JEE Main Mathematics - Straight Lines
Exam Duration: 60 Mins Total Questions : 30
Find the equation of line, which is parallel to y-axis and at a distance of 3 units from left of the origin is
- (a)
x = 3
- (b)
y = -3
- (c)
x = -3
- (d)
y - 3
The points (-a, -b), (0,0), (a, b) and (a2, ab) are
- (a)
Collinear
- (b)
Vertices of a rectangle
- (c)
Vertices of a parallelogram
- (d)
None of these
Find the equation of the line through (-2,3)with slope -4
- (a)
y - x + 2 = 0
- (b)
2x + 3y - 1 = 0
- (c)
3y + 4x + 5 = 0
- (d)
4x + y + 5 = 0
if a straight line passes through the points \(\left( \frac { -1 }{ 2 } ,1 \right) \) and (1,2) then its x - intercept is
- (a)
-2
- (b)
-1
- (c)
2
- (d)
1
Equation of the line passing through (2,2\(\sqrt { 3 } \) ) nad inclined with x - axis an angle of 750 is
- (a)
(2 + \(\sqrt { 3 } \)) x - y - 4 = 0
- (b)
(2 - \(\sqrt { 3 } \)) x - y - 4 = 0
- (c)
(2 - \(\sqrt { 3 } \)) x + y -4 =0
- (d)
None of these
Distance between the line 5x+12y-1=0 and 10x+24y+k=0 is 2 units, then value of k is
- (a)
50
- (b)
-54
- (c)
49
- (d)
Both (a) and (b)
Find the equation of the line passing through the point (-4,5) and the point of intersection of the lines 4x-3y+7=0 and 2x+3y+5=0.
- (a)
7x-8y+16=0
- (b)
7x+8y-16=0
- (c)
8x-3y-17=0
- (d)
8x+3y+17=0
The slopes of the line which makes an angles 450 with the lines 3x - y = -5 are
- (a)
1, - 1
- (b)
\(\frac { 1 }{ 2 } ,-1\)
- (c)
1, \(\frac { 1 }{ 2 } \)
- (d)
-2, \(\frac { 1 }{ 2 } \)
The angle between the lines 2x + 11y - 7 = 0 and x + 3y + 5 = 0 is equal to
- (a)
tan -1 \(\left( \frac { 17 }{ 13 } \right) \)
- (b)
tan -1\(\left( \frac { 11 }{ 35 } \right) \)
- (c)
tan -1 \(\left( \frac { 1 }{ 7 } \right) \)
- (d)
tan -1 \(\left( \frac { 33 }{ 35 } \right) \)
Find the equation of the straight line passing through (1,2) and perpendicular to the line x +y + 7 = 0
- (a)
x + y + 1 = 0
- (b)
x + y - 1 = 0
- (c)
x - y - 1 = 0
- (d)
x - y + 1 = 0
Find the new coordinates of the point (1,1)if the origin is shifted to the point (-3,-2)by a translation of axes.
- (a)
(4,3)
- (b)
(3,3)
- (c)
(5,3)
- (d)
(5,4)
A line cutting off intercept -3 from the y-axis and the tangent of angle to the x- axis is \({3\over5}\),its equation is
- (a)
5y-3x+15=0
- (b)
3y-5x+15=0
- (c)
5y-3x-15=0
- (d)
None of these
The equation of the straight line passing through the point(3,2) and perpendicular to the line y=x is
- (a)
x-y=5
- (b)
x+y=5
- (c)
x+y=1
- (d)
x-y=1
Equation of the line passing througgh (1,2) and parallel to the line y=3x-1 is
- (a)
y+2=x+1
- (b)
y+2=3(x+1)
- (c)
y-2=3(x-1)
- (d)
y-2=x-1
A point equidistant from the line 4x+3y+10=0, 5x-12y+26=0 and 7x+24y-50=0 is
- (a)
(1,-1)
- (b)
(1,1)
- (c)
(0,0)
- (d)
(0,1)
A line passes (2,2) and is perpendicular to the line 3x+y=3. Its y-intercept is
- (a)
\(1\over3\)
- (b)
\(2\over3\)
- (c)
1
- (d)
\(4\over3\)
The ratio in which the line 3x+4y+2=0 divides the distance between the line 3x+4y+5=0 and 3x+4y-5=0 is
- (a)
1:2
- (b)
3:7
- (c)
2:3
- (d)
2:5
If the line \({x\over a}+{y\over b}=1\) passes through the points (2,-3) and (4,-5), then (a,b) is
- (a)
(1,1)
- (b)
(-1,1)
- (c)
(1,-1)
- (d)
(-1,-1)
The equation of the line passing through (5,3) and perpendicular to 2x + y - 7 = 0 is
