Straight Lines and Pair of Straight Lines PYQs - Last 5 Years
MHT CET / Mathematics / Coordinate Geometry / 126 recent questions
MathematicsCoordinate Geometry2022-2026
Practice 126 MHT CET Mathematics questions from Straight Lines and Pair of Straight Lines. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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Last 5 Years Straight Lines and Pair of Straight Lines Questions
Showing 26 of 126 filtered questions.
1Straight Lines And Pair Of Straight Lines
The distance of a point \((2,5)\) from the line \(3 x+y+4=0\) measured along the line \(L_1\) and \(L_1\) are same. If slope of line \(L_1\) is \(\frac{3}{4}\), then slope of the line \(\mathrm{L}_2\) is
MCQ+2 / -02023
2Straight Lines And Pair Of Straight Lines
If the distance between the parallel lines given by the equation \(x^2+4 x y+p y^2+3 x+q y-4=0\) is \(\lambda\), then \(\lambda^2=\)
MCQ+2 / -02023
3Straight Lines And Pair Of Straight Lines
The equation of a line, whose perpendicular distance from the origin is 7 units and the angle, which the perpendicular to the line from the origin makes, is \(120^{\circ}\) with positive \(\mathrm{X}\)-axis, is
MCQ+2 / -02023
4Straight Lines And Pair Of Straight Lines
If the slope of one of the lines represented by \(a x^2+(2 a+1) x y+2 y^2=0\) is reciprocal of the slope of the other, then the sum of squares of slopes is
MCQ+2 / -02023
5Straight Lines And Pair Of Straight Lines
The perpendiculars are drawn to lines \(L_1\) and \(L_2\) from the origin making an angle \(\frac{\pi}{4}\) and \(\frac{3 \pi}{4}\) respectively with positive direction of \(\mathrm{X}\)-axis. If both the lines are at unit distance from the...
MCQ+2 / -02023
6Straight Lines And Pair Of Straight Lines
\(\mathrm{p}\) is the length of perpendicular from the origin to the line whose intercepts on the axes are a and \(\mathrm{b}\) respectively, then \(\frac{1}{\mathrm{a}^2}+\frac{1}{\mathrm{~b}^2}\) equals
MCQ+2 / -02023
7Straight Lines And Pair Of Straight Lines
The centroid of the triangle formed by the lines \(x+3 y=10\) and \(6 x^2+x y-y^2=0\) is
MCQ+2 / -02023
8Straight Lines And Pair Of Straight Lines
Let \(P \equiv(-3,0), Q \equiv(0,0)\) and \(R \equiv(3,3 \sqrt{3})\) be three points. Then the equation of the bisector of the angle \(\mathrm{PQR}\) is
MCQ+2 / -02023
9Straight Lines And Pair Of Straight Lines
A line is drawn through the point \((1,2)\) to meet the co-ordinate axes at \(\mathrm{P}\) and \(\mathrm{Q}\) such that it forms a \(\triangle \mathrm{OPQ}\), where \(\mathrm{O}\) is the origin. If the area of \(\triangle \mathrm{OPQ}\) is ...
