Straight Lines and Pair of Straight Lines · Mathematics · MHT CET

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MCQ (Single Correct Answer)

1

The joint equation of the bisectors of the angles between the lines $x=5$ and $y=3$ is

MHT CET 2025 21st April Morning Shift
2

If the line $2 x+y=\mathrm{k}$ passes though the point which divides the line segment joining the points $(1,1)$ and $(2,4)$ internally in the ratio $3: 2$ then, $(k+1):(k-1)=$

MHT CET 2025 21st April Morning Shift
3

If the equation of the median through vertex $\mathrm{A}(3, \mathrm{k})$ of $\triangle \mathrm{ABC}$ with vertices $\mathrm{B}(2,1)$ and $\mathrm{C}(-4,5)$ is $x+4 y=\mathrm{p}$, then $\mathrm{k}=$ where p and k are constants

MHT CET 2025 20th April Evening Shift
4

If the equation $\mathrm{k} x y+10 x+8 y+16=0$ represents a pair of lines, then

MHT CET 2025 20th April Evening Shift
5

The acute angle between the diagonals of a parallelogram whose vertices are $\mathrm{A}(2,-1)$, $B(0,2), C(2,3)$ and $D(4,0)$ is

MHT CET 2025 20th April Morning Shift
6

The distance between the lines represented by the equation $4 x^2+4 x y+y^2-6 x-3 y-4=0$ is

MHT CET 2025 20th April Morning Shift
7

A straight line through the origin $O$ meets the line $3 y=10-4 x$ and $8 x+6 y+5=0$ at the points $A$ and B respectively. Then O divides the segment $A B$ in the ratio

MHT CET 2025 19th April Evening Shift
8
The perpendicular distance between the lines given by $(x-2 y+1)^2+\mathrm{k}(x-2 y+1)=0$ is $\sqrt{5}$, then $\mathrm{k}=$
MHT CET 2025 19th April Evening Shift
9
The point of intersection of the diagonals of the rectangle whose sides are contained in the lines $x=8, x=10, y=11$ and $y=12$ is
MHT CET 2025 19th April Morning Shift
10
If $m_1$ and $m_2$ are the slopes of the lines represented by $a x^2+2 h x y+b y^2=0$ satisfying the condition $16 \mathrm{~h}^2=25 \mathrm{ab}$, then ............ .
MHT CET 2025 19th April Morning Shift
11

The co-ordinates of the foot of perpendicular, drawn from the point $(-2,3)$ on the line $3 x-y-1=0$ are

MHT CET 2024 16th May Evening Shift
12

If $P_1$ and $P_2$ are perpendicular distances (in units) from point $(2,-1)$ to the pair of lines $2 x^2-5 x y+2 y^2=0$, then the value of $\mathrm{P}_1 \mathrm{P}_2$ is

MHT CET 2024 16th May Evening Shift
13

If $\frac{x^2}{\mathrm{a}}+\frac{2 x y}{\mathrm{~h}}+\frac{y^2}{\mathrm{~b}}=0$ represents a pair of straight lines and slope of one of the lines is twice that of the other, then $a b: h^2$ is

MHT CET 2024 16th May Morning Shift
14

Suppose that the points $(h, k),(1,2)$ and $(-3,4)$ lie on the line $l_1$. If a line $l_2$ passing through the points $(h, k)$ and $(4,3)$ is perpendicular to $l_1$, then $\left(\frac{k}{h}\right)$ equals

MHT CET 2024 16th May Morning Shift
15

If one of the lines represented by $a x^2+2 h x y+b y^2=0$ is perpendicular to $\mathrm{m} x+\mathrm{n} y=18$, then

MHT CET 2024 15th May Evening Shift
16

If two sides of a square are $4 x+3 y-20=0$ and $4 x+3 y+15=0$, then the area of the square is

MHT CET 2024 15th May Morning Shift
17

The value of $k$, if the slope of one of the lines given by $4 x^2+k x y+y^2=0$ is four times that of the other, is given by

MHT CET 2024 15th May Morning Shift
18

The joint equation of pair of lines through the origin, each of which makes an angle of $30^{\circ}$ with Y -axis, is

MHT CET 2024 11th May Evening Shift
19

A straight line L through the point $(3,-2)$ is inclined at an angle of $60^{\circ}$ to the line $\sqrt{3} x+y=1$. If L also intersects the X -axis, then the equation of $L$ is