- (a)
2x - x + 1 = 0
- (b)
2y - x - 1 = 0
- (c)
2y - x + 2 = 0
- (d)
2y - x - 2 =0
Match the following
The value of λ, if the lines (2x + 3y + 4) + λ(6x -y + 12) = 0
Column I | Column II |
(i) parallel to y-axis is | (p) \(\lambda =-\frac { 3 }{ 4 } \quad \) |
(ii) perpendicular to 7x + y - 4 = 0 | (q) \(\lambda =-\frac { 1 }{ 3 } \) |
(iii) passes through (1, 2) is | (r) \(\lambda =-\frac { 17 }{ 41 } \) |
(iv) parallel to x-axis | (s) λ = 3 |
- (a)
(i) ➝ (s), (ii) ➝ (r), (iii) ⟶ (p), (iv) ➝ (q)
- (b)
(i) ➝ (r), (ii) ⟶ (s), (iii) ⟶ (p), (iv) ➝ (q)
- (c)
(i) ➝ (s), (ii) ➝ (r), (iii) ➝ (q), (iv) ➝ (p)
- (d)
(i) ➝ (p), (ii) ➝ (r), (iii) ⇾ (q), (iv) ⟶ (s)
Find the equation of the line perpendiucular to the line x - 2y + 3 = 0 and passing through the point (1, - 2)
- (a)
2x + y = 0
- (b)
y - 2x = 0
- (c)
x - 2y = 0
- (d)
None of these
A line passing through (2, 2) is perpendicular to the line 3x + y = 3, Its x - intercept is given by
- (a)
\(\frac { 4 }{ 3 } \)
- (b)
\(-\frac { 4 }{ 3 } \)
- (c)
-4
- (d)
4
Fill in the blanks.
(i) If a,b,c are in A.P., then the straight line ax+by+c=0 will always pass through P.
(ii) One of the points on the y-axis whose distance from the line\({x\over 3}+{y\over4}=1\) is 4 units is Q.
(iii) The points (3,4) and (2,-6) are situated on the R side of the line 3x-4y-8=0.
(iv) The equation of a line drawn perpendicular to the line \({x\over 4}+{y\over6}=1\)through the point (0,6), is S.
- (a)
P Q R S (2,1) \((0,{-32\over 3})\) opposite 3x+2y+16=0 - (b)
P Q R S (1,-2) \((0,{8\over 3})\) opposite 2x-3y+18=0 - (c)
P Q R S (2,-1) \((0,{8\over 3})\) same 3x+2y+16=0 - (d)
P Q R S (1,-2) \((0,{-32\over 3})\) opposite 2x-3y+18=0
Select the INCORRECT statement.
- (a)
The straight line 5x+4y=0 passes through the point of intersection of the straight lines x+2y-10=0 and 2x+y+5=0.
- (b)
The distance of the point (-1,1) from the line 12(x+6)=5(y-2) is 4 units.
- (c)
The equation of the line through the intersection of the lines 2x-3y=0 and 4x-5y=2 and through the point (2,1) is x-y-1=0.
- (d)
A line passes through (2,2) and is perpendicular to the line 3x+y=3. Its x-intercept is -4.
if the line px - qy = r intersects the coordinates exes at (a, 0) and (0, b), then value of a + b is equal to
- (a)
\(\left( \frac { q+p }{ pq } \right) \)
- (b)
\(\left( \frac { q-p }{ pq } \right) \)
- (c)
\(\left( \frac { p-q }{ pq } \right) \)
- (d)
\(\left( \frac { p+q }{ p-q } \right) \)
Find the distance of the point(3, -5) from the line 3x-4y-26=0
- (a)
\(\frac{2}{5}\)units
- (b)
4 units
- (c)
\(\frac{3}{5}\)units
- (d)
6 units
The distance of the poinr P(1, -3) from the line
- (a)
13 units
- (b)
\(\frac{7}{13} \sqrt{13}\) units
- (c)
\(\sqrt{13}\) units
- (d)
13\(\sqrt{7}\) units
A point equidistant from the lines \(\sqrt{3}\)x+y+4=0, \(\sqrt{13}\)x+6y+14=0 and 7x+24y-50=0 is
- (a)
(1, -1)
- (b)
(1, 1)
- (c)
(0, 0)
- (d)
(0,1)
Find the equation of the line parallel to the line 3x - 4y + 2 = 0 and passing through the point (-2,3)
- (a)
3x - 4y + 18 = 0
- (b)
3x + 4y + 18 = 0
- (c)
3x - 4y - 18 = 0
- (d)
None of these
The lines a1x + b1y + c1 = 0, a2x + b2y + C2 = 0 and a3x = 0 are concurrent if b1c1 - b2c1 is equal to
- (a)
10
- (b)
1
- (c)
0
- (d)
-1