Chapter 3: Algebra — Online MCQ Test
MATHS · CLASS 10th · Tamil Nadu State Board
Practice Chapter 3: Algebra with a free chapter-wise online MCQ test.
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....
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Chapter 3: Algebra — Important Questions & Answers
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.
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.
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.
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.
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.
Let the roots be r and 3r. Their sum is 4r = 8, so r = 2; product = 2 × 6 = 12. Hence k = 12.