Straight Lines and Pair of Straight Lines PYQs - Last 10 Years
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MathematicsCoordinate Geometry2017-2026
Practice 142 JEE Main 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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2017-2026
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Last 10 Years Straight Lines and Pair of Straight Lines Questions
Showing 50 of 142 filtered questions.
1Straight Lines And Pair Of Straight Lines
The portion of the line $4 x+5 y=20$ in the first quadrant is trisected by the lines $\mathrm{L}_1$ and $\mathrm{L}_2$ passing through the origin. The tangent of an angle between the lines $\mathrm{L}_1$ and $\mathrm{L}_2$ is :
MCQ+4 / -12024
2Straight Lines And Pair Of Straight Lines
If the sum of squares of all real values of \(\alpha\), for which the lines \(2 x-y+3=0,6 x+3 y+1=0\) and \(\alpha x+2 y-2=0\) do not form a triangle is \(p\), then the greatest integer less than or equal to \(p\) is _________.
INTEGER+4 / -12024
3Straight Lines And Pair Of Straight Lines
Let \(\mathrm{R}\) be the interior region between the lines \(3 x-y+1=0\) and \(x+2 y-5=0\) containing the origin. The set of all values of \(a\), for which the points \(\left(a^2, a+1\right)\) lie in \(R\), is :
MCQ+4 / -12024
4Straight Lines And Pair Of Straight Lines
The lines $\mathrm{L}_1, \mathrm{~L}_2, \ldots, \mathrm{L}_{20}$ are distinct. For $\mathrm{n}=1,2,3, \ldots, 10$ all the lines $\mathrm{L}_{2 \mathrm{n}-1}$ are parallel to each other and all the lines $L_{2 n}$ pass through a given point ...
INTEGER+4 / -12024
5Straight Lines And Pair Of Straight Lines
Let $A B C$ be an isosceles triangle in which $A$ is at $(-1,0), \angle A=\frac{2 \pi}{3}, A B=A C$ and $B$ is on the positve $x$-axis. If $\mathrm{BC}=4 \sqrt{3}$ and the line $\mathrm{BC}$ intersects the line $y=x+3$ at $(\alpha, \beta)$,...
INTEGER+4 / -12024
6Straight Lines And Pair Of Straight Lines
Let \(C(\alpha, \beta)\) be the circumcenter of the triangle formed by the lines
\(4 x+3 y=69\)
\(4 y-3 x=17\), and
\(x+7 y=61\).
Then \((\alpha-\beta)^{2}+\alpha+\beta\) is equal to :
\(4 x+3 y=69\)
\(4 y-3 x=17\), and
\(x+7 y=61\).
Then \((\alpha-\beta)^{2}+\alpha+\beta\) is equal to :
MCQ+4 / -12023
7Straight Lines And Pair Of Straight Lines
The straight lines \(\mathrm{l_{1}}\) and \(\mathrm{l_{2}}\) pass through the origin and trisect the line segment of the line L : \(9 x+5 y=45\) between the axes. If \(\mathrm{m}_{1}\) and \(\mathrm{m}_{2}\) are the slopes of the lines $$\m...
MCQ+4 / -12023
8Straight Lines And Pair Of Straight Lines
A light ray emits from the origin making an angle 30\(^\circ\) with the positive \(x\)-axis. After getting reflected by the line \(x+y=1\), if this ray intersects \(x\)-axis at Q, then the abscissa of Q is :
MCQ+4 / -12023
9Straight Lines And Pair Of Straight Lines
Let \(B\) and \(C\) be the two points on the line \(y+x=0\) such that \(B\) and \(C\) are symmetric with respect to the origin. Suppose \(A\) is a point on \(y-2 x=2\) such that \(\triangle A B C\) is an equilateral triangle. Then, the area...
MCQ+4 / -12023
10Straight Lines And Pair Of Straight Lines
The equations of the sides AB, BC and CA of a triangle ABC are : \(2x+y=0,x+py=21a,(a\pm0)\) and \(x-y=3\) respectively. Let P(2, a) be the centroid of \(\Delta\)ABC. Then (BC)\(^2\) is equal to ___________.
INTEGER+4 / -12023
11Straight Lines And Pair Of Straight Lines
If the orthocentre of the triangle, whose vertices are (1, 2), (2, 3) and (3, 1) is \((\alpha,\beta)\), then the quadratic equation whose roots are \(\alpha+4\beta\) and \(4\alpha+\beta\), is :
MCQ+4 / -12023
12Straight Lines And Pair Of Straight Lines
The combined equation of the two lines \(ax+by+c=0\) and \(a'x+b'y+c'=0\) can be written as
\((ax+by+c)(a'x+b'y+c')=0\).
