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Complex Numbers MCQs (Free Practice Questions)

Practice 10 carefully selected Complex Numbers MCQs with explanations. Continue practicing 500+ chapter-wise questions inside the Exam Sprinter app.

What is Complex Numbers?

Complex Numbers covers the essential principles and concepts required for NDA.

💡 Why Study Complex Numbers?

Highly important, frequently tested in NDA.

Parameter	Details / Relevance
Target Exam	NDA
Subject Category	Mathematics
Recommended Study Duration	10 Hours
Expected Questions	2 Questions
Difficulty Index	Medium
Interactive Solved MCQs	10 Questions (Complete Explanations)
Adaptive App Practice	500+ Questions & AI Tutor Supported

⚠️ Common Pitfalls to Avoid

Neglecting foundational prerequisites (make sure you review related chapters in the learning path).
Calculation and sign convention errors during numerical steps.
Confusing intermediate results with the final correct answer options.

🗺️ Recommended learning path

Sets and Functions➔Complex Numbers (Current)

What You Will Learn

✓ Complex Numbers Fundamentals
✓ Key applications of Complex Numbers
✓ Advanced problem solving in Complex Numbers

Cheat Sheet & Formulas

$$\sin^2 x + \cos^2 x = 1$$
$$\vec{a} \cdot \vec{b} = ab \cos\theta$$

Practice Questions

⏱ 60sHard

If a matrix $A$ of order $3 \times 3$ has determinant $|A| = 8$ , then find the determinant of $3A$ .

⏱ 65sMedium

Find the value of $\sin(15^\circ) + \cos(105^\circ)$ for Complex Numbers.

⏱ 70sEasy

Find the principal argument of the complex number $z = 8 + 8i$ .

⏱ 75sHard

If vectors $\vec{a} = 7\vec{i} - \vec{j} + \vec{k}$ and $\vec{b} = \vec{i} + 4\vec{j} + \lambda\vec{k}$ are perpendicular, find the value of $\lambda$ .

⏱ 80sMedium

What is the probability of getting a sum of 7 when two fair dice are thrown?

⏱ 85sEasy

The derivative of $\ln(\sin(6x))$ with respect to $x$ is:

⏱ 90sHard

Evaluate the limit: $\lim_{x \to 0} \frac{\tan(6x)}{x}$ for Complex Numbers.

⏱ 95sMedium

The coordinates of the focus of the parabola $y^2 = 16x$ are:

⏱ 100sEasy

Find the number of subsets of a set containing 6 elements.

Q10

⏱ 105sHard

The vector projection of $\vec{a} = \vec{i} + \vec{j}$ on $\vec{b} = \vec{i} - \vec{j}$ is:

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Frequently Asked Questions

Is Complex Numbers difficult for the exam?▼

Yes, Complex Numbers requires strong conceptual clarity and practice of standard NDA style questions.

✓ Key Takeaways for Complex Numbers

High exam relevance: 2 questions on average are expected from this chapter.
Standard formulas: Comprehensive formula sheets and formulas are fully covered in the cheat sheet section above.
Practice and explanation: 10 standard MCQs are solved step-by-step to clarify common numerical and conceptual methods.
Step-by-step learning: Start with the formulas, work through the questions, and then download the mobile app for extensive practice.

Complex Numbers MCQs (Free Practice Questions)

🤖 Quick AI Summary

What is Complex Numbers?

💡 Why Study Complex Numbers?

⚠️ Common Pitfalls to Avoid

🗺️ Recommended learning path

What You Will Learn

Cheat Sheet & Formulas

Practice Questions

If a matrix $A$ of order $3 \times 3$ has determinant $|A| = 8$ , then find the determinant of $3A$ .

Find the value of $\sin(15^\circ) + \cos(105^\circ)$ for Complex Numbers.

Find the principal argument of the complex number $z = 8 + 8i$ .

If vectors $\vec{a} = 7\vec{i} - \vec{j} + \vec{k}$ and $\vec{b} = \vec{i} + 4\vec{j} + \lambda\vec{k}$ are perpendicular, find the value of $\lambda$ .

What is the probability of getting a sum of 7 when two fair dice are thrown?

The derivative of $\ln(\sin(6x))$ with respect to $x$ is:

Evaluate the limit: $\lim_{x \to 0} \frac{\tan(6x)}{x}$ for Complex Numbers.

The coordinates of the focus of the parabola $y^2 = 16x$ are:

Find the number of subsets of a set containing 6 elements.

The vector projection of $\vec{a} = \vec{i} + \vec{j}$ on $\vec{b} = \vec{i} - \vec{j}$ is:

Want to master Complex Numbers?

Frequently Asked Questions

✓ Key Takeaways for Complex Numbers

🔗 Related Study Resources

Complex Numbers MCQs (Free Practice Questions)

🤖 Quick AI Summary

What is Complex Numbers?

💡 Why Study Complex Numbers?

⚠️ Common Pitfalls to Avoid

🗺️ Recommended learning path

What You Will Learn

Cheat Sheet & Formulas

Practice Questions

If a matrix AAA of order 3×33 \times 33×3 has determinant ∣A∣=8|A| = 8∣A∣=8, then find the determinant of 3A3A3A.

Find the value of sin⁡(15∘)+cos⁡(105∘)\sin(15^\circ) + \cos(105^\circ)sin(15∘)+cos(105∘) for Complex Numbers.

Find the principal argument of the complex number z=8+8iz = 8 + 8iz=8+8i.

If vectors a⃗=7i⃗−j⃗+k⃗\vec{a} = 7\vec{i} - \vec{j} + \vec{k}a=7i−j​+k and b⃗=i⃗+4j⃗+λk⃗\vec{b} = \vec{i} + 4\vec{j} + \lambda\vec{k}b=i+4j​+λk are perpendicular, find the value of λ\lambdaλ.

What is the probability of getting a sum of 7 when two fair dice are thrown?

The derivative of ln⁡(sin⁡(6x))\ln(\sin(6x))ln(sin(6x)) with respect to xxx is:

Evaluate the limit: lim⁡x→0tan⁡(6x)x\lim_{x \to 0} \frac{\tan(6x)}{x}x→0lim​xtan(6x)​ for Complex Numbers.

The coordinates of the focus of the parabola y2=16xy^2 = 16xy2=16x are:

Find the number of subsets of a set containing 6 elements.

The vector projection of a⃗=i⃗+j⃗\vec{a} = \vec{i} + \vec{j}a=i+j​ on b⃗=i⃗−j⃗\vec{b} = \vec{i} - \vec{j}b=i−j​ is:

Want to master Complex Numbers?

Frequently Asked Questions

✓ Key Takeaways for Complex Numbers

🔗 Related Study Resources

If a matrix $A$ of order $3 \times 3$ has determinant $|A| = 8$ , then find the determinant of $3A$ .

Find the value of $\sin(15^\circ) + \cos(105^\circ)$ for Complex Numbers.

Find the principal argument of the complex number $z = 8 + 8i$ .

If vectors $\vec{a} = 7\vec{i} - \vec{j} + \vec{k}$ and $\vec{b} = \vec{i} + 4\vec{j} + \lambda\vec{k}$ are perpendicular, find the value of $\lambda$ .

The derivative of $\ln(\sin(6x))$ with respect to $x$ is:

Evaluate the limit: $\lim_{x \to 0} \frac{\tan(6x)}{x}$ for Complex Numbers.

The coordinates of the focus of the parabola $y^2 = 16x$ are:

The vector projection of $\vec{a} = \vec{i} + \vec{j}$ on $\vec{b} = \vec{i} - \vec{j}$ is: