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). \( \Large 5\sqrt{3} \) |
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2). The equation of the straight line joining the origin to the point of intersection of \( \Large y-x+7=0\ and\ y+2x-2=0 \)is:
| A). \( \Large 3x+4y=0 \) |
| B). \( \Large 3x-4y=0 \) |
| C). \( \Large 4x-3y=0 \) |
| D). \( \Large 4x+3y=0 \) |
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3). The equation of the straight line which is perpendicular to\( \Large y = x \) and passes through (3, 2) is:
| A). \( \Large x-y = 5 \) |
| B). \( \Large x+y = 5 \) |
| C). \( \Large x+y = 1 \) |
| D). \( \Large x-y = 1 \) |
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4). The angle between the straight lines \( \Large x-y\sqrt{3}=5\ and\ \sqrt{3}x+y=7 \) is:
| A). \( \Large 90 ^{\circ} \) |
| B). \( \Large 60 ^{\circ} \) |
| C). \( \Large 75 ^{\circ} \) |
| D). \( \Large 30 ^{\circ} \) |
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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). \( \Large a+b=c \) |
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6). If a tangent to the curve \( \Large y=6x-x^{2} \) is parallel to the line \( \Large 4x-2y-1=0 \) then the point of tangency on the curve is: ' _
| A). (6, 1) |
| B). (8, 2) |
| C). (2, 8) |
| D). (4, 2) |
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7). Distance between the lines \( \Large 5x+3y-7=0\ and\ 15x+9y+14=0 \) is:
| A). \( \Large \frac{35}{\sqrt{34}} \) |
| B). \( \Large \frac{1}{\sqrt{34}} \) |
| C). \( \Large \frac{35}{2\sqrt{34}} \) |
| D). \( \Large \frac{35}{3\sqrt{34}} \) |
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8). The equation of the sides of a triangle are \( \Large x-3y=0.\ 4x+3y=5\ and\ 3x+y=0 \). The lines \( \Large 3x-4y=0 \) passage through
| A). the incentre |
| B). the centroid |
| C). the orthocentre |
| D). the circumcentre |
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9). If (-4, -5) is one vertex and \( \Large 7x-y+8=0 \) is one diagonal of a square then the equation of second diagonal is:
| A). \( \Large x+3y=21 \) |
| B). \( \Large 2x-3y=7 \) |
| C). \( \Large x+7y=31 \) |
| D). \( \Large 2x+3y=21 \) |
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10). The number of the straight which is equally inclined to both the axes is
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