1
JEE Advanced 2019 Paper 1 Offline
Numerical
+3
-0 Let the point B be the reflection of the point A(2, 3) with respect to the line $$8x - 6y - 23 = 0$$. Let $$\Gamma_{A}$$ and $$\Gamma_{B}$$ be circles of radii 2 and 1 with centres A and B respectively. Let T be a common tangent to the circles $$\Gamma_{A}$$ and $$\Gamma_{B}$$ such that both the circles are on the same side of T. If C is the point of intersection of T and the line passing through A and B, then the length of the line segment AC is .................
2
IIT-JEE 2011 Paper 2 Offline
Numerical
+2
-0
The straight line 2x - 3y = 1 divides the circular region $${x^2}\, + \,{y^2}\, \le \,6$$ into two parts.
If $$S = \left\{ {\left( {2,\,{3 \over 4}} \right),\,\left( {{5 \over 2},\,{3 \over 4}} \right),\,\left( {{1 \over 4} - \,{1 \over 4}} \right),\,\left( {{1 \over 8},\,{1 \over 4}} \right)} \right\}$$ then the number of points (s) in S lying inside the smaller part is
3
IIT-JEE 2009 Paper 2 Offline
Numerical
+3
-1
The centres of two circles $${C_1}$$ and $${C_2}$$ each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segement joining the centres of $${C_1}$$ and $${C_2}$$ and C a circle touching circles $${C_1}$$ and $${C_2}$$ externally. If a common tangent to $${C_1}$$ and passing through P is also a common tangent to $${C_2}$$ and C, then the radius of the circle C is
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