MHT CET 2024 11th May Evening Shift
20

The joint equation of two lines through the origin, each making an angle with measure of $30^{\circ}$ with the positive Y -axis, is

MHT CET 2024 11th May Morning Shift
21

If the slope of one of the lines given by $\mathrm{K} x^2+6 x y+y^2=0$ is three times the order, then the value of $K$ is

MHT CET 2024 11th May Morning Shift
22

Let $\mathrm{P} \equiv(-5,0), \mathrm{Q} \equiv(0,0)$ and $\mathrm{R} \equiv(2,2 \sqrt{3})$ be three points. Then the equation of the bisector of the angle $P Q R$ is

MHT CET 2024 11th May Morning Shift
23

If the length of the perpendicular to a line from the origin is $2 \sqrt{2}$ units, which makes an angle of $135^{\circ}$ with the X -axis, then the equation of line is

MHT CET 2024 10th May Evening Shift
24

The number of integer values of $m$, for which $x$-coordinate of the point of intersection of the lines $3 x+4 y=9$ and $y=m x+1$ is also an integer, is

MHT CET 2024 10th May Evening Shift
25

Let a line intersect the co-ordinate axes in points $A$ and $B$ such that the area of the triangle $O A B$ is 12 sq. units. If the line passes through the point $(2,3)$, then the equation of the line is

MHT CET 2024 10th May Morning Shift
26

$\triangle \mathrm{OAB}$ is formed by the lines $x^2-4 x y+y^2=0$ and the line $A B$. The equation of line $A B$ is $2 x+3 y-1=0$. Then the equation of the median of the triangle drawn from the origin is

MHT CET 2024 10th May Morning Shift
27

The joint equation of pair of lines through the origin and making an angle of $\frac{\pi}{6}$ with the line $3 x+y-6=0$ is

MHT CET 2024 9th May Evening Shift
28

A line $4 x+y=1$ passes through the point $\mathrm{A}(2,-7)$ meets the line BC whose equation is $3 x-4 y+1=0$ at the point $B$. The equation of the line $A C$ so that $A B=A C$ is

MHT CET 2024 9th May Evening Shift
29

If an equation $h x y+g x+f y+c=0$ represents a pair of lines, then

MHT CET 2024 9th May Morning Shift
30

The straight line, $2 x-3 y+17=0$ is perpendicular to the line passing through the points $(7,17)$ and $(15, \beta)$, then $\beta$ equals

MHT CET 2024 9th May Morning Shift
31

If $\mathrm{O}(0,0), \mathrm{A}(1,2)$ and $\mathrm{B}(3,4)$ are the vertices of triangle OAB , then the joint equation of the altitude and median drawn from O is

MHT CET 2024 4th May Evening Shift
32

The combined equation of two lines through the origin and making an angle of $45^{\circ}$ with the line $3 x+y=0$, is

MHT CET 2024 4th May Evening Shift
33

The acute angle between the lines $x \cos 30^{\circ}+y \sin 30^{\circ}=3$ and $x \cos 60^{\circ}+y \sin 60^{\circ}=5$ is

MHT CET 2024 4th May Evening Shift
34

If $4 a b=3 h^2$, then the ratio of the slope of lines represented by $a x^2+2 \mathrm{~h} x y+\mathrm{b} y^2=0$ is

MHT CET 2024 4th May Morning Shift
35

The line L given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line K is parallel to line L and has the equation $\frac{x}{c}+\frac{y}{3}=1$. Then the distance between L and K is _________ units.

MHT CET 2024 4th May Morning Shift
36

The equation of the line passing through the point of intersection of the lines $3 x-y=5$ and $x+3 y=1$ and making equal intercepts on the axes is

MHT CET 2024 3rd May Evening Shift
37

The equation of 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 lines $x^2-4 x y-5 y^2=0$ is

MHT CET 2024 3rd May Evening Shift
38

The number of possible distinct straight lines passing through $(2,3)$ and forming a triangle with co-ordinate axes whose area is 12 sq . units are,

MHT CET 2024 3rd May Morning Shift
39

The line L given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line K is parallel to L and has the equation $\frac{x}{c}+\frac{y}{3}=1$. Then the distance between $L$ and $K$ is

MHT CET 2024 3rd May Morning Shift
40

The diagonals of a parallelogram $A B C D$ are along the lines $x+3 y=4$ and $6 x-2 y=7$. Then ABCD must be a