The equation of the angle bisectors of the lines represented by the equation \(2x^2+xy-3y^2=0\) is :
\((ax+by+c)(a'x+b'y+c')=0\).
The equation of the angle bisectors of the lines represented by the equation \(2x^2+xy-3y^2=0\) is :
MCQ+4 / -12023
13Straight Lines And Pair Of Straight Lines
If $(\alpha, \beta)$ is the orthocenter of the triangle $\mathrm{ABC}$ with vertices $A(3,-7), B(-1,2)$ and $C(4,5)$, then $9 \alpha-6 \beta+60$ is equal to :
MCQ+4 / -12023
14Straight Lines And Pair Of Straight Lines
Let \((\alpha, \beta)\) be the centroid of the triangle formed by the lines \(15 x-y=82,6 x-5 y=-4\) and \(9 x+4 y=17\). Then \(\alpha+2 \beta\) and \(2 \alpha-\beta\) are the roots of the equation :
MCQ+4 / -12023
15Straight Lines And Pair Of Straight Lines
If the point \(\left(\alpha, \frac{7 \sqrt{3}}{3}\right)\) lies on the curve traced by the mid-points of the line segments of the lines \(x \cos \theta+y \sin \theta=7, \theta \in\left(0, \frac{\pi}{2}\right)\) between the co-ordinates axes...
MCQ+4 / -12023
16Straight Lines And Pair Of Straight Lines
If the line \(l_{1}: 3 y-2 x=3\) is the angular bisector of the lines \(l_{2}: x-y+1=0\) and \(l_{3}: \alpha x+\beta y+17=0\), then \(\alpha^{2}+\beta^{2}-\alpha-\beta\) is equal to _________.
INTEGER+4 / -12023
17Straight Lines And Pair Of Straight Lines
Let the equations of two adjacent sides of a parallelogram \(\mathrm{ABCD}\) be \(2 x-3 y=-23\) and \(5 x+4 y=23\). If the equation of its one diagonal \(\mathrm{AC}\) is \(3 x+7 y=23\) and the distance of A from the other diagonal is $$\ma...
INTEGER+4 / -12023
18Straight Lines And Pair Of Straight Lines
Let \(\alpha\)1, \(\alpha\)2 (\(\alpha\)1 < \(\alpha\)2) be the values of \(\alpha\) fo the points (\(\alpha\), \(-\)3), (2, 0) and (1, \(\alpha\)) to be collinear. Then the equation of the line, passing through (\(\alpha\)1, \(\alpha\)2) a...
MCQ+4 / -12022
19Straight Lines And Pair Of Straight Lines
The distance between the two points A and A' which lie on y = 2 such that both the line segments AB and A' B (where B is the point (2, 3)) subtend angle \({\pi \over 4}\) at the origin, is equal to :
MCQ+4 / -12022
20Straight Lines And Pair Of Straight Lines
The distance of the origin from the centroid of the triangle whose two sides have the equations \(x - 2y + 1 = 0\) and \(2x - y - 1 = 0\) and whose orthocenter is \(\left( {{7 \over 3},{7 \over 3}} \right)\) is :
MCQ+4 / -12022
21Straight Lines And Pair Of Straight Lines
Let the circumcentre of a triangle with vertices A(a, 3), B(b, 5) and C(a, b), ab > 0 be P(1,1). If the line AP intersects the line BC at the point Q\(\left(k_{1}, k_{2}\right)\), then \(k_{1}+k_{2}\) is equal to :
MCQ+4 / -12022
22Straight Lines And Pair Of Straight Lines
Let \(\mathrm{A}(\alpha,-2), \mathrm{B}(\alpha, 6)\) and \(\mathrm{C}\left(\frac{\alpha}{4},-2\right)\) be vertices of a \(\triangle \mathrm{ABC}\). If \(\left(5, \frac{\alpha}{4}\right)\) is the circumcentre of \(\triangle \mathrm{ABC}\), ...
MCQ+4 / -12022
23Straight Lines And Pair Of Straight Lines
Let \(m_{1}, m_{2}\) be the slopes of two adjacent sides of a square of side a such that \(a^{2}+11 a+3\left(m_{1}^{2}+m_{2}^{2}\right)=220\). If one vertex of the square is \((10(\cos \alpha-\sin \alpha), 10(\sin \alpha+\cos \alpha))\), wh...
