Circles · JEE Main previous year questions

2016 4 questions

1. Q62016 · 3 Apr 2016 · Shift 1

   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 :

   1. A.$5$
   2. B.$10$
   3. C.$5\sqrt{2}$
   4. D.$5\sqrt{3}$
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   Answer: D

2. Q82016 · 3 Apr 2016 · Shift 1

   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:

   1. A.$x=2r$
   2. B.$2x=r$
   3. C.$2x=(\pi +4)r$
   4. D.$(4-\pi )x=\pi r$
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   Answer: A

3. Q222016 · 3 Apr 2016 · Shift 1

   The centres of those circles which touch the circle, $x^2+y^2-8x-8y-4=0$, externally and also touch the $x$-axis, lie on :

   1. A.a circle
   2. B.an ellipse which is not a circle
   3. C.a hyperbola
   4. D.a parabola
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   Answer: D

4. Q232016 · 3 Apr 2016 · Shift 1

   Let $P$ be the point on the parabola, $y^2=8x$ which is at a minimum distance from the centre $C$ of the circle, $x^2+(y+6{)}^2=1$. Then the equation of the circle, passing through $C$ and having its centre at $P$ is:

   1. A.$x^2+y^2-\frac{x}{4}+2y-24=0$
   2. B.$x^2+y^2-4x+9y+18=0$
   3. C.$x^2+y^2-4x+8y+12=0$
   4. D.$x^2+y^2-x+4y-12=0$
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   Answer: C