MHT CET 2024 2nd May Evening Shift
41

If the equation $7 x^2-14 x y+p y^2-12 x+q y-4=0$ represents a pair of parallel lines then the value of $\sqrt{p^2+q^2-p q}$ is

MHT CET 2024 2nd May Evening Shift
42

The slopes of the lines given by $x^2+2 h x y+2 y^2=0$ are in the ratio $1: 2$, then $h$ is

MHT CET 2024 2nd May Morning Shift
43

If two lines $x+(a-1) y=1 \quad$ and $2 x+a^2 y=1(a \in R-\{0,1\})$ are perpendicular, then the distance of their point of intersection from the origin is

MHT CET 2024 2nd May Morning Shift
44

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

MHT CET 2023 14th May Evening Shift
45

The centroid of the triangle formed by the lines $$x+3 y=10$$ and $$6 x^2+x y-y^2=0$$ is

MHT CET 2023 14th May Evening Shift
46

$$\mathrm{p}$$ 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

MHT CET 2023 14th May Morning Shift
47

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 origin, then their joint equation is

MHT CET 2023 14th May Morning Shift
48

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

MHT CET 2023 13th May Evening Shift
49

$$P S$$ 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

MHT CET 2023 13th May Evening Shift
50

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

MHT CET 2023 13th May Morning Shift
51

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

MHT CET 2023 13th May Morning Shift
52

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 least, then the slope of the line $$\mathrm{PQ}$$ is

MHT CET 2023 13th May Morning Shift
53

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

MHT CET 2023 12th May Evening Shift
54

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

MHT CET 2023 12th May Evening Shift
55

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

MHT CET 2023 12th May Morning Shift
56

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

MHT CET 2023 12th May Morning Shift
57

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

MHT CET 2023 11th May Evening Shift
58

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

MHT CET 2023 11th May Morning Shift
59

$$\mathrm{a}$$ 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

MHT CET 2023 11th May Morning Shift
60

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

MHT CET 2023 10th May Evening Shift
61

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

MHT CET 2023 10th May Evening Shift
62

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

MHT CET 2023 10th May Morning Shift
63

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

MHT CET 2023 10th May Morning Shift
64

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

MHT CET 2023 9th May Evening Shift
65

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

MHT CET 2023 9th May Evening Shift
66

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 $$\lambda^2=$$

MHT CET 2023 9th May Morning Shift
67

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

MHT CET 2023 9th May Morning Shift
68

The joint equation of pair of lines through the origin and making an equilateral triangle with the line $$y = 5$$ is

MHT CET 2022 11th August Evening Shift
69

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

MHT CET 2022 11th August Evening Shift
70

If the polar co-ordinates of a point are $$\left(2, \frac{\pi^{\mathrm{c}}}{4}\right)$$, then its Cartesian co-ordinates are

MHT CET 2021 24th September Evening Shift
71

The acute angle between the lines $$\left(x^2+y^2\right) \sin \theta+2 x y=0$$ is

MHT CET 2021 24th September Evening Shift
72

If the lines represented by $$(k^2+2) x^2+3 x y-6 y^2=0$$ are perpendicular to each other, then the values of $$\mathrm{K}$$ are

MHT CET 2021 24th September Evening Shift
73

The equation of a line with slope $$-\frac{1}{\sqrt{2}}$$ and makes an intercept of $$2 \sqrt{2}$$ units on negative direction of $$y$$-axis is

MHT CET 2021 24th September Evening Shift
74

If the lines respresented by $$a x^2-b x y-y^2=0$$ make angle $$\alpha$$ and $$\beta$$ with the positive direction of $$\mathrm{X}$$-axis, then $$\tan (\alpha+\beta)=$$

MHT CET 2021 24th September Morning Shift
75

If the angle between the lines is $$\frac{\pi^{\mathrm{C}}}{4}$$ and slope of one of the lines is $$\frac{1}{2}$$, then slope of the other line is

MHT CET 2021 24th September Morning Shift
76

If one of the lines given by $$k x^2+x y-y^2=0$$ bisect the angle between the co-ordinate axes then the values of $$k$$ are

MHT CET 2021 24th September Morning Shift
77

The joint equation of pair of lines through the origin and having slopes $$(1+\sqrt{2})$$ and $$\frac{1}{(1+\sqrt{2})}$$ is

