
  • b
    What is ANOVA (Analysis of Var iance), and how does it help i n comparing the means of three or more groups? Explain the concep t of between-group variance and within-group variance? MATHEMATICAL FOUNDATION AI, ML AND DATA SCIENCE
  • a
    Discuss the inverse-transform method for generating random n umbers. How does it work, and in what types of distributions is this me thod useful?
  • b
    Describe Monte Carlo hypothesi s testing. How is it used to e valuate statistical hypotheses, and what advantages does it offer over traditional hypothesis testing methods?
  • a
    Describe the Gram-Schmidt process. Explain how this process can be used to convert a set of linearly independent vectors into an o rthonormal set
  • b
    Explain inner product in a vector space? Explain the propert ies of an inner product, such as linearity, symmetry, and positivity
  • a
    Explain the concept of symmetric matrices. Discuss the prope rties of symmetric matrices, particularly their eigenvalues and eigenvectors
  • b
    Discuss the concept of change of basis in the context of lin ear transformations. Explain how a basis change affects the matrix representation of a linear transformation?

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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