Preparing for the Airports Authority of India Air Traffic Control (AAI ATC) examination requires a strong understanding of mathematical concepts, regular practice, and the ability to solve questions accurately under time pressure. Mathematics preparation becomes more effective when you combine concept revision with multiple-choice questions and timed practice sessions.

At Aviate Learnings, we encourage aspirants to test their knowledge regularly rather than relying only on reading formulas and theory. In this practice session, you will find 10 multiple-choice questions covering important mathematical concepts such as relations and functions, trigonometry, matrices and determinants, continuity and differentiability, applications of derivatives, integration, linear programming, and probability.

This practice set is designed to help you revise concepts, identify weak areas, and develop a consistent preparation routine for AAI ATC 2026.

Recommended practice time: 15 minutes Total questions: 10 Question type: Multiple-choice questions (MCQs)

Note: This is a practice resource for revision, not an official AAI question paper. Always check the latest official recruitment notification for the applicable examination pattern and syllabus.

Why Practise Mathematics MCQs for AAI ATC 2026?

Solving MCQs is an important part of competitive examination preparation. It helps you move beyond memorising formulas and understand how to apply them in different situations.

Here are four reasons to practise Mathematics questions regularly:

1. Improve calculation speed

Timed practice helps you become more comfortable with algebraic manipulation, trigonometric identities, differentiation, integration, and probability calculations.

2. Strengthen conceptual understanding

A formula may look simple in your notes, but applying it correctly requires understanding the conditions under which it works. Practice questions reveal whether you understand the concept or have only memorised the formula.

3. Identify weak topics

You may be comfortable with matrices but struggle with calculus or probability. Recording your performance topic by topic helps you decide what to revise next.

4. Build examination confidence

Regular practice reduces hesitation when you encounter unfamiliar question formats. It also teaches you to manage time and avoid spending too long on a single problem.

AAI ATC 2026 Mathematics Practice Set – 01

Attempt the following 10 questions before checking the answer key. Try to solve each question independently and note the time you take.

Question 1: Relations and Functions

If

then the value of \(f^{-1}(2)\) is:

A. \(5\)

B. \(-5\)

C. \(\frac{1}{5}\)

D. \(-\frac{1}{5}\)

Question 2: Trigonometry

The exact value of \(\sin 75^\circ\) is:

A. \(\frac{\sqrt6+\sqrt2}{4}\)

B. \(\frac{\sqrt6-\sqrt2}{4}\)

C. \(\frac{\sqrt3+\sqrt2}{4}\)

D. \(\frac{\sqrt3-\sqrt2}{4}\)

Question 3: Matrices and Determinants

If

then \(|A|\) is:

A. \(1\)

B. \(3\)

C. \(4\)

D. \(5\)

Question 4: Continuity and Differentiability

Consider the piecewise function

For the function to be differentiable at \(x=0\), the value of \(a\) must be:

A. \(0\)

B. \(1\)

C. \(-1\)

D. \(2\)

Question 5: Applications of Derivatives

The maximum value of the function

for all real values of \(x\) is:

A. \(0\)

B. \(\frac94\)

C. \(\frac32\)

D. \(3\)

Question 6: Integrals

Evaluate:

A. \(e^x(x-1)+C\)

B. \(e^x(x+1)+C\)

C. \(xe^x+C\)

D. \(\frac{e^x}{x}+C\)

Question 7: Linear Programming

Maximise

subject to the constraints

The maximum value of \(Z\) is:

A. \(18\)

B. \(20\)

C. \(22\)

D. \(24\)

Question 8: Conditional Probability

A bag contains 5 red balls and 3 blue balls. Two balls are drawn successively without replacement. What is the probability that the first ball is red and the second ball is blue?

A. \(\frac{5}{28}\)

B. \(\frac{15}{28}\)

C. \(\frac{5}{56}\)

D. \(\frac{3}{28}\)

Question 9: Bayes’ Theorem

Two machines, \(M_1\) and \(M_2\), produce 60% and 40% of the total items, respectively. Their defective rates are 2% and 5%, respectively. If a randomly selected item is defective, the probability that it was produced by \(M_1\) is approximately:

A. \(0.2\)

B. \(0.3\)

C. \(0.375\)

D. \(0.4\)

Question 10: Binomial Distribution

A fair coin is tossed 6 times. The probability of getting at least 4 heads is:

A. \(\frac{5}{16}\)

B. \(\frac{11}{32}\)

C. \(\frac{21}{32}\)

D. \(\frac{11}{16}\)

Answer Key with Explanations

Try all 10 questions before opening this section.

Important editorial note: Questions 1, 3, 4, and 8 contain incorrect or inconsistent answer options in the poster draft. Correct these before publishing the poster or blog as an answer-key resource. For Question 1, choose a target value that lies in the function’s range; for Question 4, adjust the piecewise definition to make continuity possible.

How to Improve Your Mathematics Preparation for AAI ATC 2026

A focused routine can make your practice sessions more productive.

• Revise formulas daily: Maintain a compact formula sheet for trigonometry, calculus, matrices, and probability.

• Practise with a timer: Begin with 10–15 questions and gradually increase the number as your accuracy improves.

• Maintain an error notebook: Record mistakes and write down the correct method, especially for questions involving signs, limits, or conditional probability.

• Reattempt incorrect questions: Solve them again after a day or two without looking at the solution.

• Balance speed with accuracy: Avoid guessing blindly. Follow the marking scheme and examination instructions published in the official notification.

• Use topic-wise resources: Practise one chapter at a time before attempting mixed-topic sets.

Frequently Asked Questions

1. What Mathematics topics should I practise for AAI ATC 2026?

Start by reviewing the Mathematics topics listed in the latest official recruitment notification and applicable syllabus. Your revision can include algebra, functions, trigonometry, matrices, calculus, and probability wherever relevant to the notified syllabus.

2. How many questions should I practise daily?

Start with 10–20 well-reviewed MCQs per day if you are building consistency. Increase the number based on your available study time and the accuracy of your solutions.

3. Is solving MCQs enough for AAI ATC Mathematics preparation?

No. Combine conceptual study, formula revision, worked examples, timed MCQs, and error analysis. Practising questions without understanding your mistakes may lead to repeated errors.

4. How should I analyse my practice-set score?

Record your score, time taken, and mistakes by topic. A low score in one topic indicates where you should revise first; a high score is a reason to continue practising, not to stop revising entirely.

5. Where can I find more AAI ATC preparation resources?

Visit Aviate Learnings for AAI ATC preparation resources and chapter-wise revision material.

Final Words

Consistent practice is one of the most useful habits you can build while preparing for AAI ATC 2026. Use this set to assess your understanding, revise the concepts you find difficult, and keep track of your progress over time.

Remember, the goal is not simply to solve more questions. It is to solve them accurately, efficiently, and with a clear understanding of the underlying concepts.

Keep learning, keep practising, and keep improving with Aviate Learnings — Prepare Higher. Aim Farther.