MHT CET 2021 23rd September Evening Shift
78

If $$4 a b=3 h^2$$, then the ratio of slopes of the lines represented by $$a x^2+2 h x y+b y^2=0$$ is

MHT CET 2021 23rd September Evening Shift
79

The distance between the lines $$3 x+4 y=9$$ and $$6 x+8 y=15$$ is

MHT CET 2021 23rd September Evening Shift
80

If the slopes of the lines given by the equation $$a x^2+2 h x y+b y^2=0$$ are in the ratio $$5: 3$$, then the ratio $$h^2: a b=$$

MHT CET 2021 23rd September Evening Shift
81

The equation of line, where length of the perpendicular segment from origin to the line is 4 and the inclination of this perpendicular segment with the positive direction of X-axis is 30$$^\circ$$, is

MHT CET 2021 23th September Morning Shift
82

If two lines represented by $$a x^2+2 h x y+b y^2=0$$ makes angles $$\alpha$$ and $$\beta$$ with positive direction of $$\mathrm{X}$$-axis, then $$\tan (\alpha+\beta)=$$

MHT CET 2021 23th September Morning Shift
83

The combined equation of a pair of lines passing through the origin and inclined at $$60^{\circ}$$ and $$30=$$ respectively with $$x$$-axis is

MHT CET 2021 23th September Morning Shift
84

If the sum of slopes of lines represented by $$\mathrm{ax^2+8xy+5y^2=0}$$ is twice their product, then a =

MHT CET 2021 22th September Evening Shift
85

If the line joining two points $$\mathrm{A}(2,0)$$ and $$\mathrm{B}(3,1)$$ is rotated about $$\mathrm{A}$$ in anticlockwise direction through an angle of $$15^{\circ}$$, then the equation of the line in new position is

MHT CET 2021 22th September Evening Shift
86

If lines represented by the equation $$\mathrm{px}^2-\mathrm{qy^{2 }}=0$$ are distinct, then

MHT CET 2021 22th September Evening Shift
87

If slope of one of the lines ax$$^2$$ + 2hxy + by$$^2$$ = 0 is twice that of the other, then h$$^2$$ : ab is

MHT CET 2021 22th September Morning Shift
88

Area of the triangle formed by the lines $$y^2-9 x y+18 x^2=0$$ and $$y=9$$ is

MHT CET 2021 22th September Morning Shift
89

The equation of perpendicular bisector of the line segment joining $$A(-2,3)$$ and $$B(6,-5)$$ is

MHT CET 2021 22th September Morning Shift
90

If $$\mathrm{(m+3 n)(3 m+n)=4 h^2}$$, then the acute angle between the lines represented by $$\mathrm{m x^2+2 h x y+n y^2=0}$$ is

MHT CET 2021 21th September Evening Shift
91

If $$\mathrm{p}$$ is the length of the perpendicular from origin to the line whose intercepts on the axes are a and $$b$$, then $$\frac{1}{a^2}+\frac{1}{b^2}=$$

MHT CET 2021 21th September Evening Shift
92

If the lines $$x^2-4xy+y^2=0$$ make angles $$\alpha$$ and $$\beta$$ with positive direction X-axis, then $$\cot^2\alpha+\cot^2\beta=$$

MHT CET 2021 21th September Evening Shift
93

If the two lines given by $$a x^2+2 h x y+b y^2=0$$ make inclinations $$\propto$$ and $$\beta$$, then $$\tan (\alpha+\beta)=$$

MHT CET 2021 21th September Morning Shift
94

If the polar co-ordinates of a point are $$\left(\sqrt{2}, \frac{\pi}{4}\right)$$, then its Cartesian co-ordinates are

MHT CET 2021 21th September Morning Shift
95

The equation of a line passing through $$(\mathrm{p} \cos \propto, \mathrm{p} \sin \propto)$$ ) and making an angle $$(90+\propto)$$ with positive direction of $$\mathrm{X}$$-axis is

MHT CET 2021 21th September Morning Shift
96

The product of the perpendicular distances from $$(2,-1)$$ to the pair of lines $$2 x^2-5 x y+2 y^2=0$$ is

MHT CET 2021 21th September Morning Shift
97

The x-intercept of a line passing through the points $$\left(\frac{-1}{2}, 1\right)$$ and (1, 2) is :

MHT CET 2021 20th September Evening Shift
98

If the equation $$3x^2-kxy-3y^2=0$$ represents the bisectors of angles between the lines $$x^2-3xy-4y^2=0$$, then value of k is

