Chapter Exam

Chapter 3: Algebra — Online MCQ Test

Q: A linear equation in three variables x, y and z is generally written as ______.

Answer: A. ax + by + cz = d — A linear equation in three variables has first degree terms in x, y and z, and is written as ax + by + cz = d.

Q: For the quadratic equation ax^2 + bx + c = 0, the product of roots is ______.

Answer: C. c/a — If α and β are the roots of ax^2 + bx + c = 0, then αβ = c/a.

Q: Solve: x + y + z = 6, x - y = 0 and z = 2. What is the value of x?

Answer: B. 2 — Since z = 2, x + y = 4. Also x = y, so 2x = 4 and x = 2.

Q: Solve: x + y + z = 6, 2x - y + z = 6, x + 2y - z = 1.

Answer: B. x = 2, y = 1, z = 3 — Substituting x = 2, y = 1, z = 3 satisfies all three equations. Elimination also gives the same solution.

Q: If the roots of x^2 - 8x + k = 0 are in the ratio 1 : 3, find k.

Answer: C. 12 — Let the roots be r and 3r. Their sum is 4r = 8, so r = 2; product = 2 × 6 = 12. Hence k = 12.

MATHS · CLASS 10th · Tamil Nadu State Board

Practice Chapter 3: Algebra with a free chapter-wise online MCQ test for Tamil Nadu State Board CLASS 10th MATHS. This chapter covers: Linear equations Three variables Elimination method Substitution method Quadratic equations Polynomial GCD LCM Square root of polynomial Factorisation Algebraic identities Roots of.... AI-generated questions from basic to board-exam level, with instant results and explanations.

Questions

20m

Time Limit

Attempts Left

10 random questions from this chapter (mixed difficulty)
Questions you've seen before won't repeat until the pool resets
You have 20 minutes — exam auto-submits when time is up
Maximum 3 attempts per chapter
Results and explanations shown immediately after submission

New here? Register free — includes 3 free chapter exams.

Chapter 3: Algebra — Important Questions & Answers (FAQ)

Frequently asked questions from Tamil Nadu State Board CLASS 10th MATHS — Chapter 3: Algebra, with answers and explanations. These are sample questions; the exam has its own separate question set.

A linear equation in three variables x, y and z is generally written as ______.

A. ax + by + cz = d ✓
B. ax^2 + by + c = 0
C. ax + by = 0 only
D. xyz = d

Answer: A. ax + by + cz = d
A linear equation in three variables has first degree terms in x, y and z, and is written as ax + by + cz = d.

For the quadratic equation ax^2 + bx + c = 0, the product of roots is ______.

A. -b/a
B. b/a
C. c/a ✓
D. -c/a

Answer: C. c/a
If α and β are the roots of ax^2 + bx + c = 0, then αβ = c/a.

Solve: x + y + z = 6, x - y = 0 and z = 2. What is the value of x?

A. 1
B. 2 ✓
C. 3
D. 4

Answer: B. 2
Since z = 2, x + y = 4. Also x = y, so 2x = 4 and x = 2.

Solve: x + y + z = 6, 2x - y + z = 6, x + 2y - z = 1.

A. x = 1, y = 2, z = 3
B. x = 2, y = 1, z = 3 ✓
C. x = 3, y = 1, z = 2
D. x = 2, y = 3, z = 1

Answer: B. x = 2, y = 1, z = 3
Substituting x = 2, y = 1, z = 3 satisfies all three equations. Elimination also gives the same solution.

If the roots of x^2 - 8x + k = 0 are in the ratio 1 : 3, find k.

A. 8
B. 10
C. 12 ✓
D. 16

Answer: C. 12
Let the roots be r and 3r. Their sum is 4r = 8, so r = 2; product = 2 × 6 = 12. Hence k = 12.

Choose Your Plan & Start Practising

All plans cover every subject and chapter of your registered grade.

Free

₹0

3 exams · 1 year

Start Free →

Active

₹350

12 exams · 1 year

Get Active →

Pro

₹899

Unlimited exams · 1 year

Get Pro →

Compare all plans in detail →