Chapter Exam

Chapter-3 PAIR OF LINEAR EQUATIONS IN TWO VARIABLES — Online MCQ Test

Q: A pair of linear equations in two variables is of the form a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0. What condition must be satisfied for the system to have a unique solution?

Answer: B. a₁/a₂ ≠ b₁/b₂ — For a unique solution, the lines must intersect at exactly one point, which occurs when a₁/a₂ ≠ b₁/b₂ (the lines are not parallel).

Q: Which of the following is the correct definition of consistent equations?

Answer: B. Equations that have at least one solution — Consistent equations are those that have at least one common solution, either unique or infinitely many.

Q: Solve the system: x + y = 5 and x - y = 3. What is the value of x?

Answer: D. 4 — Adding both equations: 2x = 8, so x = 4. Verification: 4 + 1 = 5 and 4 - 1 = 3 ✓

Q: Analyze the system: 4x + 6y = 8 and 2x + 3y = 4. The nature of this system is:

Answer: C. Consistent with infinitely many solutions — The first equation simplifies to 2x + 3y = 4 when divided by 2, which is identical to the second equation, so infinitely many solutions exist.

Q: If the pair of equations px + qy = m and rx + sy = n represent two perpendicular lines, which statement is always true?

Answer: A. pr + qs = 0 — For perpendicular lines, the product of their slopes equals -1. The slopes are -p/q and -r/s, so (-p/q)(-r/s) = -1, which simplifies to pr + qs = 0.

MATHS · Grade 10 · CBSE(NCERT)

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Chapter-3 PAIR OF LINEAR EQUATIONS IN TWO VARIABLES — Important Questions & Answers (FAQ)

Frequently asked questions from CBSE(NCERT) Grade 10 MATHS — Chapter-3 PAIR OF LINEAR EQUATIONS IN TWO VARIABLES, with answers and explanations. These are sample questions; the exam has its own separate question set.

A pair of linear equations in two variables is of the form a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0. What condition must be satisfied for the system to have a unique solution?

A. a₁/a₂ = b₁/b₂
B. a₁/a₂ ≠ b₁/b₂ ✓
C. a₁/a₂ = b₁/b₂ = c₁/c₂
D. a₁ × a₂ = b₁ × b₂

Answer: B. a₁/a₂ ≠ b₁/b₂
For a unique solution, the lines must intersect at exactly one point, which occurs when a₁/a₂ ≠ b₁/b₂ (the lines are not parallel).

Which of the following is the correct definition of consistent equations?

A. Equations that have no solution
B. Equations that have at least one solution ✓
C. Equations that have exactly two solutions
D. Equations that are always contradictory

Answer: B. Equations that have at least one solution
Consistent equations are those that have at least one common solution, either unique or infinitely many.

Solve the system: x + y = 5 and x - y = 3. What is the value of x?

A. 1
B. 2
C. 3
D. 4 ✓

Answer: D. 4
Adding both equations: 2x = 8, so x = 4. Verification: 4 + 1 = 5 and 4 - 1 = 3 ✓

Analyze the system: 4x + 6y = 8 and 2x + 3y = 4. The nature of this system is:

A. Inconsistent (parallel lines)
B. Consistent with unique solution
C. Consistent with infinitely many solutions ✓
D. Degenerate

Answer: C. Consistent with infinitely many solutions
The first equation simplifies to 2x + 3y = 4 when divided by 2, which is identical to the second equation, so infinitely many solutions exist.

If the pair of equations px + qy = m and rx + sy = n represent two perpendicular lines, which statement is always true?

A. pr + qs = 0 ✓
B. p/r = q/s
C. ps = qr
D. p + r = q + s

Answer: A. pr + qs = 0
For perpendicular lines, the product of their slopes equals -1. The slopes are -p/q and -r/s, so (-p/q)(-r/s) = -1, which simplifies to pr + qs = 0.