MCQ+2 / -02023
10Straight Lines And Pair Of Straight Lines
The base of an equilateral triangle is represented by the equation \(2 x-y-1=0\) and its vertex is \((1,2)\), then the length (in units) of the side of the triangle is
MCQ+2 / -02023
11Straight Lines And Pair Of Straight Lines
If the angle between the lines given by \(x^2-3 x y+\lambda y^2+3 x-5 y+2=0 ; \lambda \geq 0\) is \(\tan ^{-1}\left(\frac{1}{3}\right)\), then the value of \(\lambda\) is
MCQ+2 / -02023
12Straight Lines And Pair Of Straight Lines
\(P S\) is the median of the triangle with vertices at \(P(2,2), Q(6,-1)\) and \(R(7,3)\), then the intercepts on the coordinate axes of the line passing through point \((1,-1)\) and parallel to PS are respectively
MCQ+2 / -02023
13Straight Lines And Pair Of Straight Lines
Let \(P Q R\) be a right angled isosceles triangle, right angled at \(Q(2,1)\). If the equation of the line \(P R\) is \(2 x+y=3\), then the combined equation representing the pair of lines \(P Q\) and \(Q R\) is
MCQ+2 / -02023
14Straight Lines And Pair Of Straight Lines
Let \(\mathrm{PQR}\) be a right angled isosceles triangle, right angled at \(\mathrm{P}(2,1)\). If the equation of the line \(\mathrm{QR}\) is \(2 x+y=3\), then the equation representing the pair of lines \(P Q\) and \(P R\) is
MCQ+2 / -02023
15Straight Lines And Pair Of Straight Lines
The co-ordinates of the points on the line \(2 x-y=5\) which are the distance of 1 unit from the line \(3 x+4 y=5\) are
MCQ+2 / -02023
16Straight Lines And Pair Of Straight Lines
If \(\mathrm{k}_{\mathrm{i}}\) are possible values of \(\mathrm{k}\) for which lines \(\mathrm{k} x+2 y+2=0,2 x+\mathrm{k} y+3=0\) and \(3 x+3 y+\mathrm{k}=0\) are concurrent, then \(\sum \mathrm{k}_{\mathrm{i}}\) has the value
MCQ+2 / -02023
17Straight Lines And Pair Of Straight Lines
If the pair of lines given by \((x \cos \alpha+y \sin \alpha)^2=\left(x^2+y^2\right) \sin ^2 \alpha\) are perpendicular to each other, then \(\alpha\) is
MCQ+2 / -02023
18Straight Lines And Pair Of Straight Lines
\(\mathrm{a}\) and \(\mathrm{b}\) are the intercepts made by a line on the co-ordinate axes. If \(3 \mathrm{a}=\mathrm{b}\) and the line passes through \((1,3)\), then the equation of the line is
MCQ+2 / -02023
19Straight Lines And Pair Of Straight Lines
If the angle between the lines represented by the equation \(x^2+\lambda x y-y^2 \tan ^2 \theta=0\) is \(2 \theta\), then the value of \(\lambda\) is
MCQ+2 / -02023
20Straight Lines And Pair Of Straight Lines
The joint equation of the lines pair of lines passing through the point \((3,-2)\) and perpendicular to the lines \(5 x^2+2 x y-3 y^2=0\) is
MCQ+2 / -02023
21Straight Lines And Pair Of Straight Lines
The points \((1,3),(5,1)\) are opposite vertices of a diagonal of a rectangle. If the other two vertices lie on the line \(y=2 x+\mathrm{c}\), then one of the vertex on the other diagonal is
MCQ+2 / -02023
22Straight Lines And Pair Of Straight Lines
The number of integral values of \(\mathrm{p}\) in the domain \([-5,5]\), such that the equation \(2 x^2+4 x y-p y^2+4 x+q y+1=0\) represents pair of lines, are
MCQ+2 / -02023
23Straight Lines And Pair Of Straight Lines
Two sides of a square are along the lines \(5 x-12 y+39=0\) and \(5 x-12 y+78=0\), then area of the square is
MCQ+2 / -02023
24Straight Lines And Pair Of Straight Lines
The joint equation of a pair of lines passing through the origin and making an angle of \(\frac{\pi}{4}\) with the line \(3 x+2 y-8=0\) is
MCQ+2 / -02023
25Straight Lines And Pair Of Straight Lines
The equations of the lines passing through the point \((3,2)\) and making an acute angle of \(45^{\circ}\) with the line \(x-2 y-3=0\) are
MCQ+2 / -02022
26Straight Lines And Pair Of Straight Lines
The joint equation of pair of lines through the origin and making an equilateral triangle with the line \(y = 5\) is
MCQ+2 / -02022