MCQ+4 / -12022
24Straight Lines And Pair Of Straight Lines
A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ratio 2 : 1. Let the co-ordin...
INTEGER+4 / -12022
25Straight Lines And Pair Of Straight Lines
Let a triangle be bounded by the lines L1 : 2x + 5y = 10; L2 : \(-\)4x + 3y = 12 and the line L3, which passes through the point P(2, 3), intersects L2 at A and L1 at B. If the point P divides the line-segment AB, internally in the ratio 1 ...
MCQ+4 / -12022
26Straight Lines And Pair Of Straight Lines
In an isosceles triangle ABC, the vertex A is (6, 1) and the equation of the base BC is 2x + y = 4. Let the point B lie on the line x + 3y = 7. If (\(\alpha\), \(\beta\)) is the centroid of \(\Delta\)ABC, then 15(\(\alpha\) + \(\beta\)) is ...
MCQ+4 / -12022
27Straight Lines And Pair Of Straight Lines
Let \(A(1,1), B(-4,3), C(-2,-5)\) be vertices of a triangle \(A B C, P\) be a point on side \(B C\), and \(\Delta_{1}\) and \(\Delta_{2}\) be the areas of triangles \(A P B\) and \(A B C\), respectively. If \(\Delta_{1}: \Delta_{2}=4: 7\), ...
MCQ+4 / -12022
28Straight Lines And Pair Of Straight Lines
The equations of the sides \(\mathrm{AB}, \mathrm{BC}\) and CA of a triangle ABC are \(2 x+y=0, x+\mathrm{p} y=39\) and \(x-y=3\) respectively and \(\mathrm{P}(2,3)\) is its circumcentre. Then which of the following is NOT true?
MCQ+4 / -12022
29Straight Lines And Pair Of Straight Lines
Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle. Then the area of \(\Delta\)PQR is :
MCQ+4 / -12022
30Straight Lines And Pair Of Straight Lines
The equations of the sides \(\mathrm{AB}, \mathrm{BC}\) and \(\mathrm{CA}\) of a triangle \(\mathrm{ABC}\) are \(2 x+y=0, x+\mathrm{p} y=15 \mathrm{a}\) and \(x-y=3\) respectively. If its orthocentre is \((2, a),-\frac{1}{2}<\mathrm{a}<2\),...
INTEGER+4 / -12022
31Straight Lines And Pair Of Straight Lines
A point \(P\) moves so that the sum of squares of its distances from the points \((1,2)\) and \((-2,1)\) is 14. Let \(f(x, y)=0\) be the locus of \(\mathrm{P}\), which intersects the \(x\)-axis at the points \(\mathrm{A}\), \(\mathrm{B}\) a...
MCQ+4 / -12022
32Straight Lines And Pair Of Straight Lines
A line, with the slope greater than one, passes through the point \(A(4,3)\) and intersects the line \(x-y-2=0\) at the point B. If the length of the line segment \(A B\) is \(\frac{\sqrt{29}}{3}\), then \(B\) also lies on the line :
MCQ+4 / -12022
33Straight Lines And Pair Of Straight Lines
Let the point \(P(\alpha, \beta)\) be at a unit distance from each of the two lines \(L_{1}: 3 x-4 y+12=0\), and \(L_{2}: 8 x+6 y+11=0\). If \(P\) lies below \(L_{1}\) and above \({ }{L_{2}}\), then \(100(\alpha+\beta)\) is equal to :
MCQ+4 / -12022
34Straight Lines And Pair Of Straight Lines
Let \(A\left( {{3 \over {\sqrt a }},\sqrt a } \right),\,a > 0\), be a fixed point in the xy-plane. The image of A in y-axis be B and the image of B in x-axis be C. If \(D(3\cos \theta ,a\sin \theta )\) is a point in the fourth quadrant such...
INTEGER+4 / -12022
35Straight Lines And Pair Of Straight Lines
Let the area of the triangle with vertices A(1, \(\alpha\)), B(\(\alpha\), 0) and C(0, \(\alpha\)) be 4 sq. units. If the points (\(\alpha\), \(-\)\(\alpha\)), (\(-\)\(\alpha\), \(\alpha\)) and (\(\alpha\)2, \(\beta\)) are collinear, then $...
