Mathematics - Straight Lines
Exam Duration: 45 Mins Total Questions : 30
Passing through the points (3,8) and (3,4)
- (a)
0
- (b)
\(\frac { 3 }{ 2 } \)
- (c)
6
- (d)
not defined
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
The points (P + 1,1), (2p + 1,3) and (2p + 2,2p) are collinear, if p =
- (a)
-1,2
- (b)
\(\frac { 1 }{ 2 } \),2
- (c)
2,1
- (d)
\(-\frac { 1 }{ 2 } \),2
The points (k -1, K + 2), (K,K +1) and (K + 1, k) are collinear for
- (a)
any value of K
- (b)
K = \(\frac { 1 }{ 2 } \) only
- (c)
not value of k
- (d)
Integral values of k only
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
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
Find perpendicular distance of the line joining the points (cos \(\theta\), sin\(\theta\) ) and (cos\(\phi\) , sin \(\phi\)) from the origin.
- (a)
\(\left| cos\left( \frac { \theta -\phi }{ 2 } \right) \right| \)
- (b)
\(\left| cos\left( \frac { \theta +\phi }{ 2 } \right) \right| \)
- (c)
\(\left| sin\left( \frac { \theta +\phi }{ 2 } \right) \right| \)
- (d)
None of these
Find the equation of the lines through the point of intersection of the lines x-y+1=0 and 2x-3y+5=0 and whose distance from the point (3,2) is \({7\over5}.\)
- (a)
4x+3y+1=0
- (b)
3x+4y-6=0
- (c)
4x-3y+1=0
- (d)
3x+4y+6=0
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, \(\sqrt{2}l\)
The Fahrenheit temperature F and absolute temperature K satisfy a linear equation. Given that K - 273 when F = 32 and that K = 373 when F = 212 Find the value of F, When K = 0
- (a)
459.4
- (b)
-459.4
- (c)
287.3
- (d)
-287.3
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
Find the equation of the line where length of the perpendicular segment from the origin to the line is 4 and the inclination of the perpendicular segment with the postive direction of x - axis is 300
- (a)
x - \(\sqrt { 3 } \) y = 8
- (b)
x + \(\sqrt { 3 } \) y = 8
- (c)
\(\sqrt { 3 } \) x +y = 8
- (d)
\(\sqrt { 3 } \) x - y = 8
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 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)
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
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
For specifying a straight line, how many geometrical parameters should be known?
- (a)
1
- (b)
2
- (c)
4
- (d)
3
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)
\(({7\over2},{7\over2})\)
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)
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
Equation of line is 3x - 4y + 10 = 0, find its x and y -intercept respectively
- (a)
\(\frac { -10 }{ 3 } ,\frac { 5 }{ 2 } \)
- (b)
\(-5,\frac { 10 }{ 3 } \)
- (c)
\(\frac { 3 }{ 2 } ,\frac { -5 }{ 2 } \)
- (d)
\(1,\frac { -5 }{ 3 } \)
Reduce the equation \(\sqrt { 3 } \)x + y - 8 = 0, into normal form, Find the Length of perpendicular from the origin to the given line and angle made by the perpendicular with x - axis.
- (a)
8,1200
- (b)
6,1200
- (c)
4,300
- (d)
5,150
A line is such that its segment between the lines 5x - y + 4 = 0 and 3x + 4y - 4 = 0 is bisectes at the point (1, 5), obtain is equation.
- (a)
107x - 3y + 92 = 0
- (b)
3x + 107y + 92 = 0
- (c)
107x - 3y -92 = 0
- (d)
3x - 107y - 92 = 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 equation of the sides of a triangle are x - 3y = 0, 4x + 3y = 5 and 3x + y = 0 the line 3x -4y = 0 passes through the
- (a)
Incemture
- (b)
Centroid
- (c)
Orthocenter
- (d)
Circumcentre
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)
A point moves such that its distance from the point (4, 0) is half that of its distance from the line x=16. The locus of the point is
- (a)
3x2+4y2=192
- (b)
4x2+3y2=192
- (c)
x2+y2=192
- (d)
3x2-4y2=192
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