1
JEE Advanced 2022 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Let $G$ be a circle of radius $R>0$. Let $G_{1}, G_{2}, \ldots, G_{n}$ be $n$ circles of equal radius $r>0$. Suppose each of the $n$ circles $G_{1}, G_{2}, \ldots, G_{n}$ touches the circle $G$ externally. Also, for $i=1,2, \ldots, n-1$, the circle $G_{i}$ touches $G_{i+1}$ externally, and $G_{n}$ touches $G_{1}$ externally. Then, which of the following statements is/are TRUE?
A
If $n=4$, then $(\sqrt{2}-1) r < R$
B
If $n=5$, then $r < R$
C
If $n=8$, then $(\sqrt{2}-1) r < R$
D
If $n=12$, then $\sqrt{2}(\sqrt{3}+1) r > R$
2
JEE Advanced 2016 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Let RS be the diameter of the circle $${x^2}\, + \,{y^2} = 1$$, where S is the point (1, 0). Let P be a variable point (other than R and S) on the circle and tangents to the circle at S and P meet at the point Q. The normal to the circle at P intersects a line drawn through Q parallel to RS at point E. Then the locus of E passes through the point (s)
A
$$\left( {{1 \over 3}\,,{1 \over {\sqrt 3 }}} \right)$$
B
$$\left( {{1 \over 4}\,,{1 \over 2}} \right)$$
C
$$\left( {{1 \over 3}\,, - {1 \over {\sqrt 3 }}} \right)$$
D
$$\left( {{1 \over 4}\,,-{1 \over 2}} \right)$$
3
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+3
-0
A circle S passes through the point (0, 1) and is orthogonal to the circles $${(x - 1)^2}\, + \,{y^2} = 16\,\,and\,\,{x^2}\, + \,{y^2} = 1$$. Then
A
radius of S is 8
B
radius of S is 7
C
centre of S is (- 7, 1)
D
centre of S is (- 8, 1)
4
JEE Advanced 2013 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Circle (s) touching x-axis at a distance 3 from the origin and having an intercept of length $$2\sqrt 7$$ on y-axis is (are)
A
$${x^2}\, + \,{y^2}\, - \,6x\,\, + 8y\, + 9 = 0$$
B
$${x^2}\, + \,{y^2}\, - \,6x\,\, + 7y\, + 9 = 0$$
C
$${x^2}\, + \,{y^2}\, - \,6x\,\, - 8y\, + 9 = 0$$
D
$${x^2}\, + \,{y^2}\, - \,6x\,\,- 7y\, + 9 = 0$$
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