IIT-JEE 2008 Paper 1 Offline | Circle Question 23 | Mathematics

IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

-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

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

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

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

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

IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

-1

Equations of the sides QR, RP are

$$y = {2 \over {\sqrt 3 }}\,x + \,1,\,\,y = \, - {2 \over {\sqrt 3 }}\,x - 1$$

$$y = {1 \over {\sqrt 3 }}\,x,\,\,y = \,0$$

$$y = {{\sqrt 3 } \over 2}\,x + \,1,\,\,y = \, - {{\sqrt 3 } \over 2}\,x - 1$$

$$y = \sqrt 3 \,x,\,\,y = \,0$$

IIT-JEE 2006

MCQ (Single Correct Answer)

-1.25

ABCD is a square of side length 2 units. $$C_1$$ is the circle touching all the sides of the square ABCD and $$C_2$$ is the circumcircle of square ABCD. L is a fixed line in the same plane and R is a fixed point.

If a circle is such that it touches the line L and the circle $$C_1$$ externally, such that both the circles are on the same side of the line, then the locus of centre of the circle is

ellipse

hyper bola

parabola

pair of straight line

IIT-JEE 2006

MCQ (Single Correct Answer)

-1.25

A line L' through A is drawn parallel to BD. Point S moves such that its distances from the BD and the vertex A are equal. If locus of S cuts L' at $$T_2$$ and $$T_3$$ and AC at $$T_1$$, then area of $$\Delta \,{T_1}\,{T_2}\,{T_3}$$ is

$${1 \over 2}\,sq.\,units$$

$${2 \over 3}\,sq.\,units$$

1 sq. units

2 sq.units

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