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IOE Entrance Math Past Questions 10 MCQs with Solutions Part 1

Q: Is this practice quiz completely free?

Yes, 100% free. No signup, no payment, no hidden costs. We believe quality IOE preparation shouldn't be limited to students who can afford expensive institutes.

Q: How many past questions should I practice for IOE?

At least 1500-2000 questions before exam day. That works out to roughly 30-35 questions daily for 2 months. Quality matters more than quantity though — understanding 100 questions deeply is better than rushing through 1000 without learning.

Q: Can I crack IOE without joining a physical institute?

Yes, completely. Many students every year crack IOE through disciplined self-study. You need: structured content (video lectures), practice material (MCQs and past papers), doubt solving support (community or teacher), and consistent daily discipline. Veedhyapeeth provides the first three.

Q: I scored very low. Should I give up on IOE?

Absolutely not. Low practice scores show you where to focus, not whether you'll succeed. Many of our students started at 2-3 out of 10 and cracked IOE within 3-4 months of consistent practice. The exam doesn't care about your practice scores — only your final exam performance.

Q: How is Veedhyapeeth different from other IOE preparation options?

Three things: Affordable - Rs 2500 for full video lectures and Mock test Accessible — Works on any Android phone, perfect for students outside Kathmandu. Authentic— Taught by Pulchowk Campus passed engineers who personally cracked IOE.

Q: When should I start preparing for IOE?

Ideally from Class 11. Most students wait until +2 ends, then panic. Starting earlier means less pressure and better results. If you're already in +2 — start today. 4 focused months can still get you there.

Q: Where can I get help if I'm stuck on a specific question?

Join our Discord community https://discord.gg/zjdm9kesV — that's where doubts get solved in real time. You can also email support@veedhyapeeth.com . We respond within 24 hours.

By ER. Bishal Bastola 13 May 2026

Veedhyapeeth article banner IOE Entrance Math Past Questions 10 MCQs with Solutions Part 1

Let me ask you something honest.

If you're preparing for the IOE entrance exam right now, how many past year questions have you actually solved?

Not just glanced at. Not read solutions of. Actually solved on your own.

If your answer is "less than 200," we need to talk.

Here's what I learned during my own IOE journey — and what I've seen with hundreds of students preparing for IOE — past questions are not just practice material. They're the closest thing you have to seeing tomorrow's exam paper today.

The Institute of Engineering doesn't reinvent its question patterns every year. The topics repeat. The trick types repeat. The traps repeat. Students who've solved 200+ past questions walk into the exam hall feeling like they've already seen half the paper before.

But here's the problem most aspirants face — finding good past questions with proper solutions in Nepal is harder than it should be. YouTube videos are scattered across hundreds of channels. Most coaching centers charge thousands just for "past paper sessions."

That's why we built this.

This page is a free, interactive quiz of carefully selected IOE math past questions — the kind that appear year after year. Each question comes with a step-by-step solution. No fluff. No shortcuts that don't work in the exam. Just clean, exam-tested approaches.

What You'll Get Below?

Below this introduction, you'll find an interactive quiz with past IOE math questions covering important topics that frequently appear in the entrance exam:

- Sets, Functions and Relations

- Vectors

- Trigonometry

- Coordinate Geometry

- Calculus

- Matrices and Determinants

- Complex Numbers

Each question is one you'd realistically face in your IOE exam. Not random math problems from textbooks.

How to Use This Quiz Effectively?

I'll be straight with you. Most students do practice quizzes wrong. They look at the question, panic, click "show answer", and move on. They feel productive but learn nothing.

Here's the right way:

Solve on paper first: Open a notebook and your timer to check your time(this matters more than you think). Work through the question completely before clicking anything. Even if you're stuck — struggle for at least 3-4 minutes. The struggle is where learning happens.
Check your answer: Right or wrong, look at the detailed solution we've provided.
Understand the method, not just the answer: If you got it right by guessing, that's a wrong answer for your preparation. Understand WHY the correct approach works.
Note your weak topics: If you keep getting any topic or chapter questions wrong — that's gold. Now you know exactly what to study. In which topic or chapter you're weak work on that.
Come back tomorrow: Retake the same quiz. Aim to solve in half the time with the same accuracy.

Ready? Scroll down and let's begin.

Your future self in Pulchowk Campus will thank you for the work you do today.

