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1

JEE Advanced 2013 Paper 1 Offline

For $$a > b > c > 0,$$ the distance between $$(1, 1)$$ and the point of intersection of the lines $$ax + by + c = 0$$ and $$bx + ay + c = 0$$ is less than $$\left( {2\sqrt 2 } \right)$$. Then
A
$$a + b - c > 0$$
B
$$a - b + c < 0$$
C
$$a - b + c = > 0$$
D
$$a + b - c < 0$$
2

IIT-JEE 2011 Paper 1 Offline

A straight line $$L$$ through the point $$(3, -2)$$ is inclined at an angle $${60^ \circ }$$ to the line $$\sqrt {3x} + y = 1.$$ If $$L$$ also intersects the x-axis, then the equation of $$L$$ is
A
$$y + \sqrt {3x} + 2 - 3\sqrt 3 = 0$$
B
$$y - \sqrt {3x} + 2 + 3\sqrt 3 = 0$$
C
$$\sqrt {3y} - x + 3 + 2\sqrt 3 = 0$$
D
$$\sqrt {3y} + x - 3 + 2\sqrt 3 = 0$$
3

IIT-JEE 2007

The lines $${L_1}:y - x = 0$$ and $${L_2}:2x + y = 0$$ intersect the line $${L_3}:y + 2 = 0$$ at $$P$$ and $$Q$$ respectively. The bisector of the acute angle between $${L_1}$$ and $${L_2}$$ intersects $${L_3}$$ at $$R$$.

Statement-1: The ratio $$PR$$ : $$RQ$$ equals $$2\sqrt 2 :\sqrt 5$$. because
Statement-2: In any triangle, bisector of an angle divides the triangle into two similar triangles.

A
Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement- 1
B
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
C
Statement-1 is True, Statement-2 is False.
D
Statement-1 is False, Statement-2 is True.
4

IIT-JEE 2007

Let $$O\left( {0,0} \right),P\left( {3,4} \right),Q\left( {6,0} \right)$$ be the vertices of the triangles $$OPQ$$. The point $$R$$ inside the triangle $$OPQ$$ is such that the triangles $$OPR$$, $$PQR$$, $$OQR$$ are of equal area. The coordinates of $$R$$ are
A
$$\left( {{4 \over 3},3} \right)$$
B
$$\left( {3,{2 \over 3}} \right)$$
C
$$\left( {3,{4 \over 3}} \right)$$
D
$$\left( {{4 \over 3},{2 \over 3}} \right)$$

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