1
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
If the lines $$3x - 4y - 7 = 0$$ and $$2x - 3y - 5 = 0$$ are two diameters of a circle of area $$49\pi $$ square units, the equation of the circle is :
A
$$\,{x^2} + {y^2} + 2x\, - 2y - 47 = 0\,$$
B
$$\,{x^2} + {y^2} + 2x\, - 2y - 62 = 0\,$$
C
$${x^2} + {y^2} - 2x\, + 2y - 62 = 0$$
D
$${x^2} + {y^2} - 2x\, + 2y - 47 = 0$$
2
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
Let $$C$$ be the circle with centre $$(0, 0)$$ and radius $$3$$ units. The equation of the locus of the mid points of the chords of the circle $$C$$ that subtend an angle of $${{2\pi } \over 3}$$ at its center is :
A
$${x^2} + {y^2} = {3 \over 2}$$
B
$${x^2} + {y^2} = 1$$
C
$${x^2} + {y^2} = {{27} \over 4}$$
D
$${x^2} + {y^2} = {{9} \over 4}$$
3
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
In the ellipse, the distance between its foci is $$6$$ and minor axis is $$8$$. Then its eccentricity is :
A
$${3 \over 5}$$
B
$${1 \over 2}$$
C
$${4 \over 5}$$
D
$${1 \over {\sqrt 5 }}$$
4
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
The locus of the vertices of the family of parabolas
$$y = {{{a^3}{x^2}} \over 3} + {{{a^2}x} \over 2} - 2a$$ is :
A
$$xy = {{105} \over {64}}$$
B
$$xy = {{3} \over {4}}$$
C
$$xy = {{35} \over {16}}$$
D
$$xy = {{64} \over {105}}$$
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