Mbzuai Entry Exam Sample Questions Best May 2026

The Mohamed bin Zayed University of Artificial Intelligence (MBZUAI) entry exam is a critical 45-to-60-minute screening test designed to assess foundational knowledge in mathematics, programming, and machine learning. Success on the exam requires mastery of core computer science principles and mathematical theory, with no negative marking for incorrect answers. Core Exam Topics

The exam typically consists of 40 multiple-choice questions. Key areas include:

Mathematics: Calculus, linear algebra (eigenvalues, rank, and matrix inversion), probability theory, and trigonometry.

Programming: Python-specific knowledge, data structures (linked lists), and fundamental concepts like recursion and time complexity.

Machine Learning: Core concepts such as supervised vs. unsupervised learning, overfitting, gradient descent, and the differences between linear and logistic regression.

Specialization Subjects: For PhD or specific MSc tracks, questions may cover theory of computation, computer architecture, and operating systems. Sample Question Types Candidates often encounter problems similar to these:

Mathematics: Solving systems of trigonometric equations (e.g., finding angles equations).

Programming Output: Determining the result of a nested while loop or a recursive function in Python.

Conceptual AI: Identifying which regression type predicts continuous versus categorical variables.

Probability: Calculating outcomes for drawing colored balls from a bag without replacement or rolling dice. Preparation and Strategy MBZUAI Online Entry Exam Guidelines

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Sample questions (by topic)

• Mathematics (calculus & linear algebra)

  1. Compute the limit: lim_x→0 (sin(3x) - 3x + (3x)^3/6) / x^5.
  2. Let A = [[2,1],[1,2]]. Find eigenvalues and eigenvectors of A; diagonalize A if possible.
  3. Evaluate the integral ∫_0^1 ln(1 + x^2) dx.

• Probability & statistics

  1. A fair die is rolled twice. What is the probability the second roll is higher than the first?
  2. Let X ~ N(0,1). Compute P(|X| > 1.96) and interpret.
  3. Given independent samples with means μ1, μ2 and variances σ1^2, σ2^2, state and apply the formula for a pooled two-sample t-test.

• Discrete math & logic

  1. Prove by induction that 1 + 2 + ... + n = n(n+1)/2.
  2. Give a truth table for (p → q) ∧ (¬q → ¬p) and identify the logical relationship.

• Algorithms & programming (pseudo-code acceptable) mbzuai entry exam sample questions best

  1. Write a function to reverse a singly linked list in-place; give time and space complexity.
  2. Explain binary search and show why its time complexity is O(log n). Provide edge cases.
  3. Given an array of integers, find the longest increasing subsequence length (outline DP solution and complexity).

• Machine learning fundamentals

  1. Explain bias vs variance trade-off and give examples of high-bias and high-variance models.
  2. Derive the gradient descent update for linear regression with mean squared error loss.
  3. Describe cross-validation and why it’s used.

• Short answer / reasoning

  1. You have 3 containers with capacities 8L, 5L, and 3L. How do you measure exactly 4L?
  2. Interpret the output of a confusion matrix and compute precision, recall, and F1-score given counts.

Final Verdict: What the “Best” Candidates Know

The MBZUAI entry exam is not a hazing ritual; it is a predictor of your survival in the MSc program. The candidates who pass are not necessarily geniuses—they are the ones who practiced proofs, vectorized code, and distribution theory relentlessly.

Use the sample questions above as your baseline. The actual exam will be harder, but the type of difficulty is identical. If you can derive the gradient of a least-squares loss function in your sleep and reverse a linked list blindfolded, you are ready.

Your next step: Set a timer for 90 minutes. Open a notebook. Tackle Questions 1, 2, 5, and 7 right now. The future of AI in Abu Dhabi is waiting for your solution.

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Good luck from the MBZUAI applicant community. May your gradients converge and your p-values be small.

MBZUAI Online Screening Exam is a mandatory, proctored assessment designed to evaluate your foundational knowledge in Mathematics, Programming, and Machine Learning. The exam is fully automated, lasts approximately 45 to 60 minutes , and does use negative marking.

MBZUAI - Mohamed bin Zayed University of Artificial Intelligence 📐 Mathematics Section (40%)

This section focuses on the mathematical foundations required for Artificial Intelligence. Focus on conceptual understanding and geometric intuition.

