1
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Change Language
The equation of a circle with origin as a center and passing through an equilateral triangle whose median is of length $$3$$$$a$$ is :
A
$${x^2}\, + \,{y^2} = 9{a^2}$$
B
$${x^2}\, + \,{y^2} = 16{a^2}$$
C
$${x^2}\, + \,{y^2} = 4{a^2}$$
D
$${x^2}\, + \,{y^2} = {a^2}$$
2
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
The centres of a set of circles, each of radius 3, lie on the circle $${x^2}\, + \,{y^2} = 25$$. The locus of any point in the set is :
A
$$4\, \le \,\,{x^2}\, + \,{y^2}\, \le \,\,64$$
B
$${x^2}\, + \,{y^2}\, \le \,\,25$$
C
$${x^2}\, + \,{y^2}\, \ge \,\,25$$
D
$$3\, \le \,\,{x^2}\, + \,{y^2}\, \le \,\,9$$
3
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Two common tangents to the circle $${x^2} + {y^2} = 2{a^2}$$ and parabola $${y^2} = 8ax$$ are :
A
$$x = \pm \left( {y + 2a} \right)$$
B
$$y = \pm \left( {x + 2a} \right)$$
C
$$x = \pm \left( {y + a} \right)$$
D
$$y = \pm \left( {x + a} \right)$$
4
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$y = {\left( {x + \sqrt {1 + {x^2}} } \right)^n},$$ then $$\left( {1 + {x^2}} \right){{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}}$$ is
A
$${n^2}y$$
B
$$-{n^2}y$$
C
$$-y$$
D
$$2{x^2}y$$
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