1
AIEEE 2012
+4
-1
If the line $$2x + y = k$$ passes through the point which divides the line segment joining the points $$(1, 1)$$ and $$(2, 4)$$ in the ratio $$3 : 2$$, then $$k$$ equals :
A
$${{29 \over 5}}$$
B
$$5$$
C
$$6$$
D
$${{11 \over 5}}$$
2
AIEEE 2011
+4
-1
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 $$2\sqrt 2 :\sqrt 5$$
Statement-2: In any triangle, bisector of an angle divide 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 false.
C
Statement-1 is false, Statement-2 is true.
D
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
3
AIEEE 2010
+4
-1
The line $$L$$ given by $${x \over 5} + {y \over b} = 1$$ passes through the point $$\left( {13,32} \right)$$. The line K is parrallel to $$L$$ and has the equation $${x \over c} + {y \over 3} = 1.$$ Then the distance between $$L$$ and $$K$$ is
A
$$\sqrt {17}$$
B
$${{17} \over {\sqrt {15} }}$$
C
$${{23} \over {\sqrt {17} }}$$
D
$${{23} \over {\sqrt {15} }}$$
4
AIEEE 2009
+4
-1
The shortest distance between the line $$y - x = 1$$ and the curve $$x = {y^2}$$ is :
A
$${{2\sqrt 3 } \over 8}$$
B
$${{3\sqrt 2 } \over 5}$$
C
$${{\sqrt 3 } \over 4}$$
D
$${{3\sqrt 2 } \over 8}$$
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