Chapter Exam

Unit 4: Pair of Straight Lines — Online MCQ Test

Q: A homogeneous second-degree equation in x and y represents a pair of straight lines passing through the ______.

Answer: A. origin — A homogeneous equation of degree 2 has all terms of the same degree and represents lines passing through the origin.

Q: The equation representing two straight lines through the origin is generally of the form:

Answer: B. ax^2 + 2hxy + by^2 = 0 — A pair of lines through the origin is represented by a homogeneous quadratic equation in x and y.

Q: Which of the following is NOT a homogeneous second-degree equation?

Answer: D. x^2 + y^2 + x = 0 — A homogeneous second-degree equation must contain only terms of degree 2. The term x makes option D non-homogeneous.

Q: If the pair of lines represented by x^2 + 2hxy + y^2 = 0 are equally inclined to the x-axis in opposite directions, then the angle between them is:

Answer: D. 90° — Lines equally inclined to the x-axis in opposite directions are symmetric about an axis, and in this homogeneous pair the relevant case is perpendicular when the coefficient of x^2 and y^2 are equal and opposite conditions lead to 90°.

Q: For the equation x^2 - 2xy + y^2 = 0, which of the following is the correct pair of lines?

Answer: C. x = y only — x^2 - 2xy + y^2 = (x - y)^2 = 0, so it represents the same line x = y twice.

MATHEMATICS - 1B · CLASS 11 INTERMEDIATE 1 YEAR · Telangana State Board

Practice Unit 4: Pair of Straight Lines with a free chapter-wise online MCQ test for Telangana State Board CLASS 11 INTERMEDIATE 1 YEAR MATHEMATICS - 1B. This chapter covers: This chapter covers homogeneous second-degree equations pair of lines passing through origin angle between lines bisectors of angles and condition for general second-degree equatio.... AI-generated questions from basic to board-exam level, with instant results and explanations.

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Unit 4: Pair of Straight Lines — Important Questions & Answers (FAQ)

Frequently asked questions from Telangana State Board CLASS 11 INTERMEDIATE 1 YEAR MATHEMATICS - 1B — Unit 4: Pair of Straight Lines, with answers and explanations. These are sample questions; the exam has its own separate question set.

A homogeneous second-degree equation in x and y represents a pair of straight lines passing through the ______.

A. origin ✓
B. point (1,1)
C. x-axis
D. y-axis

Answer: A. origin
A homogeneous equation of degree 2 has all terms of the same degree and represents lines passing through the origin.

The equation representing two straight lines through the origin is generally of the form:

A. ax + by + c = 0
B. ax^2 + 2hxy + by^2 = 0 ✓
C. x^2 + y^2 = 1
D. x^2 + y^2 + 2gx + 2fy + c = 0

Answer: B. ax^2 + 2hxy + by^2 = 0
A pair of lines through the origin is represented by a homogeneous quadratic equation in x and y.

Which of the following is NOT a homogeneous second-degree equation?

A. x^2 + 2xy + y^2 = 0
B. x^2 - y^2 = 0
C. 3x^2 + 5xy - 2y^2 = 0
D. x^2 + y^2 + x = 0 ✓

Answer: D. x^2 + y^2 + x = 0
A homogeneous second-degree equation must contain only terms of degree 2. The term x makes option D non-homogeneous.

If the pair of lines represented by x^2 + 2hxy + y^2 = 0 are equally inclined to the x-axis in opposite directions, then the angle between them is:

A. 30°
B. 45°
C. 60°
D. 90° ✓

Answer: D. 90°
Lines equally inclined to the x-axis in opposite directions are symmetric about an axis, and in this homogeneous pair the relevant case is perpendicular when the coefficient of x^2 and y^2 are equal and opposite conditions lead to 90°.

For the equation x^2 - 2xy + y^2 = 0, which of the following is the correct pair of lines?