MBZUAI - Mohamed bin Zayed University of Artificial Intelligence Linear Algebra

: Matrix operations, determinants, eigenvalues, eigenvectors, and solving systems of linear equations.

: Single and multivariate calculus, including limits, derivatives (chain rule), and optimization. Probability & Statistics

: Discrete and continuous distributions, Bayes' Theorem, mean, variance, and standard deviation. Optimization : Gradients, Jacobians, and Hessians. The Mohamed bin Zayed University of Artificial Intelligence

MBZUAI - Mohamed bin Zayed University of Artificial Intelligence Sample Questions:

Find the probability that the sum of two rolled dice equals 7. Compute the determinant of a 3x3 matrix.

Find the probability that the second ball drawn from a bag (6 red, 2 blue) is red without replacement. 💻 Programming Section (40%) Most questions use

, but the focus is on algorithmic logic rather than specific language syntax. You may be asked to find the output of code or identify errors. Data Structures

: Basic understanding of Arrays, Stacks, Queues, Linked Lists, and Binary Trees. Algorithms

: Searching and sorting algorithms (e.g., Bubble Sort, Binary Search) and their time complexity.

: Recursion, loops, and Object-Oriented Programming (OOP) including classes and inheritance. Sample Questions:

What is the worst-case time complexity of searching a singly linked list of length

Write a Python function to check if a number is prime or a string is a palindrome.

Identify which WHILE loop produces the same output as a provided FOR loop. 🤖 Machine Learning Basics (20%)

This section tests your grasp of fundamental ML theory and model evaluation. Learning Paradigms

: Differences between supervised, unsupervised, and reinforcement learning. Model Theory

: Overfitting vs. underfitting, the bias-variance tradeoff, and gradient descent. Evaluation Metrics Sample questions (by topic)

: Confusion matrix, accuracy, precision, recall, and F1-score. Algorithms

: Key differences between Linear Regression and Logistic Regression. Sample Questions:

Gradient Descent computes the derivative of the loss function with respect to what? (Input, Weight, or Activation)

Explain how decision trees split data using Gini Index or Entropy. 🛠️ Preparation Resources & Tools Official Demo : A demo exam is provided within the Exam Portal software (use PIN: ) to help you test the interface.

: Search for "Mathematical for Machine Learning" or specific calculus/algebra tests. Learning Platforms : Courses on covering "Linear Algebra for ML" are highly recommended. Prep Guides : Third-party resources like the MBZUAI Master's Test Prep Guide offer up to 155 practice MCQs.

MBZUAI - Mohamed bin Zayed University of Artificial Intelligence 📋 Exam Day Checklist

: Use Windows 10/11 or macOS 10.15+. Google Chromebooks and Linux are supported. Environment

: A quiet, well-lit room. Your face must remain visible to the AI Proctor at all times.

: You are allowed blank paper, a pen, and a calculator (though minimal use is advised).

: Have a valid passport or government ID ready for the system's identity check.

MBZUAI - Mohamed bin Zayed University of Artificial Intelligence If you'd like, I can help you: Drill specific math topics like eigenvalues or probability. Practice Python coding for common data structures. Explain ML concepts like the bias-variance tradeoff in detail. subject area would you like to start with? MBZUAI Online Screening Exam Instructions

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Best Sample Questions: Probability & Statistics

Question 3 (Bayes for NLP) In a spam detection model, 20% of emails are spam. The word "winner" appears in 60% of spam emails but only 5% of non-spam emails.

• What is the probability that an email containing "winner" is spam?
• If the classifier uses a Naive Bayes assumption, why might the above calculation still be valid even with multiple words?

Question 4 (Convergence & Distributions) Let ( Z_1, Z_2, ..., Z_n ) be i.i.d. random variables with mean ( \mu ) and variance ( \sigma^2 ). Define the sample mean ( \barZ_n ).

• State the Weak Law of Large Numbers (WLLN).
• State the Central Limit Theorem (CLT).
• Why is the CLT critical for training neural networks with mini-batch gradient descent?

MBZUAI insight: The exam frequently connects pure statistics to optimization. They want you to know that CLT explains why the noisy gradient (from a mini-batch) approximates the true gradient.

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