MCQ+4 / -12022
36Straight Lines And Pair Of Straight Lines
If p and q are the lengths of the perpendiculars from the origin on the lines,x cosec \(\alpha\) \(-\) y sec \(\alpha\) = k cot 2\(\alpha\) andx sin\(\alpha\) + y cos\(\alpha\) = k sin2\(\alpha\)respectively, then k2 is equal to :
MCQ+4 / -12021
37Straight Lines And Pair Of Straight Lines
Let A be the set of all points (\(\alpha\), \(\beta\)) such that the area of triangle formed by the points (5, 6), (3, 2) and (\(\alpha\), \(\beta\)) is 12 square units. Then the least possible length of a line segment joining the origin to...
MCQ+4 / -12021
38Straight Lines And Pair Of Straight Lines
Two sides of a parallelogram are along the lines 4x + 5y = 0 and 7x + 2y = 0. If the equation of one of the diagonals of the parallelogram is 11x + 7y = 9, then other diagonal passes through the point :
MCQ+4 / -12021
39Straight Lines And Pair Of Straight Lines
The point P (a, b) undergoes the following three transformations successively :(a) reflection about the line y = x.(b) translation through 2 units along the positive direction of x-axis.(c) rotation through angle \({\pi \over 4}\) about th...
MCQ+4 / -12021
40Straight Lines And Pair Of Straight Lines
Let A be a fixed point (0, 6) and B be a moving point (2t, 0). Let M be the mid-point of AB and the perpendicular bisector of AB meets the y-axis at C. The locus of the mid-point P of MC is :
MCQ+4 / -12021
41Straight Lines And Pair Of Straight Lines
The intersection of three lines x \(-\) y = 0, x + 2y = 3 and 2x + y = 6 is a :
MCQ+4 / -12021
42Straight Lines And Pair Of Straight Lines
Let ABC be a triangle with A(\(-\)3, 1) and \(\angle\)ACB = \(\theta\), 0 < \(\theta\) < \({\pi \over 2}\). If the equation of the median through B is 2x + y \(-\) 3 = 0 and the equation of angle bisector of C is 7x \(-\) 4y \(-\) 1 = 0, t...
MCQ+4 / -12021
43Straight Lines And Pair Of Straight Lines
Let the equation of the pair of lines, y = px and y = qx, can be written as (y \(-\) px) (y \(-\) qx) = 0. Then the equation of the pair of the angle bisectors of the lines x2 \(-\) 4xy \(-\) 5y2 = 0 is :
MCQ+4 / -12021
44Straight Lines And Pair Of Straight Lines
The image of the point (3, 5) in the line x \(-\) y + 1 = 0, lies on :
MCQ+4 / -12021
45Straight Lines And Pair Of Straight Lines
A man is walking on a straight line. The arithmetic mean
of the reciprocals of the intercepts of this line on the
coordinate axes is \({1 \over 4}\). Three stones A, B and C are placed at the points
(1, 1), (2, 2) and (4, 4) respectively. T...
of the reciprocals of the intercepts of this line on the
coordinate axes is \({1 \over 4}\). Three stones A, B and C are placed at the points
(1, 1), (2, 2) and (4, 4) respectively. T...
MCQ+4 / -12021
46Straight Lines And Pair Of Straight Lines
Consider a triangle having vertices A(\(-\)2, 3), B(1, 9) and C(3, 8). If a line L passing through the circum-centre of triangle ABC, bisects line BC, and intersects y-axis at point \(\left( {0,{\alpha \over 2}} \right)\), then the value o...
INTEGER+4 / -12021
47Straight Lines And Pair Of Straight Lines
A man starts walking from the point P(\(-\)3, 4), touches the x-axis at R, and then turns to reach at the point Q(0, 2). The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then $$50\left( {{{(PR)}^2}...
INTEGER+4 / -12021
48Straight Lines And Pair Of Straight Lines
Let the points of intersections of the lines x \(-\) y + 1 = 0, x \(-\) 2y + 3 = 0 and 2x \(-\) 5y + 11 = 0 are the mid points of the sides of a triangle \(\Delta\)ABC. Then, the area of the \(\Delta\)ABC is _____________.
INTEGER+4 / -12021
49Straight Lines And Pair Of Straight Lines
A square ABCD has all its vertices on the curve x2y2 = 1. The midpoints of its sides also lie on the same curve. Then, the square of area of ABCD is _________.
INTEGER+4 / -12021
50Straight Lines And Pair Of Straight Lines
The number of integral values of m so that the abscissa of point of intersection of lines 3x + 4y = 9 and y = mx + 1 is also an integer, is :
MCQ+4 / -12021