Straight Lines and Pair of Straight Lines PYQs - Last 10 Years
COMEDK / Mathematics / Coordinate Geometry / 39 recent questions
MathematicsCoordinate Geometry2017-2026
Practice 39 COMEDK 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 10 Years Straight Lines and Pair of Straight Lines Questions
Showing 39 of 39 filtered questions.
1Straight Lines And Pair Of Straight Lines
If a straight line passing through a fixed point $(a, b)$, where $\boldsymbol{a}, \boldsymbol{b}>\mathbf{0}$, makes positive intercepts OA and OB on the coordinate axes, then the least value of $\mathbf{O A}+\mathbf{O B}$ is:
MCQ+1 / -02026
2Straight Lines And Pair Of Straight Lines
$$ \begin{aligned} &\text { Find the co-ordinates of the orthocentre of the triangle formed by the lines }\\ &\begin{aligned} & L_1: y-x=2 \\ & L_2: y+2 x=8 \\ & L_3: 3 y-x=18 \end{aligned} \end{aligned} $$
MCQ+1 / -02026
3Straight Lines And Pair Of Straight Lines
A straight line passes through the point $P\left(\log _2 16, \log _3 27\right)$ such that the portion of the line intercepted between the co-ordinate axes is divided by $P$ in the ratio $1: 2$ internally (starting from the $x$-axis). Then t...
MCQ+1 / -02026
4Straight Lines And Pair Of Straight Lines
Distance between $8 x+15 y-20=0$ and $8 x+15 y+14=0$ is:
MCQ+1 / -02026
5Straight Lines And Pair Of Straight Lines
A line L passes through the point of intersection of the lines $3 x+y-10=0$ and $x-y-2=0$.
If the perpendicular distance of the line $L$ from the point $(5,1)$ is exactly $\frac{2}{\sqrt{5}}$ units, which of the following represents the cor...
If the perpendicular distance of the line $L$ from the point $(5,1)$ is exactly $\frac{2}{\sqrt{5}}$ units, which of the following represents the cor...
MCQ+1 / -02026
6Straight Lines And Pair Of Straight Lines
Let the line $L_1$ be a line passing through the point $(\mathbf{0},-\mathbf{6})$ and making an angle of $\mathbf{1 5 0}^{\circ}$ with the positive $x$-axis. Then the equation of a line $L_2$ parallel to $L_1$ and crossing the $y$-axis 2 un...
MCQ+1 / -02026
7Straight Lines And Pair Of Straight Lines
Let point Q be the image of point $P(2,-1)$ in the line $3 x+5=4 y$.
Find the area of the circle that has the segment PQ as the diameter.
Find the area of the circle that has the segment PQ as the diameter.
MCQ+1 / -02026
8Straight Lines And Pair Of Straight Lines
Distance of the point $(-2,3)$ from the line $12 x-5 y-2=0$ is $\frac{41}{k}$. Then the value of $k$ is
MCQ+1 / -02025
9Straight Lines And Pair Of Straight Lines
A line $L_1$ passes through the points $(h, k),(1,2)$ and $(-3,4)$. The points $(4,3)$ and $(h, k)$ lie on the line $L_2$. Given $L_1 \perp L_2$ then $(k-h)$ equals to
MCQ+1 / -02025
10Straight Lines And Pair Of Straight Lines
If two vertices of a triangle are $(3,-2)$ and $(-2,3)$ and its orthocentre is $(-6,1)$.
Then the difference between ordinate and abscissa of the third vertex of the triangle is
Then the difference between ordinate and abscissa of the third vertex of the triangle is
MCQ+1 / -02025
11Straight Lines And Pair Of Straight Lines
A straight line makes positive intercepts on the coordinate axes whose sum is 5 . If the line passes through the point $P(-3,4)$ then the equation of a line is
MCQ+1 / -02025
12Straight Lines And Pair Of Straight Lines
If the line $(3 x+14 y+7)+k(5 x+7 y+6)=0$ is perpendicular to $x$-axis then the value of ' $k$ ' is
MCQ+1 / -02025
13Straight Lines And Pair Of Straight Lines
The angle between two lines is $45^{\circ}$ and slope of one line is $\frac{1}{4}$ then which is the possible value of the slope of the other line.
MCQ+1 / -02025
14Straight Lines And Pair Of Straight Lines
The line $A B$ passes through the point $P(-4,3)$ and the portion of the line intercepted between the axes is divided internally in the ratio $5: 3$ by the point $P$. Given that the point A lies on $x$-axis and B lies on $y$-axis, then the ...
MCQ+1 / -02025
15Straight Lines And Pair Of Straight Lines
In a triangle $A B C$ the coordinate of the vertex $A$ is $(1,2)$. Equations of the median through $B$ and $C$ are respectively $x+y=5$ and $x=4$. Then the equation of side $\mathbf{A B}$ is
MCQ+1 / -02025
16Straight Lines And Pair Of Straight Lines
The point on the line $x+y=4$ that lie at a unit distance from the line $4 x+3 y=10$ is
MCQ+1 / -02025
17Straight Lines And Pair Of Straight Lines
The perpendicular distance of a line from the origin is 5 units and its slope is \(-1\).
