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Probability and Statistics MCQs (Free Practice Questions)

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

What is Probability and Statistics?

Probability and Statistics covers the essential principles and concepts required for NIMCET.

💡 Why Study Probability and Statistics?

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	Easy
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

Set Theory➔Probability and Statistics (Current)➔Algebra

What You Will Learn

✓ Probability and Statistics Fundamentals
✓ Key applications of Probability and Statistics
✓ Advanced problem solving in Probability and Statistics

Cheat Sheet & Formulas

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

Practice Questions

⏱ 60sHard

In a survey of 440 candidates, 264 were proficient in C++ and 220 in Java. If 88 were proficient in both, how many were proficient in neither?

⏱ 65sMedium

Evaluate the limit: $\lim_{x \to 0} \frac{\sin(4x)}{x}$ for Probability and Statistics.

⏱ 70sEasy

Find the equation of the circle concentric with $x^2 + y^2 - 8x + 16y - 10 = 0$ and passing through the origin.

⏱ 75sHard

If vectors $\vec{a} = \vec{i} + \lambda\vec{j} + \vec{k}$ and $\vec{b} = 5\vec{i} - 2\vec{j} + 2\vec{k}$ are orthogonal, find $\lambda$ .

⏱ 80sMedium

A box contains 4 red and 6 black balls. If two balls are drawn at random, what is the probability that both are red?

⏱ 85sEasy

If the 5th term of an AP is 74 and the 6th term is 100, find the common difference.

⏱ 90sHard

Solve the inequality: $x^2 - 10x + 12 < 0$ .

⏱ 95sMedium

The number of ways to arrange 2 students in a circle is:

⏱ 100sEasy

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

Q10

⏱ 105sHard

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

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Frequently Asked Questions

Is Probability and Statistics difficult for the exam?▼

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

✓ Key Takeaways for Probability and Statistics

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.

Probability and Statistics MCQs (Free Practice Questions)

🤖 Quick AI Summary

What is Probability and Statistics?

💡 Why Study Probability and Statistics?

⚠️ Common Pitfalls to Avoid

🗺️ Recommended learning path

What You Will Learn

Cheat Sheet & Formulas

Practice Questions

In a survey of 440 candidates, 264 were proficient in C++ and 220 in Java. If 88 were proficient in both, how many were proficient in neither?

Evaluate the limit: $\lim_{x \to 0} \frac{\sin(4x)}{x}$ for Probability and Statistics.

Find the equation of the circle concentric with $x^2 + y^2 - 8x + 16y - 10 = 0$ and passing through the origin.

If vectors $\vec{a} = \vec{i} + \lambda\vec{j} + \vec{k}$ and $\vec{b} = 5\vec{i} - 2\vec{j} + 2\vec{k}$ are orthogonal, find $\lambda$ .

A box contains 4 red and 6 black balls. If two balls are drawn at random, what is the probability that both are red?

If the 5th term of an AP is 74 and the 6th term is 100, find the common difference.

Solve the inequality: $x^2 - 10x + 12 < 0$ .

The number of ways to arrange 2 students in a circle is:

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

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

Want to master Probability and Statistics?

Frequently Asked Questions

✓ Key Takeaways for Probability and Statistics

🔗 Related Study Resources

Probability and Statistics MCQs (Free Practice Questions)

🤖 Quick AI Summary

What is Probability and Statistics?

💡 Why Study Probability and Statistics?

⚠️ Common Pitfalls to Avoid

🗺️ Recommended learning path

What You Will Learn

Cheat Sheet & Formulas

Practice Questions

In a survey of 440 candidates, 264 were proficient in C++ and 220 in Java. If 88 were proficient in both, how many were proficient in neither?

Evaluate the limit: lim⁡x→0sin⁡(4x)x\lim_{x \to 0} \frac{\sin(4x)}{x}x→0lim​xsin(4x)​ for Probability and Statistics.

Find the equation of the circle concentric with x2+y2−8x+16y−10=0x^2 + y^2 - 8x + 16y - 10 = 0x2+y2−8x+16y−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=5i⃗−2j⃗+2k⃗\vec{b} = 5\vec{i} - 2\vec{j} + 2\vec{k}b=5i−2j​+2k are orthogonal, find λ\lambdaλ.

A box contains 4 red and 6 black balls. If two balls are drawn at random, what is the probability that both are red?

If the 5th term of an AP is 74 and the 6th term is 100, find the common difference.

Solve the inequality: x2−10x+12<0x^2 - 10x + 12 < 0x2−10x+12<0.

The number of ways to arrange 2 students in a circle is:

Find the value of sin⁡(2θ)\sin(2\theta)sin(2θ) if tan⁡θ=12\tan\theta = \frac1{2}tanθ=21​.

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

Want to master Probability and Statistics?

Frequently Asked Questions

✓ Key Takeaways for Probability and Statistics

🔗 Related Study Resources

Evaluate the limit: $\lim_{x \to 0} \frac{\sin(4x)}{x}$ for Probability and Statistics.

Find the equation of the circle concentric with $x^2 + y^2 - 8x + 16y - 10 = 0$ and passing through the origin.

If vectors $\vec{a} = \vec{i} + \lambda\vec{j} + \vec{k}$ and $\vec{b} = 5\vec{i} - 2\vec{j} + 2\vec{k}$ are orthogonal, find $\lambda$ .

Solve the inequality: $x^2 - 10x + 12 < 0$ .

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

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