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Limits, Continuity & Differentiability MCQs (Free Practice Questions)

Practice 10 carefully selected Limits, Continuity & Differentiability MCQs with explanations. Continue practicing 500+ chapter-wise questions inside the Exam Sprinter app.

What is Limits, Continuity & Differentiability?

Limits, Continuity & Differentiability covers the essential principles and concepts required for JEE Main.

💡 Why Study Limits, Continuity & Differentiability?

Highly important, frequently tested in JEE Main.

Parameter	Details / Relevance
Target Exam	JEE Main
Subject Category	Mathematics
Recommended Study Duration	10 Hours
Expected Questions	2 Questions
Difficulty Index	Hard
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

Sequences & Series➔Limits, Continuity & Differentiability (Current)➔Integral Calculus

What You Will Learn

✓ Limits, Continuity & Differentiability Fundamentals
✓ Key applications of Limits, Continuity & Differentiability
✓ Advanced problem solving in Limits, Continuity & Differentiability

Cheat Sheet & Formulas

$$E = mc^2$$
$$\int e^x dx = e^x + C$$

Practice Questions

⏱ 60sHard

If $\int_{0}^{\pi/2} \frac{\sin^{0}(x)}{\sin^{0}(x) + \cos^{0}(x)} dx = I$ , what is the value of $I$ ?

⏱ 65sMedium

Let $z$ be a complex number such that $|z - 1i| = 2$ . The locus of $z$ is:

⏱ 70sEasy

The number of real roots of the equation $x^2 - 4x + 2 = 0$ is:

⏱ 75sHard

If $\int_{0}^{\pi/2} \frac{\sin^{3}(x)}{\sin^{3}(x) + \cos^{3}(x)} dx = I$ , what is the value of $I$ ?

⏱ 80sMedium

Let $z$ be a complex number such that $|z - 4i| = 5$ . The locus of $z$ is:

⏱ 85sEasy

The number of real roots of the equation $x^2 - 7x + 5 = 0$ is:

⏱ 90sHard

If $\int_{0}^{\pi/2} \frac{\sin^{6}(x)}{\sin^{6}(x) + \cos^{6}(x)} dx = I$ , what is the value of $I$ ?

⏱ 95sMedium

Let $z$ be a complex number such that $|z - 7i| = 8$ . The locus of $z$ is:

⏱ 100sEasy

The number of real roots of the equation $x^2 - 10x + 8 = 0$ is:

Q10

⏱ 105sHard

If $\int_{0}^{\pi/2} \frac{\sin^{9}(x)}{\sin^{9}(x) + \cos^{9}(x)} dx = I$ , what is the value of $I$ ?

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Frequently Asked Questions

Is Limits, Continuity & Differentiability difficult for the exam?▼

Yes, Limits, Continuity & Differentiability requires strong conceptual clarity and practice of standard JEE Main style questions.

✓ Key Takeaways for Limits, Continuity & Differentiability

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.

Limits, Continuity & Differentiability MCQs (Free Practice Questions)

🤖 Quick AI Summary

What is Limits, Continuity & Differentiability?

💡 Why Study Limits, Continuity & Differentiability?

⚠️ Common Pitfalls to Avoid

🗺️ Recommended learning path

What You Will Learn

Cheat Sheet & Formulas

Practice Questions

If $\int_{0}^{\pi/2} \frac{\sin^{0}(x)}{\sin^{0}(x) + \cos^{0}(x)} dx = I$ , what is the value of $I$ ?

Let $z$ be a complex number such that $|z - 1i| = 2$ . The locus of $z$ is:

The number of real roots of the equation $x^2 - 4x + 2 = 0$ is:

If $\int_{0}^{\pi/2} \frac{\sin^{3}(x)}{\sin^{3}(x) + \cos^{3}(x)} dx = I$ , what is the value of $I$ ?

Let $z$ be a complex number such that $|z - 4i| = 5$ . The locus of $z$ is:

The number of real roots of the equation $x^2 - 7x + 5 = 0$ is:

If $\int_{0}^{\pi/2} \frac{\sin^{6}(x)}{\sin^{6}(x) + \cos^{6}(x)} dx = I$ , what is the value of $I$ ?

