1
IIT-JEE 1999
MCQ (Single Correct Answer)
+2
-0.5
Lt $$PQR$$ be a right angled isosceles triangle, right angled at $$P(2, 1)$$. If the equation of the line $$QR$$ is $$2x + y = 3,$$ then the equation representing the pair of lines $$PQ$$ and $$PR$$ is
A
$$3{x^2} - 3{y^2} + 8xy + 20x + 10y + 25 = 0$$
B
$$3{x^2} - 3{y^2} + 8xy - 20x - 10y + 25 = 0$$
C
$$3{x^2} - 3{y^2} + 8xy + 10x + 15y + 20 = 0$$
D
$$3{x^2} - 3{y^2} - 8xy - 10x - 15y - 20 = 0$$
2
IIT-JEE 1999
MCQ (Single Correct Answer)
+2
-0.5
If $${x_1},\,{x_2},\,{x_3}$$ as well as $${y_1},\,{y_2},\,{y_3}$$, are in G.P. with the same common ratio, then the points $$\left( {{x_1},\,{y_1}} \right),\left( {{x_2},\,{y_2}} \right)$$ and $$\left( {{x_3},\,{y_3}} \right).$$
A
lie on a straight line
B
lie on an ellipse
C
lie on a circle
D
are vertices of a triangle
3
IIT-JEE 1999
MCQ (More than One Correct Answer)
+3
-0.75
Let $${L_1}$$ be a straight line passing through the origin and $${L_2}$$ be the straight line $$x + y = 1$$. If the intercepts made by the circle $${x^2} + {y^2} - x + 3y = 0$$ on $${L_1}$$ and $${L_2}$$ are equal, then which of the following equations can represent $${L_1}$$?
A
$$x + y = 0$$
B
$$x -y = 0$$
C
$$x + 7y = 0$$
D
$$x - 7y = 0$$
4
IIT-JEE 1999
MCQ (Single Correct Answer)
+2
-0.5
In a triangle $$PQR,\angle R = \pi /2$$. If $$\,\,\tan \left( {P/2} \right)$$ and $$\tan \left( {Q/2} \right)$$ are the roots of the equation $$a{x^2} + bx + c = 0\left( {a \ne 0} \right)$$ then.
A
$$a + b = c$$
B
$$a + c = b$$
C
$$b + c = a$$
D
$$b = c$$
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