IIT-JEE 2008 Paper 1 Offline | Circle Question 28 | Mathematics

1

IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation $$\sqrt 3 x\, + \,y\, - \,6 = 0$$ and the point D is $$\left( {{{3\,\sqrt 3 } \over 2},\,{3 \over 2}} \right)$$. Further, it is given that the origin and the centre of C are on the same side of the line PQ.

Points E and F are given by

A

$$\left( {{{\,\sqrt 3 } \over 2},\,{3 \over 2}} \right),\,\left( {\sqrt 3 ,\,0} \right)$$

B

$$\left( {{{\,\sqrt 3 } \over 2},\,{1 \over 2}} \right),\,\left( {\sqrt 3 ,\,0} \right)$$

C

$$\left( {{{\,\sqrt 3 } \over 2},\,{3 \over 2}} \right),\,\left( {{{\,\sqrt 3 } \over 2},\,{1 \over 2}} \right)$$

D

$$\left( {{{\,3} \over 2},\,{{\sqrt 3 } \over 2}} \right),\,\left( {{{\,\sqrt 3 } \over 2},\,{1 \over 2}} \right)$$

2

IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation $$\sqrt 3 x\, + \,y\, - \,6 = 0$$ and the point D is $$\left( {{{3\,\sqrt 3 } \over 2},\,{3 \over 2}} \right)$$. Further, it is given that the origin and the centre of C are on the same side of the line PQ.

The equation of circle C is

A

$${\left( {x\, - 2\sqrt 3 \,} \right)^2} + {(y - 1)^2} = 1$$

B

$${\left( {x\, - 2\sqrt 3 \,} \right)^2} + {(y + {1 \over 2})^2} = 1$$

C

$${\left( {x\, - \sqrt 3 \,} \right)^2} + {(y + 1)^2} = 1$$

D

$${\left( {x\, - \sqrt 3 \,} \right)^2} + {(y - 1)^2} = 1$$

3

IIT-JEE 2007 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-1

Let $$\mathrm{ABCD}$$ be a quadrilateral with area 18 , with side $$\mathrm{A B}$$ parallel to the side $$\mathrm{C D}$$ and $$\mathrm{A B}=2 \mathrm{CD}$$. Let $$\mathrm{AD}$$ be perpendicular to $$\mathrm{AB}$$ and $$\mathrm{CD}$$. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is :

A

3

B

2

C

$$\frac{3}{2}$$

D

1

4

IIT-JEE 2007 Paper 2 Offline

MCQ (Single Correct Answer)

+4

-0

Match the statements in Column I with the properties Column II.

	Column I		Column II
(A)	Two intersecting circles	(P)	have a common tangent
(B)	Two mutually external circles	(Q)	have a common normal
(C)	Two circles, one strictly inside the other	(R)	do not have a common tangent
(D)	Two branches of a hyperbola	(S)	do not have a common normal

A

$$\mathrm{A-(p);B-(p),(q);C-(q),(r);D-(q)}$$

B

$$\mathrm{A-(p),(q);B-(q);C-(r);D-(q),(r)}$$

C

$$\mathrm{A-(q);B-(p),(q);C-(q),(r);D-(r)}$$

D

$$\mathrm{A-(p),(q);B-(p),(q);C-(q),(r);D-(q),(r)}$$

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