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Algebra MCQs (Free Practice Questions)

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

What is Algebra?

Algebra covers the essential principles and concepts required for NIMCET.

💡 Why Study Algebra?

Highly important, frequently tested in NIMCET.

Parameter	Details / Relevance
Target Exam	NIMCET
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

Probability and Statistics➔Algebra (Current)➔Coordinate Geometry

What You Will Learn

✓ Algebra Fundamentals
✓ Key applications of Algebra
✓ Advanced problem solving in Algebra

Cheat Sheet & Formulas

$$\lim_{x \to 0} \frac{\sin x}{x} = 1$$
$$A(A + B) = A$$

Practice Questions

⏱ 60sHard

In a survey of 630 candidates, 378 were proficient in C++ and 315 in Java. If 126 were proficient in both, how many were proficient in neither?

⏱ 65sMedium

Evaluate the limit: $\lim_{x \to 0} \frac{\sin(5x)}{x}$ for Algebra.

⏱ 70sEasy

Find the equation of the circle concentric with $x^2 + y^2 - 12x + 24y - 10 = 0$ and passing through the origin.

⏱ 75sHard

If vectors $\vec{a} = \vec{i} + \lambda\vec{j} + \vec{k}$ and $\vec{b} = 4\vec{i} - 2\vec{j} + 2\vec{k}$ are orthogonal, find $\lambda$ .

⏱ 80sMedium

A box contains 3 red and 5 black balls. If two balls are drawn at random, what is the probability that both are red?

⏱ 85sEasy

If the 3th term of an AP is 76 and the 4th term is 82, find the common difference.

⏱ 90sHard

Solve the inequality: $x^2 - 25x + 30 < 0$ .

⏱ 95sMedium

The number of ways to arrange 5 students in a circle is:

⏱ 100sEasy

Find the value of $\sin(2\theta)$ if $\tan\theta = \frac1{6}$ .

Q10

⏱ 105sHard

If matrix $A$ is symmetric, then the matrix $A^T$ is equal to:

Chapter Guide ✓→Formulas ✓→10 Questions ✓→Next: 500+ Questions in App

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Frequently Asked Questions

Is Algebra difficult for the exam?▼

Yes, Algebra requires strong conceptual clarity and practice of standard NIMCET style questions.

✓ Key Takeaways for Algebra

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.

Algebra MCQs (Free Practice Questions)

🤖 Quick AI Summary

What is Algebra?

💡 Why Study Algebra?

⚠️ Common Pitfalls to Avoid

🗺️ Recommended learning path

What You Will Learn

Cheat Sheet & Formulas

Practice Questions

In a survey of 630 candidates, 378 were proficient in C++ and 315 in Java. If 126 were proficient in both, how many were proficient in neither?

Evaluate the limit: $\lim_{x \to 0} \frac{\sin(5x)}{x}$ for Algebra.

Find the equation of the circle concentric with $x^2 + y^2 - 12x + 24y - 10 = 0$ and passing through the origin.

If vectors $\vec{a} = \vec{i} + \lambda\vec{j} + \vec{k}$ and $\vec{b} = 4\vec{i} - 2\vec{j} + 2\vec{k}$ are orthogonal, find $\lambda$ .

A box contains 3 red and 5 black balls. If two balls are drawn at random, what is the probability that both are red?

If the 3th term of an AP is 76 and the 4th term is 82, find the common difference.

Solve the inequality: $x^2 - 25x + 30 < 0$ .

The number of ways to arrange 5 students in a circle is:

Find the value of $\sin(2\theta)$ if $\tan\theta = \frac1{6}$ .

If matrix $A$ is symmetric, then the matrix $A^T$ is equal to:

Want to master Algebra?

Frequently Asked Questions

✓ Key Takeaways for Algebra

🔗 Related Study Resources

Algebra MCQs (Free Practice Questions)

🤖 Quick AI Summary

What is Algebra?

💡 Why Study Algebra?

⚠️ Common Pitfalls to Avoid

🗺️ Recommended learning path

What You Will Learn

Cheat Sheet & Formulas

Practice Questions

In a survey of 630 candidates, 378 were proficient in C++ and 315 in Java. If 126 were proficient in both, how many were proficient in neither?

Evaluate the limit: lim⁡x→0sin⁡(5x)x\lim_{x \to 0} \frac{\sin(5x)}{x}x→0lim​xsin(5x)​ for Algebra.

Find the equation of the circle concentric with x2+y2−12x+24y−10=0x^2 + y^2 - 12x + 24y - 10 = 0x2+y2−12x+24y−10=0 and passing through the origin.

If vectors a⃗=i⃗+λj⃗+k⃗\vec{a} = \vec{i} + \lambda\vec{j} + \vec{k}a=i+λj​+k and b⃗=4i⃗−2j⃗+2k⃗\vec{b} = 4\vec{i} - 2\vec{j} + 2\vec{k}b=4i−2j​+2k are orthogonal, find λ\lambdaλ.

A box contains 3 red and 5 black balls. If two balls are drawn at random, what is the probability that both are red?

If the 3th term of an AP is 76 and the 4th term is 82, find the common difference.

Solve the inequality: x2−25x+30<0x^2 - 25x + 30 < 0x2−25x+30<0.

The number of ways to arrange 5 students in a circle is:

Find the value of sin⁡(2θ)\sin(2\theta)sin(2θ) if tan⁡θ=16\tan\theta = \frac1{6}tanθ=61​.

If matrix AAA is symmetric, then the matrix ATA^TAT is equal to:

Want to master Algebra?

Frequently Asked Questions

✓ Key Takeaways for Algebra

🔗 Related Study Resources

Evaluate the limit: $\lim_{x \to 0} \frac{\sin(5x)}{x}$ for Algebra.

Find the equation of the circle concentric with $x^2 + y^2 - 12x + 24y - 10 = 0$ and passing through the origin.

If vectors $\vec{a} = \vec{i} + \lambda\vec{j} + \vec{k}$ and $\vec{b} = 4\vec{i} - 2\vec{j} + 2\vec{k}$ are orthogonal, find $\lambda$ .

Solve the inequality: $x^2 - 25x + 30 < 0$ .

Find the value of $\sin(2\theta)$ if $\tan\theta = \frac1{6}$ .

If matrix $A$ is symmetric, then the matrix $A^T$ is equal to: