1
JEE Main 2016 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
If one of the diameters of the circle, given by the equation, $${x^2} + {y^2} - 4x + 6y - 12 = 0,$$ is a chord of a circle $$S$$, whose centre is at $$(-3, 2)$$, then the radius of $$S$$ is :
A
$$5$$
B
$$10$$
C
$$5\sqrt 2 $$
D
$$5\sqrt 3 $$
2
JEE Main 2016 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
The eccentricity of the hyperbola whose length of the latus rectum is equal to $$8$$ and the length of its conjugate axis is equal to half of the distance between its foci, is :
A
$${2 \over {\sqrt 3 }}$$
B
$${\sqrt 3 }$$
C
$${{4 \over 3}}$$
D
$${4 \over {\sqrt 3 }}$$
3
JEE Main 2016 (Offline)
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Let $$P$$ be the point on the parabola, $${{y^2} = 8x}$$ which is at a minimum distance from the centre $$C$$ of the circle, $${x^2} + {\left( {y + 6} \right)^2} = 1$$. Then the equation of the circle, passing through $$C$$ and having its centre at $$P$$ is:
A
$${{x^2} + {y^2} - {x \over 4} + 2y - 24 = 0}$$
B
$${{x^2} + {y^2} - 4x + 9y + 18 = 0}$$
C
$${{x^2} + {y^2} - 4x + 8y + 12 = 0}$$
D
$${{x^2} + {y^2} - x + 4y - 12 = 0}$$
4
JEE Main 2016 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
A wire of length $$2$$ units is cut into two parts which are bent respectively to form a square of side $$=x$$ units and a circle of radius $$=r$$ units. If the sum of the areas of the square and the circle so formed is minimum, then:
A
$$x=2r$$
B
$$2x=r$$
C
$$2x = \left( {\pi + 4} \right)r$$
D
$$\left( {4 - \pi } \right)x = \pi \,\, r$$
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