# SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 1 - Pair of Lines [Latest edition]

## Chapter 1: Pair of Lines

MCQ

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 1 Pair of Lines MCQ

#### 2 marks each

MCQ | Q 1

The combined equation of the two lines passing through the origin, each making angle 45° and 135° with the positive X-axis is ______

• x2 + y2 = 0

• xy = 1

• x2 − y2 = 0

• x2 + xy =0

MCQ | Q 2

The separate equations of the lines represented by 3x^2 - 2sqrt(3)xy - 3y^2 = 0 are ______

• x + sqrt(3)y = 0 and sqrt(3)x + y = 0

• x - sqrt(3)y = 0 and sqrt(3)x - y = 0

• x - sqrt(3)y = 0 and sqrt(3)x + y = 0

• x + sqrt(3)y = 0 and sqrt(3)x - y = 0

MCQ | Q 3

The equation 4x2 + 4xy + y2 = 0 represents two ______

• real and distinct lines

• real and coincident lines

• imaginary lines

• perpendicular lines

MCQ | Q 4

If the lines represented by kx2 − 3xy + 6y2 = 0 are perpendicular to each other, then

• k = 6

• k = − 6

• k = 3

• k = − 3

MCQ | Q 5

Auxillary equation of 2x2 + 3xy − 9y2 = 0 is ______

• 2m2 + 3m − 9 = 0

• 9m2 − 3m − 2 = 0

• 2m2 − 3m + 9 = 0

• −9m2 − 3m + 2 = 0

MCQ | Q 6

The combined equation of the lines through origin and perpendicular to the pair of lines 3x2 + 4xy − 5y2 = 0 is ______

• 5x2 + 4xy − 3y2 = 0

• 3x2 + 4xy − 5y2 = 0

• 3x2 - 4xy + 5y2 = 0

• 5x2 + 4xy + 3y2 = 0

MCQ | Q 7

The acute angle between the lines represented by x2 + xy = 0 is ______

• pi/2

• pi/4

• pi/6

• pi/3

MCQ | Q 8

If 2x + y = 0 is one of the line represented by 3x2 + kxy + 2y2 = 0 then k = ______

• 1/2

• 11/2

• 2/3

• 3/2

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 1 Pair of Lines Very Short Answers

#### 2 mark

Very Short Answers | Q 1

Find the combined equation of the following pair of lines passing through (2, 3) and parallel to the coordinate axes.

Very Short Answers | Q 2

Find the separate equations of the lines given by x2 + 2xy tan α − y2 = 0

Very Short Answers | Q 3

Find k, if the sum of the slopes of the lines represented by x2 + kxy − 3y2 = 0 is twice their product.

Very Short Answers | Q 4

Find the measure of the acute angle between the lines given by x2 − 4xy + y2 = 0

Very Short Answers | Q 5

Find the value of h, if the measure of the angle between the lines 3x2 + 2hxy + 2y2 = 0 is 45°.

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 1 Pair of Lines Short Answers I

#### 3 marks

Short Answers I | Q 1

Find the combined equation of the following pair of line passing through (−1, 2), one is parallel to x + 3y − 1 = 0 and other is perpendicular to 2x − 3y − 1 = 0

Short Answers I | Q 2

Find the joint equation of pair of lines through the origin which is perpendicular to the lines represented by 5x2 + 2xy - 3y2 = 0

Short Answers I | Q 3

Find the condition that the line 4x + 5y = 0 coincides with one of the lines given by ax2 + 2hxy + by2 = 0

Short Answers I | Q 4

Find the measure of the acute angle between the line represented by 3"x"^2 - 4sqrt3"xy" + 3"y"^2 = 0

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 1 Pair of Lines Short Answers II

#### 4 Marks

Short Answers II | Q 1

Show that the combined equation of pair of lines passing through the origin is a homogeneous equation of degree 2 in x and y. Hence find the combined equation of the lines 2x + 3y = 0 and x − 2y = 0

Short Answers II | Q 2

Show that the homogeneous equation of degree 2 in x and y represents a pair of lines passing through the origin if h2 ab 0.

Short Answers II | Q 3

If θ is the acute angle between the lines given by ax2 + 2hxy + by2 = 0 then prove that tan θ = |(2sqrt("h"^2) - "ab")/("a" + "b")|. Hence find acute angle between the lines 2x2 + 7xy + 3y2 = 0

Short Answers II | Q 4

If the angle between the lines represented by ax2 + 2hxy + by2 = 0 is equal to the angle between the lines 2x2 − 5xy + 3y2 = 0, then show that 100(h2 − ab) = (a + b)2

## SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 1 - Pair of Lines

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 1 (Pair of Lines) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 1 Pair of Lines are Combined Equation of a Pair Lines, Homogeneous Equation of Degree Two, Angle between lines represented by ax2 + 2hxy + by2 = 0, General Second Degree Equation in x and y, Equation of a Line in Space.

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