#### Online Mock Tests

#### Chapters

Chapter 1.2: Matrics

Chapter 1.3: Trigonometric Functions

Chapter 1.4: Pair of Lines

Chapter 1.5: Vectors and Three Dimensional Geometry

Chapter 1.6: Line and Plane

Chapter 1.7: Linear Programming Problems

Chapter 2.1: Differentiation

Chapter 2.2: Applications of Derivatives

Chapter 2.3: Indefinite Integration

Chapter 2.4: Definite Integration

Chapter 2.5: Application of Definite Integration

Chapter 2.6: Differential Equations

Chapter 2.7: Probability Distributions

Chapter 2.8: Binomial Distribution

## 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 MCQ

#### 2 marks each

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

x

^{2}+ y^{2}= 0xy = 1

x

^{2}− y^{2}= 0x

^{2}+ xy =0

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

The equation 4x^{2} + 4xy + y^{2} = 0 represents two ______

real and distinct lines

real and coincident lines

imaginary lines

perpendicular lines

If the lines represented by kx^{2} − 3xy + 6y^{2} = 0 are perpendicular to each other, then

k = 6

k = − 6

k = 3

k = − 3

Auxillary equation of 2x^{2} + 3xy − 9y^{2} = 0 is ______

2m

^{2}+ 3m − 9 = 09m

^{2}− 3m − 2 = 02m

^{2}− 3m + 9 = 0−9m

^{2}− 3m + 2 = 0

The combined equation of the lines through origin and perpendicular to the pair of lines 3x^{2} + 4xy − 5y^{2} = 0 is ______

5x

^{2}+ 4xy − 3y^{2}= 03x

^{2}+ 4xy − 5y^{2}= 03x

^{2}- 4xy + 5y^{2}= 05x

^{2}+ 4xy + 3y^{2}= 0

The acute angle between the lines represented by x^{2} + xy = 0 is ______

`pi/2`

`pi/4`

`pi/6`

`pi/3`

If 2x + y = 0 is one of the line represented by 3x^{2} + kxy + 2y^{2} = 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

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

Find the separate equations of the lines given by x^{2} + 2xy tan α − y^{2} = 0

Find k, if the sum of the slopes of the lines represented by x^{2} + kxy − 3y^{2} = 0 is twice their product.

Find the measure of the acute angle between the lines given by x^{2} − 4xy + y^{2} = 0

Find the value of h, if the measure of the angle between the lines 3x^{2} + 2hxy + 2y^{2} = 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

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

Find the joint equation of pair of lines through the origin which is perpendicular to the lines represented by 5x^{2} + 2xy - 3y^{2} = 0

Find the condition that the line 4x + 5y = 0 coincides with one of the lines given by ax^{2} + 2hxy + by^{2} = 0

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

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

Show that the homogeneous equation of degree 2 in x and y represents a pair of lines passing through the origin if h^{2 }− ab ≥ 0.

If θ is the acute angle between the lines given by ax^{2} + 2hxy + by^{2} = 0 then prove that tan θ = `|(2sqrt("h"^2) - "ab")/("a" + "b")|`. Hence find acute angle between the lines 2x^{2} + 7xy + 3y^{2} = 0

If the angle between the lines represented by ax^{2} + 2hxy + by^{2} = 0 is equal to the angle between the lines 2x^{2} − 5xy + 3y^{2} = 0, then show that 100(h^{2} − ab) = (a + b)^{2}

## 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

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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