The equation of the line is
The equation of the line is
MCQ+1 / -02024
18Straight Lines And Pair Of Straight Lines
Find the direction in which a straight line must be drawn through the point \((1,2)\) so that its point of intersection with the line \(x+y=4\) may be at a distance of \(\sqrt{\frac{2}{3}}\) from this point.
MCQ+1 / -02024
19Straight Lines And Pair Of Straight Lines
The points on the \(x\)-axis whose perpendicular distance from the line \(\frac{x}{3}+\frac{y}{4}=1\) is 4 units are
MCQ+1 / -02024
20Straight Lines And Pair Of Straight Lines
The area of the triangle whose vertices are \((-2, a)(2,-6)\) and \((5,4)\) is 35 sq units then the value of '\(\mathrm{a}\)' is
MCQ+1 / -02024
21Straight Lines And Pair Of Straight Lines
The line joining two points \(A(2,0) B(3,1)\) is rotated about \(A\) in anticlockwise direction through an angle of \(15^{\circ}\). If \(B\) goes to \(C\) in the new position, then the coordinates of \(C\) is
MCQ+1 / -02024
22Straight Lines And Pair Of Straight Lines
For what value of \(\mathrm{a}\) and \(\mathrm{b}\) the intercepts cut off on the co-ordinate axes by the line \(a x-b y+8=0\) are equal in length but opposite in signs to those cut off by the line \(2 x-3 y+6=0\) on the axes
MCQ+1 / -02024
23Straight Lines And Pair Of Straight Lines
Let \(\mathrm{ABC}\) be a triangle with equations of its sides \(\mathrm{AB}, \mathrm{BC}\). \(\mathrm{CA}\) respectively are \(x-2=0, y-5=0\) and \(5 x+2 y-10=0\). Then the orthocentre of triangle lies on the line
MCQ+1 / -02024
24Straight Lines And Pair Of Straight Lines
In a \(\triangle A B C\), if coordinates of point \(A\) is \((1,2)\) and equation of the medians through \(B\) and \(C\) are \(x+y=5\) and \(x=4\) respectively, then the coordinates of \(B\) is
MCQ+1 / -02023
25Straight Lines And Pair Of Straight Lines
The ratio in which the line \(3 x+4 y+2=0\) divides the distance between the lines \(3 x+4 y+5=0\) and \(3 x+4 y-5=0\) is
MCQ+1 / -02023
26Straight Lines And Pair Of Straight Lines
What can be said regarding a line if its slope is negative?
MCQ+1 / -02023
27Straight Lines And Pair Of Straight Lines
3 and 5 are intercepts of a line \(L=0\), then the distance of \(L=0\) from \((3,7)\) is
MCQ+1 / -02023
28Straight Lines And Pair Of Straight Lines
The slope of lines which makes an angle \(60^{\circ}\) with the line \(y-3 x+18=0\)
MCQ+1 / -02023
29Straight Lines And Pair Of Straight Lines
The distance of the point \((3,4)\) from the line \(3 x+2 y+7=0\) measured along the line parallel to \(y-2 x+7=0\) is equal to
MCQ+1 / -02023
30Straight Lines And Pair Of Straight Lines
Let the equation of pair of lines \(y=m_1 x\) and \(y=m_2 x\) can be written as \(\left(y-m_1 x\right)\left(y-m_2 x\right)=0\). Then, the equation of the pair of the angle bisector of the line \(3 y^2-5 x y-2 x^2=0\) is
MCQ+1 / -02023
31Straight Lines And Pair Of Straight Lines
If 2 and 3 are intercepts of a line L = 0, then the distance of L \(\equiv\) 0 from the origin is
MCQ+1 / -02022
32Straight Lines And Pair Of Straight Lines
The slope of lines which makes an angle 45\(^\circ\) with the line \(2x-y=-7\)
MCQ+1 / -02022
33Straight Lines And Pair Of Straight Lines
The distance of the point \((1,2)\) from the line \(x+y+2=0\) measured along the line parallel to \(2 x-y=5\) is equal to
MCQ+1 / -02022
34Straight Lines And Pair Of Straight Lines
Let the equation of the pair of lines \(y=p x\) and \(y=q x\) can be written as \((y-p x)(y-q x)=0\). Then the equation of the pair of the angle bisectors of the line \(x^2-4 x y-5 y^2=0\) is
MCQ+1 / -02022
35Straight Lines And Pair Of Straight Lines
If 3 and 4 are intercepts of a line L = 0, then the distance of L \(\equiv\) 0 from the origin is
MCQ+1 / -02021
36Straight Lines And Pair Of Straight Lines
The slopes of the lines, which make an angle 45\(^\circ\) with the line \(3x-y=-5\), are
MCQ+1 / -02021
37Straight Lines And Pair Of Straight Lines
The distance of the point (1, 2) from the line \(x+y+5=0\) measured along the line parallel to \(3x-y=7\) is equal to
MCQ+1 / -02021
38Straight Lines And Pair Of Straight Lines
If two pairs of lines \(x^2-2mxy-y^2=0\) and \(x^2-2nxy-y^2=0\) are such that one of them represents the bisector of the angles between the other, then
MCQ+1 / -02021
39Straight Lines And Pair Of Straight Lines
The coordinates of the foot of the perpendicular drawn from the point (3, 4) on the line \(2x+y-7=0\) is
MCQ+1 / -02020