Let $z$ be a complex number such that $|z - 7i| = 8$ . The locus of $z$ is:

The number of real roots of the equation $x^2 - 10x + 8 = 0$ is:

If $\int_{0}^{\pi/2} \frac{\sin^{9}(x)}{\sin^{9}(x) + \cos^{9}(x)} dx = I$ , what is the value of $I$ ?

Want to master Limits, Continuity & Differentiability?

Frequently Asked Questions

✓ Key Takeaways for Limits, Continuity & Differentiability

🔗 Related Study Resources

Limits, Continuity & Differentiability MCQs (Free Practice Questions)

🤖 Quick AI Summary

What is Limits, Continuity & Differentiability?

💡 Why Study Limits, Continuity & Differentiability?

⚠️ Common Pitfalls to Avoid

🗺️ Recommended learning path

What You Will Learn

Cheat Sheet & Formulas

Practice Questions

If ∫0π/2sin⁡0(x)sin⁡0(x)+cos⁡0(x)dx=I\int_{0}^{\pi/2} \frac{\sin^{0}(x)}{\sin^{0}(x) + \cos^{0}(x)} dx = I∫0π/2​sin0(x)+cos0(x)sin0(x)​dx=I, what is the value of III?

Let zzz be a complex number such that ∣z−1i∣=2|z - 1i| = 2∣z−1i∣=2. The locus of zzz is:

The number of real roots of the equation x2−4x+2=0x^2 - 4x + 2 = 0x2−4x+2=0 is:

If ∫0π/2sin⁡3(x)sin⁡3(x)+cos⁡3(x)dx=I\int_{0}^{\pi/2} \frac{\sin^{3}(x)}{\sin^{3}(x) + \cos^{3}(x)} dx = I∫0π/2​sin3(x)+cos3(x)sin3(x)​dx=I, what is the value of III?

Let zzz be a complex number such that ∣z−4i∣=5|z - 4i| = 5∣z−4i∣=5. The locus of zzz is:

The number of real roots of the equation x2−7x+5=0x^2 - 7x + 5 = 0x2−7x+5=0 is:

If ∫0π/2sin⁡6(x)sin⁡6(x)+cos⁡6(x)dx=I\int_{0}^{\pi/2} \frac{\sin^{6}(x)}{\sin^{6}(x) + \cos^{6}(x)} dx = I∫0π/2​sin6(x)+cos6(x)sin6(x)​dx=I, what is the value of III?

Let zzz be a complex number such that ∣z−7i∣=8|z - 7i| = 8∣z−7i∣=8. The locus of zzz is:

The number of real roots of the equation x2−10x+8=0x^2 - 10x + 8 = 0x2−10x+8=0 is:

If ∫0π/2sin⁡9(x)sin⁡9(x)+cos⁡9(x)dx=I\int_{0}^{\pi/2} \frac{\sin^{9}(x)}{\sin^{9}(x) + \cos^{9}(x)} dx = I∫0π/2​sin9(x)+cos9(x)sin9(x)​dx=I, what is the value of III?

Want to master Limits, Continuity & Differentiability?

Frequently Asked Questions

✓ Key Takeaways for Limits, Continuity & Differentiability

🔗 Related Study Resources

If $\int_{0}^{\pi/2} \frac{\sin^{0}(x)}{\sin^{0}(x) + \cos^{0}(x)} dx = I$ , what is the value of $I$ ?

Let $z$ be a complex number such that $|z - 1i| = 2$ . The locus of $z$ is:

The number of real roots of the equation $x^2 - 4x + 2 = 0$ is:

If $\int_{0}^{\pi/2} \frac{\sin^{3}(x)}{\sin^{3}(x) + \cos^{3}(x)} dx = I$ , what is the value of $I$ ?

Let $z$ be a complex number such that $|z - 4i| = 5$ . The locus of $z$ is:

The number of real roots of the equation $x^2 - 7x + 5 = 0$ is:

If $\int_{0}^{\pi/2} \frac{\sin^{6}(x)}{\sin^{6}(x) + \cos^{6}(x)} dx = I$ , what is the value of $I$ ?

Let $z$ be a complex number such that $|z - 7i| = 8$ . The locus of $z$ is:

The number of real roots of the equation $x^2 - 10x + 8 = 0$ is:

If $\int_{0}^{\pi/2} \frac{\sin^{9}(x)}{\sin^{9}(x) + \cos^{9}(x)} dx = I$ , what is the value of $I$ ?