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Online Mock Tests
Chapters
1.2: Matrics
1.3: Trigonometric Functions
▶ 1.4: Pair of Lines
1.5: Vectors and Three Dimensional Geometry
1.6: Line and Plane
1.7: Linear Programming Problems
2.1: Differentiation
2.2: Applications of Derivatives
2.3: Indefinite Integration
2.4: Definite Integration
2.5: Application of Definite Integration
2.6: Differential Equations
2.7: Probability Distributions
2.8: Binomial Distribution
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Solutions for Chapter 1.4: Pair of Lines
Below listed, you can find solutions for Chapter 1.4 of Maharashtra State Board SCERT Maharashtra for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC.
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 1.4 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 ______
x2 + y2 = 0
xy = 1
x2 − y2 = 0
x2 + 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 4x2 + 4xy + y2 = 0 represents two ______
real and distinct lines
real and coincident lines
imaginary lines
perpendicular lines
If the lines represented by kx2 − 3xy + 6y2 = 0 are perpendicular to each other, then
k = 6
k = − 6
k = 3
k = − 3
Auxillary equation of 2x2 + 3xy − 9y2 = 0 is ______
2m2 + 3m − 9 = 0
9m2 − 3m − 2 = 0
2m2 − 3m + 9 = 0
−9m2 − 3m + 2 = 0
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
The acute angle between the lines represented by x2 + xy = 0 is ______.
`pi/2`
`pi/4`
`pi/6`
`pi/3`
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 solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 1.4 Pair of Lines Very Short Answers
2 mark
Find the combined equation of the following pair of lines passing through point (2, 3) and parallel to the coordinate axes.
Find the separate equations of the lines given by x2 + 2xy tan α − y2 = 0
Find k, if the sum of the slopes of the lines represented by x2 + kxy − 3y2 = 0 is twice their product.
Find the measure of the acute angle between the lines given by x2 − 4xy + y2 = 0
Find the value of h, if the measure of the angle between the lines 3x2 + 2hxy + 2y2 = 0 is 45°.
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 1.4 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 5x2 + 2xy - 3y2 = 0
Find the condition that the line 4x + 5y = 0 coincides with one of the lines given by ax2 + 2hxy + by2 = 0
Find the measure of the acute angle between the line represented by `3"x"^2 - 4sqrt3"xy" + 3"y"^2 = 0`
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 1.4 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 h2 − ab ≥ 0.
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
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
Solutions for 1.4: Pair of Lines
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC chapter 1.4 - Pair of Lines
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Concepts covered in Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC chapter 1.4 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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