1). The distance of the point (2, 3) from the line x y = 5 is:
A). \( \Large 5\sqrt{2} \) 
B). \( \Large 2\sqrt{5} \) 
C). \( \Large 3\sqrt{5} \) 
D). \( \Large 5\sqrt{3} \) 

2). The equation of the straight line joining the origin to the point of intersection of \( \Large yx+7=0\ and\ y+2x2=0 \)is:
A). \( \Large 3x+4y=0 \) 
B). \( \Large 3x4y=0 \) 
C). \( \Large 4x3y=0 \) 
D). \( \Large 4x+3y=0 \) 

3). The equation of the straight line which is perpendicular to\( \Large y = x \) and passes through (3, 2) is:
A). \( \Large xy = 5 \) 
B). \( \Large x+y = 5 \) 
C). \( \Large x+y = 1 \) 
D). \( \Large xy = 1 \) 

4). The angle between the straight lines \( \Large xy\sqrt{3}=5\ and\ \sqrt{3}x+y=7 \) is:
A). \( \Large 90 ^{\circ} \) 
B). \( \Large 60 ^{\circ} \) 
C). \( \Large 75 ^{\circ} \) 
D). \( \Large 30 ^{\circ} \) 

5). The three straight lines \( \Large ax+by=c,\ bx+cy=a\ and\ cx+ay=b \) are collinear if:
A). \( \Large a+b+c = 0 \) 
B). \( \Large c+a=b \) 
C). \( \Large b+c=a \) 
D). \( \Large a+b=c \) 

6). If a tangent to the curve \( \Large y=6xx^{2} \) is parallel to the line \( \Large 4x2y1=0 \) then the point of tangency on the curve is: ' _
A). (6, 1) 
B). (8, 2) 
C). (2, 8) 
D). (4, 2) 

7). Distance between the lines \( \Large 5x+3y7=0\ and\ 15x+9y+14=0 \) is:
A). \( \Large \frac{35}{\sqrt{34}} \) 
B). \( \Large \frac{1}{\sqrt{34}} \) 
C). \( \Large \frac{35}{2\sqrt{34}} \) 
D). \( \Large \frac{35}{3\sqrt{34}} \) 

8). The equation of the sides of a triangle are \( \Large x3y=0.\ 4x+3y=5\ and\ 3x+y=0 \). The lines \( \Large 3x4y=0 \) passage through
A). the incentre 
B). the centroid 
C). the orthocentre 
D). the circumcentre 

9). If (4, 5) is one vertex and \( \Large 7xy+8=0 \) is one diagonal of a square then the equation of second diagonal is:
A). \( \Large x+3y=21 \) 
B). \( \Large 2x3y=7 \) 
C). \( \Large x+7y=31 \) 
D). \( \Large 2x+3y=21 \) 

10). The number of the straight which is equally inclined to both the axes is
