IIT-JEE 2002 | Straight Lines and Pair of Straight Lines Question 20 | Mathematics

IIT-JEE 2002

MCQ (Single Correct Answer)

-1

Locus of mid point of the portion between the axes of $$x$$ $$\cos \alpha + y\sin \alpha = p$$ where $$p$$ is constant is

$${x^2} + {y^2} = {4 \over {{p^2}}}\,\,\,$$

$${x^2} + {y^2} = 4{p^2}$$

$${1 \over {{x^2}}} + {1 \over {{y^2}}} = {2 \over {{p^2}}}$$

$${1 \over {{x^2}}} + {1 \over {{y^2}}} = {4 \over {{p^2}}}$$

IIT-JEE 2002

MCQ (Single Correct Answer)

-1

If the pair of lines $$a{x^2} + 2hxy + b{y^2} + 2gx + 2fy + c = 0$$ intersect on the $$y$$ axis then

$$2fgh = b{g^2} + c{h^2}$$

$$b{g^2} \ne c{h^2}$$

$$\,abc = 2fgh$$

none of these

IIT-JEE 2002

MCQ (Single Correct Answer)

-1

The pair of lines represented by
$$3a{x^2} + 5xy + \left( {{a^2} - 2} \right){y^2} = 0$$ are perpendicular to each other for

two values of $$a$$

$$\forall \,a$$

for one values of $$a$$

for no values of $$a$$

IIT-JEE 2002 Screening

MCQ (Single Correct Answer)

-0.75

Let $$0 < \alpha < {\pi \over 2}$$ be fixed angle. If $$P = \left( {\cos \theta ,\,\sin \theta } \right)$$ and $$Q = \left( {\cos \left( {\alpha - \theta } \right),\,\sin \left( {\alpha - \theta } \right)} \right),$$ then $$Q$$ is obtained from $$P$$ by

clockwise rotation around origin through an angle $$\alpha $$

anticlockwise rotation around origin through an angle $$\alpha $$

reflection in the line through origin with slope tan $$\alpha $$

reflection in the line through origin with slope tan $$\left( {\alpha /2} \right)$$

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