MHT CET 2021 20th September Evening Shift
99

The joint equation of pair of lines through the origin and making an equilateral triangle with the line $$y=3$$ is

MHT CET 2021 20th September Evening Shift
100

If the acute angle between the lines given by $$\mathrm{a x^2+2 h x y+b y^2=0}$$ is $$\frac{\pi}{4}$$, then $$\mathrm{4 h^2=}$$

MHT CET 2021 20th September Morning Shift
101

The joint equation of the pair of lines through the origin and making an equilateral triangle with the line $$x=3$$ is

MHT CET 2021 20th September Morning Shift
102

The slope of the line through the origin which makes an angle of 30$$^\circ$$ with the positive direction of Y-axis measured anticlockwise is :

MHT CET 2021 20th September Morning Shift
103

If the slopes of the lines given by the equation $a x^2+2 h x y+b y^2=0$ are in the ratio $5: 3$, then the ratio $h^2: a b=$

MHT CET 2020 19th October Evening Shift
104

The equation of a line passing through the point $(7,-4)$ and perpendicular to the line passing through the points $(2,3)$ and $(1,-2)$ is

MHT CET 2020 19th October Evening Shift
105

If the equation $3 x^2+10 x y+3 y^2+16 y+k=0$ represents a pair of lines, then the value of kis

MHT CET 2020 19th October Evening Shift
106

If the equation $$a x^2+2 h x y+b y^2+2 g x+2 f y=0$$ has one line as the bisector of the angle between co-ordinate axes, then

MHT CET 2020 16th October Evening Shift
107

The straight lines represented by the equation $$9 x^2-12 x y+4 y^2=0$$ are

MHT CET 2020 16th October Evening Shift
108

If the equation $$k x y+5 x+3 y+2=0$$ represents a pair of lines, then $$k=$$

MHT CET 2020 16th October Morning Shift
109

If $$(a,-2 a), a>0$$ is the mid-point of a line segment intercepted between the co-ordinate axes, then the equation of the line is

MHT CET 2020 16th October Morning Shift
110

If the angle between the lines given by the equation $$x^2-3 x y+\lambda y^2+3 x-5 y+2=0, \lambda \geq 0$$, is $$\tan ^{-1}\left(\frac{1}{3}\right)$$, then $$\lambda=$$

MHT CET 2020 16th October Morning Shift
111

The joint equation of lines passing through origin and having slopes $(1+\sqrt{2})$ and $\frac{-1}{1+\sqrt{2}}$ is ..........

MHT CET 2019 3rd May Morning Shift
112

The polar co-ordinates of $P$ are $\left(2, \frac{\pi}{6}\right)$. If $Q$ is the image of $P$ about the $X$-axis then the polar co-ordinates of $Q$ are.....̣...

MHT CET 2019 3rd May Morning Shift
113

The acute angle between lines $x-3=0$ and $x+y=19$ is.......

MHT CET 2019 3rd May Morning Shift
114

If sum of the slopes of the lines given by $x^2-4 p x y+8 y^2=0$ is three times their product then $p=$ ...........

MHT CET 2019 3rd May Morning Shift
115

If lines represented by $$\left(1+\sin ^2 \theta\right) x^2+2 h x y+2 \sin \theta y^2=0, \theta \in[0,2 \pi]$$ are perpendicular to each other then $\theta=$ ...........

MHT CET 2019 2nd May Evening Shift
116

If $(-\sqrt{2}, \sqrt{2})$ are cartesian co-ordinates of the point, then its polar co-ordinates are .........

MHT CET 2019 2nd May Evening Shift
117

The $y$-intercept of the line passing through $A(6,1)$ and perpendicular to the line $x-2 y=4$ is ...........

MHT CET 2019 2nd May Evening Shift
118
 

The joint equation of pair of straight lines passing through origin and having slopes $(1+\sqrt{2})$ and $\left(\frac{1}{1+\sqrt{2}}\right)$ is .......

MHT CET 2019 2nd May Morning Shift
119

The joint equation of the lines passing through the origin and trisecting the first quadrant is

MHT CET 2019 2nd May Morning Shift
120

If $P(2,2), Q(-2,4)$ and $R(3,4)$ are the vertices of $\triangle P Q R$ then the equation of the median through vertex $R$ is ......

MHT CET 2019 2nd May Morning Shift
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