AIEEE 2011 | Straight Lines and Pair of Straight Lines Question 95 | Mathematics

AIEEE 2011

MCQ (Single Correct Answer)

-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.

Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

Statement-1 is true, Statement-2 is false.

Statement-1 is false, Statement-2 is true.

Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

AIEEE 2010

MCQ (Single Correct Answer)

-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

$$\sqrt {17} $$

$${{17} \over {\sqrt {15} }}$$

$${{23} \over {\sqrt {17} }}$$

$${{23} \over {\sqrt {15} }}$$

AIEEE 2009

MCQ (Single Correct Answer)

-1

The shortest distance between the line $$y - x = 1$$ and the curve $$x = {y^2}$$ is :

$${{2\sqrt 3 } \over 8}$$

$${{3\sqrt 2 } \over 5}$$

$${{\sqrt 3 } \over 4}$$

$${{3\sqrt 2 } \over 8}$$

AIEEE 2009

MCQ (Single Correct Answer)

-1

The lines $$p\left( {{p^2} + 1} \right)x - y + q = 0$$ and $$\left( {{p^2} + 1} \right){}^2x + \left( {{p^2} + 1} \right)y + 2q$$ $$=0$$ are perpendicular to a common line for :

exactly one values of $$p$$

exactly two values of $$p$$

more than two values of $$p$$

no value of $$p$$

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