IOE Entrance Math Past Questions 10 MCQs with Solutions Part 2

IOE Entrance Math Past Questions: 10 MCQs with Solutions Part 2

So you came back.

That already tells me something about you.

Most students take one practice quiz, feel good about themselves, and disappear for two weeks. You're here for Part 2 — and that habit of coming back is exactly what separates students who crack IOE from students who just "prepare" for it.

If you haven't done Part 1 of our IOE math past questions series yet, start there first. These sets are designed to be done in order, and Part 1 covers the foundation topics.

Now, a hard truth before we begin.

In Part 1, I told you the IOE doesn't reinvent its question patterns. Here's the second half of that truth: the exam doesn't reward students who know concepts. It rewards students who recognize patterns under time pressure.

You have roughly a minute per math question in the real exam. A minute. That's not enough time to derive anything from scratch. Either you've seen the pattern before and your hand starts moving, or you burn three minutes on one question and sacrifice two others.

This is why past questions matter more than any textbook. Every question below is a pattern the IOE has used before — and patterns repeat.

What You'll Get Below?

This second interactive quiz continues from where Part 1 stopped, covering more frequently-tested IOE math topics:

• Limits and Continuity
• Differentiation and Its Applications
• Probability and Permutation-Combination
• Conic Sections (Parabola, Ellipse, Hyperbola)
• Sequence and Series
• Logarithms and Exponentials
• Straight Lines and Pair of Lines

Same rule as Part 1: every question is one you'd realistically face in your IOE exam. No random textbook filler.

How to Use This Quiz Effectively?

If you did Part 1 properly, you know the drill. If you skipped the instructions there, here's the short version:

1. Solve on paper first. Notebook open, timer running. Struggle for at least 3-4 minutes before touching any option. The struggle is where learning happens.
2. Check the solution even when you're right. A correct answer by guessing is a wrong answer for your preparation.
3. Compare with your Part 1 performance. This is new for Part 2. Are the same topics troubling you again? If vectors hurt you in Part 1 and calculus hurts you here, your weak-topic list is writing itself.
4. Note the trap in each question. IOE questions almost always have one option designed for the student who rushes. Learn to spot it.
5. Retake after one week. Same quiz, half the time, full accuracy. That's when a topic is truly yours.

Ready? Timer on. Let's begin.

10 IOE Math Past Questions – Set 2

How Did You Do?

Before you check your score against the scale below, answer one question honestly: was your score better than Part 1?

Improvement across sets matters more than any single score.

• 8-10 correct: You're exam-ready on these topics. Your next enemy is time, not concepts. Start doing mixed full-length sets under a strict timer.
• 5-7 correct: The most common zone — and the most dangerous one, because it feels "okay." Okay doesn't crack IOE. Identify the 2-3 chapters costing you marks and give them one focused week each.
• Below 5: If this is your first month of preparation, this is normal. Genuinely. What matters is that you now have a precise list of what to study. Students who score 3/10 in practice and fix it beat students who never find out where they stand.

And if your score dropped compared to Part 1 — don't panic. Part 2 topics (calculus, probability, conics) are heavier for most students. A dip here is information, not failure.

The One Habit That Separates Toppers

After two sets, let me tell you what I've observed in students who eventually reach Pulchowk.

It's not intelligence. It's not expensive coaching. It's not even hours studied.

It's the error notebook.

Toppers keep one notebook where every wrong answer goes — the question, the trap they fell for, and the correct method in their own words. Before every mock test, they revise only this notebook. Twenty minutes of reading your own mistakes is worth more than three hours of re-reading a textbook chapter you already understand.

You now have 20 questions from Part 1 and Part 2. Start your error notebook today with the ones you got wrong. Thank me after the result.

A Personal Word

Somewhere reading this, there's a student who has been preparing for months and still scored 4/10 on this quiz.

I want to talk to you directly.

A low practice score  means nothing about your result in the actual exam. I have watched students go from failing every practice set to securing ranks — not in years, in months. The only students who are truly out of the race are the ones who stop showing up.

You showed up for Part 1. You showed up for Part 2. Show up tomorrow.

That's the whole secret. There isn't another one.

Continue Your IOE Preparation

Ready to go deeper? Here's what's available on Veedhyapeeth:

Complete IOE preparation: 300+ hours of video lectures, MCQ practice sets, past paper solutions from Pulchowk pass-out engineers, and Discord doubt solving 24/7.

For students already studying with institutes who need extra practice: weekly live mock tests, MCQ sets, and performance tracking.

• Explore the Engineering Entrance Preparation Course
• Download the Veedhyapeeth App from the Play Store

Join Our Discord — Where Doubts Get Solved

Stuck on any question in this set? Post it in our Discord. Hundreds of IOE aspirants from across Nepal are solving the same questions, and Pulchowk-passed teachers answer doubts directly. Past papers get discussed. Study groups form organically.

It's free to join. Just real help.

Join Veedhyapeeth Discord: https://discord.gg/zjdm9kesV

Missed Part 1?

This series is built to be practiced in order. If you landed here first, go back and solve Part 1: 10 IOE entrance math past questions with solutions covering sets, vectors, trigonometry, coordinate geometry, calculus, matrices, and complex numbers.