IISER 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
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
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)
\({1\over 2p^2}\)
The slope of the straight line which does not interest x - axis is equal to
- (a)
\(\frac { 1 }{ 2 } \)
- (b)
\(\frac { 1 }{ \sqrt { 2 } } \)
- (c)
\(\sqrt { 3 } \)
- (d)
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)
\(x+\sqrt { 3 } y=0\)
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 line through the points (1,-1) and (3,5)
- (a)
2x - y = 3
- (b)
y = 2x - 4
- (c)
3x - y = 4
- (d)
y = 4x - 3
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
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 lines for which tan \(\theta\) = \(\frac { 1 }{ 2 } \), where \(\theta\) is the inclinction of the line and
(i) y - intercept is \(-\frac { 3 }{ 2 } \) (ii) x - intercept is 4
- (a)
(i) (ii) y - 2x + 3 = 0 2y - x + 4 =0 - (b)
(i) (ii) 2y - x + 3 = 0 2y - x + 4 = 0 - (c)
(i) (ii) 2y - x + 3 = 0 y - 2x + 4 =0 - (d)
(i) (ii) y - 2x + 3 = 0 y - 2x + 4 = 0
The intercept cut off by a line on y - axis is twice than that on a x - axis , and the line passes through the point (1, 2) the equation of the line is
- (a)
2x + y = 4
- (b)
2x + y + 4 = 0
- (c)
2x - y = 4
- (d)
2x - y + 4 = 0
The inclination of the line x - y + 3 = 0 with the postive direction of x -axis is
- (a)
450
- (b)
1350
- (c)
-450
- (d)
-1350
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
Slope of a line which cuts off intercepts of equal lengths on the axes is
- (a)
-1
- (b)
0
- (c)
0
- (d)
\(\sqrt{3}\)
The equation of the line passing through the point (1,2) and perpendicular to the line x+y+1=0 is
- (a)
y-x+1=0
- (b)
y-x-1=0
- (c)
y-x+2=0
- (d)
y-x-2=0
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)
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
The equations of the lines passing through the point (1,0) and at a distance of \({\sqrt{3}\over2}\) from the origin, are
- (a)
\(\sqrt{3}x+y-\sqrt{3}=0,\sqrt{3}x-y-\sqrt{3}=0\)
- (b)
\(\sqrt{3}x+y+\sqrt{3}=0,\sqrt{3}x-y+\sqrt{3}=0\)
- (c)
\(x+\sqrt{3}y-\sqrt{3}=0,x-\sqrt{3}y-\sqrt{3}=0\)
- (d)
None of these
State T for true and F for false.
(i) If the vertices of a triangle have integral coordinates, then the triangle cannot be equilateral.
(ii) Line joining the points (3, -4) and (-2, 6) is perpendicular to the line joining the points (-3, 6) and (9, -18).
(iii) The angle between the lines y = \(\left( 2-\sqrt { 3 } \right) \left( x+5 \right) \) and y = \(\left( 2+\sqrt { 3 } \right) \left( x-7 \right) \) is 450 .
(iv) The points A (-2, 1), B(0, 5) and C(-1, 2) are collinear.
- (a)
(i) (ii) (iii) (iv) F T T F - (b)
(i) (ii) (iii) (iv) T F F T - (c)
(i) (ii) (iii) (iv) T F F F - (d)
(i) (ii) (iii) (iv) F T T T
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)
\(1,\frac { -5 }{ 3 } \)
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 image of the point (2, 3) on the line x + 3y + 4 = 0 is
- (a)
(1, 6)
- (b)
(-1, -6)
- (c)
(-1, 6)
- (d)
(1, -6)
Consider the lines \(L_1\equiv x+3y-7=0\)and\(L_2\equiv 3x-y-1=0\) . Which of the following statement is/are true?
- (a)
L1 and L2 are perpendicular to each other
- (b)
The point of intersection of L1 and L2 is (1,2).
- (c)
The image of the point (3,8) w.r.t the line L1 assuming L1 to be plane mirror is (-1,-4).
- (d)
All of these
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
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
If p and p' be the perpendiculars from the origin upon the straight lines x sec\(\theta\) +y cosec\(\theta\)=a and x cos\(\theta\)-y sin\(\theta\)=a cos 2\(\theta\) respectively, then the value of the expression 4p2p2 is
- (a)
a2
- (b)
3a2
- (c)
2a2
- (d)
4 a2
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