The points (2, 1), (8, 5) and (x, 7) lie on a straight line. Then the values of x is
10
11
11 2/3
12
The point on the line 3x+4y=5 which is equidistance from (1, 2) and (3, 4) is
(7, -4)
(15, -10)
(1/7, 8/7)
(0, 5/4)
In a triangle, the orthocentre and the circumcentre are (-4, 0), (8, 6 ) respectively; the centroid is
(0, 2)
(2, 3)
(4, 4)
(5, 9/2)
The perpendicular bisector of the line segment joining P(1, 4) and Q (k, 3) has y-intercept-4. Then a possible value of k is
2
-2
-4
1
If (1, 2),(4, 3),(6, 4) are the midpoints of the sides BC,CA,AB of Δ ABC, then the equation of AB is
2x-3y-13=0
2x+3y-1=0
x-3y+6=0
x+3y+12=0
If 9x2-24xy+ky2-12x+16y-12=0 represents a pair of parallel lines, then k=
4
8
16
The equation of the line dividing the line segment joining the points (2, -3), (1, 2) in the ratio 2:3 and perpendicular to 2x+5y-1=0. Is
x+2y-12=0
5x-2y-10=0
3x-2y-24=0
5x-2y+4=0
P and Q are points on the line joining A(-2,5), B(3,-1) such that AP=PQ=QB. Then the mid point of PQ is
(1/2,2)
(-1/2,4)
(2,3)
(1,4)
If (2,4), (4,2) are the extremities of the hypotenuse of a right angled isosceles triangle, then the third vertex is
(2,2) or (4,4)
(3,3) or (4,4)
(2,2) or (3,3)
(2,3) or (3,2)
If the sides of ?ABC are 5,7,8 units then AG2 "+ BG2 + CG2 =
46
138
92
69
The chord through (1,-2) cuts the curve 3x2-y2-2x+4y=0 in p and Q. Then PQ subtends at the origin an angle of
300
450
600
900
If the area of the triangle with vertices (2a,a), (a,a), (a,2a) is 18sq.unit5, then the circumcentre of the triangle is
(3,3)
(6,6)
(9,9)
(0,0)
Two equation sides of an isosceles triangle are 7x-y+3=0, x+y-3=0 and its third side passes through the point (1, -10). The equation of the third side is
3x+y+7=0
x-3y+29=0
3x+y+3=0
3x+y-3=0
If the orthocentre and circumcentre of a triangle are (2,-3), (5,6) then the centroid is
(2,7)
(-3,-4/3)
(4,3)
(-1,-3)
The equation of the line passing through the point P (1, 2) such that P bisects the part intercepted between the axes is
x+2y=5
x-y+1=0
x+y-31=0
2x+y-4=0
The lines 2x+y-1=0, ax+3y-3=0, 3x+2y-2=0 are concurrent
for all a
for a=4 only
for -1≤a≤3
for a>0 only
The orthocentre of the triangle formed by the lines 6x2-5xy-6y2+x+5y-1=0, x+y-1=0 is
(-1/13,5/13)
(1/13,5/13)
(1/13,-5/13)
(-1/13,-5/13)
If (2, 1),(-1, -2),(3, 3) are the midpoints of the sides BC,CA,AB of Δ ABC, then the equation of AB is
x-y=1/2
x+y=1
x-y=9
x=y
If the distance the points(5,-1,7) and (c,5,1) is 9 then c=
-8
The point equidistant from (24, 7),(7, 24) and (0, 25) is
(- 24, 7)
(24,- 7)
(0, 0)
(-24,-7)
The circumcentre of the triangle formed by(2,-5), (2,7), (4,7) is
(3,1)
(2,-9)
(4,-1)
(3/2,5/2)
The length of the intercept on the y-axis cut by the pair of lines 2x2+4xy-6y2+3x+y+1=0 is
6/5
5/6
√5/6
√5/3
The distance between the points(-1,2,-3),(5,4,-6) is
3
6
7
The equation of the straight line perpendicular to 5x-2y=7 and passing through the point of intersection of the lines 2x+3y=1and 3x+4y=6 is
2x+5y+17=0
2x+5y-17=0
2x-5y+17=0
2x-5y=17
The equation of the line having inclination 1200 and y-intercepts -3 is
x+y-5=0
√3x+y+3=0
x+y-2=0
x-y-5=0
The angle between the lines joining the origin to the points of intersection of x+2y+1=0 and 2x2-2xy+3y2+2x-y-1=0 is
cos-1((13)/(√17))
cos-1((10)/(√122))
π/2
cos-1((13)/(√193))
The value of k such that the straight line 2x+3y+4+k (6x-y+12) =0 is perpendicular to the line7x+5y=c
29/37
-29/37
-27/37
-28/37
The orthocentre of the triangle formed by(2,-1/2), (1/2,-1/2)and (2,√3-1/2) is
(3/2,(9√3-3)/6)
(2,-1/2)
(5/4,(√3-2)/4)
(1/2,-1/2)
If ax2+2hxy+by2+2gx+2fy+c=0 represents two straight lines equidistant from the origin, then f4-g4=
Bf2-ag2
Ag2-bf2
C(Bf2-ag2)
C(Ag2-bf2)
The quadrilateral formed by the pairs of lines xy+x+y+1=0, xy+3x+3y+9=0 is
Parallelogram
Rhombus
Rectangle
Square