The range of the function ${c o t}^{- 1} x$ is [IOE 2074]

If $\vec{a}$ is position vector (12, p) and $∣ \vec{a} ∣ = 13$ , the value of p may be [IOE 2075]

The distance of (1,−6,2) from XZ plane is [IOE 2074]

$\int_{1}^{2} \frac{d x}{x + 2}$ [IOE 2076]

The area bounded by the curve $y = x^{3}$ from $x = - 1$ to $x = 1$ is [IOE 2074]

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Geometric mean of the series $7, 7^{2}, 7^{3}, \dots, 7^{n}$ is [IOE 2077]

The constant coefficient of $(x^{3} - \frac{1}{x^{2}})^{15}$ is [IOE 2078]

If $\cos^{- 1} x + \cos^{- 1} y + \cos^{- 1} z =$ $3 π, x y + y z + z x =$

In ∆ABC, (a+b+c)(a-b+c) = 3ac then, $∠$ B = ? [IOE 2078]

If $∣ \vec{a} ∣ = 5, ∣ \vec{b} ∣ = 4$ , Find $(\vec{a} \cdot \vec{b})^{2} + (\vec{a} \times \vec{b})^{2}$ ? [IOE 2078]

How Did You Do?

Now that you've finished the quiz, take a deep breath.

The number you scored matters less than what you do next.

Here's how to interpret your results honestly:

8-10 correct : Strong fundamentals. You're not behind. Focus now on speed and tougher topics. Try our other series that's where most IOE selections are won or lost.
5-7 correct : Good base, but inconsistent. You know the concepts but make calculation errors or fall for traps. This is the most common stage. Practice 70-80 questions daily and clear every concepts.
Below 5 : Don't be discouraged. Seriously. I've seen students who scored 2/10 on practice quizzes crack IOE in 4 months of focused work.

Wrong answers in practice are good news — they show you exactly what to study tonight.The students who fail IOE aren't those who do practice and get questions wrong. They're those who never practice and hope they'll figure it out on exam day.

Where Most Students Go Wrong After Practice Quizzes ?

After taking quizzes like this, students typically make these mistakes:

Mistake 1-They don't write down their weak topics: You took the quiz. Now grab a notebook. Write down which specific topics gave you trouble. Set, vectors, trigonometry — whatever. Be specific. "Math is weak" is not useful. "Vector dot product applications" — now you can study that.
Mistake 2-They don't revisit: Most aspirants take a quiz once and move on. Smart students retake the same quiz after 1 week. If you can solve the same 10 questions faster and with full accuracy a week later, your foundation is solid.
Mistake 3-They jump to harder questions too fast: If you're at 5/10 on basic past questions, don't immediately attempt advanced level. Build foundation first. We've seen this pattern destroy student confidence repeatedly.

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A Personal Word

Look, I'll be honest with you.

If you're reading this article from any places outside Kathmandu — I know what you're feeling.

I know there's this voice in your head saying "Kathmandu ko students le dherai padisake holan."

That voice is lying to you.

I've taught students from every corner of Nepal at Veedhyapeeth. Some of our best performers are kids who've never set foot in Kathmandu. They watch videos whenever they want or need. They solve MCQs daily. They ask doubts on Discord at anytime.

These are the students who crack IOE.

Not because they're geniuses. Because they're consistent.

You can be that student too. Today, with this quiz, you just took one step. Tomorrow take another. In 90 days, you'll be unrecognizable from who you are today.

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 our Pulchowk pass outs engineers , Discord doubt solving 24/7.

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

Download Veedhyapeeth App:

Website

Discord Community

Join Our Discord — Where Doubts Get Solved

If you got stuck on any question in this quiz, you're not alone. Hundreds of IOE aspirants face the exact same confusions. The difference between students who push through and those who give up?

A community that helps each other.

Our Discord server has students from across Nepal . 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

FAQs

Are these questions from actual IOE past papers?▼

Yes. Every question in this quiz is based on patterns from real IOE entrance exams across recent years. We've selected questions that test the most frequently appearing concepts — the ones you must master before exam day.

Is this practice quiz completely free?▼

How many past questions should I practice for IOE?▼

Can I crack IOE without joining a physical institute?▼

I scored very low. Should I give up on IOE?▼

How is Veedhyapeeth different from other IOE preparation options?▼

When should I start preparing for IOE?▼

Where can I get help if I'm stuck on a specific question?▼

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