Mathematics - Straight Lines
Exam Duration: 45 Mins Total Questions : 30
Passing through the points (3,2) and (7,2)
- (a)
0
- (b)
1
- (c)
2
- (d)
None of three
If the slope the line joining the points (3,4) and (-2,a) is equal to \(-\frac { 2 }{ 5 } \), then the value of a is equal to
- (a)
6
- (b)
4
- (c)
3
- (d)
2
The line through the points (-2,6) and (4,8) is perpendicular to the line through the points (8,12) and (x,24), find the value of x
- (a)
1
- (b)
2
- (c)
3
- (d)
4
Find the angle between the x-axis and the line joining the points (3,-1) and (4,-2)
- (a)
1300
- (b)
1350
- (c)
1500
- (d)
None of these
The points \(\left( 0,\frac { 8 }{ 3 } \right) \) , (1,3) and (82,30) are vertices of a/an
- (a)
obyuse angled triangle
- (b)
actute angled triangled
- (c)
right angled triangle
- (d)
none of these
If the points (-2,0) (-1,1,\(\sqrt { 3 } \)) and (cos \(\theta\), sin \(\theta\)) are collinerar , then the number of values of \(\theta\) \(\epsilon \) [0,2 \(\pi\)] is
- (a)
0
- (b)
11
- (c)
2
- (d)
None of these
If the points (k, 3), (2, k), (-k,3) are collinear then the values k are
- (a)
2,3
- (b)
0,3
- (c)
1,0
- (d)
1,2
If p is the length of perpendicular from origin to the line whose intercepts on the axes are a and b, then\({1\over a^2}+{1\over b^2}\) is equal to
- (a)
p2
- (b)
\({1\over p^2}\)
- (c)
2p2
- (d)
\({1\over 2p^2}\)
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
Find the equation of a line which passes through the point (2,3) and makes an abgles of 300 with the postive direction of x -axis
- (a)
\(x-\sqrt { 3 } y+(3-\sqrt { 3 } -2)=0\)
- (b)
\(x+\sqrt { 3 } y+\left( 3\sqrt { 3 } -2 \right) =0\)
- (c)
\(x-\sqrt { 3 } y=0\)
- (d)
\(x+\sqrt { 3 } y=0\)
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
Find the distance between the line 3x+4y=9 and 6x+8y=15.
- (a)
3 units
- (b)
0.3 units
- (c)
5 units
- (d)
0.5 units
If lx+ ly + p=0 and lx + ly-r=0 are two parallel lines, then distance between them is equal to\(|{m\over n}|\), where m and n respectively are
- (a)
p-r, \(\sqrt{2}l\)
- (b)
r-p, \(\sqrt{2}l\)
- (c)
p+r, \(\sqrt{2}l\)
- (d)
p+r, \(\sqrt{2}l\)
Find the equation of the line, which make intercepts -3 and 2 on the x and y axes respectively
- (a)
x - y - 6 = 0
- (b)
x + y -1 = 0
- (c)
2x - y +6 = 0
- (d)
2x - 3y + 6 = 0
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 a straight line passing through the point of intersection of the lines 3x+4y-7=0 and x=y-2, and slope 5.
- (a)
35x-7y+18=0
- (b)
33x-7y+18=0
- (c)
35x-8y+18=0
- (d)
35x-7y+20=0
Obtain the equation of the line passing through the intersection of the lines 2x-3y+4=0 and 3x+4y=5, and drawn parallel to y-axis.
- (a)
20x+1=0
- (b)
17x+1=0
- (c)
10x+1=0
- (d)
2x+1=0
Find the transformed equation of the straight line xy-x-y+1=0, when the origin is shifted to the point (1,1) after translation of axes.
- (a)
xy=5
- (b)
xy=2
- (c)
xy=0
- (d)
xy=8
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
The point (4,1)undergoes the following two successive transformations:
(i) Reflection about the line y=x.
(ii) Translation through a distance of 2 units along the positive x-axis.
Then the final coordinates of the point are
- (a)
(4,3)
- (b)
(3,4)
- (c)
(1,4)
- (d)
\(({7\over2},{7\over2})\)
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 tanget of angle between the lines whose intercepts on the axes are a,-b and b, -a respectively, is
- (a)
\({a^2-b^2\over ab}\)
- (b)
\({b^2-a^2\over2}\)
- (c)
\({b^2-a^2\over2ab}\)
- (d)
None of these
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
The reflection of the point (4, - 13) about the line 5x +y + 6 = 0 is
- (a)
(-1,-14)
- (b)
(3,4)
- (c)
(0,0)
- (d)
(1,2)
The line passing through (1, 1) and parallel to the line 2x - 3y + 5 = 0 is
- (a)
3x + 2y = 5
- (b)
2x - 3y + 1 = 0
- (c)
3x - 2y = 1
- (d)
2x + 3y = 5
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
The equation of a straight line which passes through the point (acos3 \(\theta\) sin3 \(\theta\)) and perpendicular to x sec \(\theta\) + y cosec \(\theta\) = a is
- (a)
\(\frac { x }{ a } +\frac { y }{ a } =acos\theta \)
- (b)
xcos\(\theta\) - ysin \(\theta\) = acos2\(\theta\)
- (c)
xcos\(\theta\) + ysin\(\theta\) = acos2\(\theta\)
- (d)
xcos\(\theta\) + ysin\(\theta\) - acos2\(\theta\) = 1
One of the equation of the straight lines which passes through the point (3, 2) and are inclined to x -2y = 3 at an angle of 450, is
- (a)
3x - y - 9 = 0
- (b)
3x - y - 7 = 0
- (c)
x + 3y - 9 = 0
- (d)
Both (b) and (C)
Find the Equation of the line perpendicular to the line x - 7y + 5 = 0 and having x - intercept 3.
- (a)
7x + y + 21 = 0
- (b)
7x + y - 21 = 0
- (c)
7x - y - 21 = 0
- (d)
None of these