1
JEE Advanced 2021 Paper 2 Online
+3
-1
Let $$M = \{ (x,y) \in R \times R:{x^2} + {y^2} \le {r^2}\}$$, where r > 0. Consider the geometric progression $${a_n} = {1 \over {{2^{n - 1}}}}$$, n = 1, 2, 3, ...... . Let S0 = 0 and for n $$\ge$$ 1, let Sn denote the sum of the first n terms of this progression. For n $$\ge$$ 1, let Cn denote the circle with center (Sn$$-$$1, 0) and radius an, and Dn denote the circle with center (Sn$$-$$1, Sn$$-$$1) and radius an.
Consider M with $$r = {{1025} \over {513}}$$. Let k be the number of all those circles Cn that are inside M. Let l be the maximum possible number of circles among these k circles such that no two circles intersect. Then
A
k + 2l = 22
B
2k + l = 26
C
2k + 3l = 34
D
3k + 2l = 40
2
JEE Advanced 2021 Paper 2 Online
+3
-1
Let $$M = \{ (x,y) \in R \times R:{x^2} + {y^2} \le {r^2}\}$$, where r > 0. Consider the geometric progression $${a_n} = {1 \over {{2^{n - 1}}}}$$, n = 1, 2, 3, ...... . Let S0 = 0 and for n $$\ge$$ 1, let Sn denote the sum of the first n terms of this progression. For n $$\ge$$ 1, let Cn denote the circle with center (Sn$$-$$1, 0) and radius an, and Dn denote the circle with center (Sn$$-$$1, Sn$$-$$1) and radius an.
Consider M with $$r = {{({2^{199}} - 1)\sqrt 2 } \over {{2^{198}}}}$$. The number of all those circles Dn that are inside M is
A
198
B
199
C
200
D
201
3
JEE Advanced 2021 Paper 1 Online
+3
-1
Consider a triangle $$\Delta$$ whose two sides lie on the x-axis and the line x + y + 1 = 0. If the orthocenter of $$\Delta$$ is (1, 1), then the equation of the circle passing through the vertices of the triangle $$\Delta$$ is
A
x2 + y2 $$-$$ 3x + y = 0
B
x2 + y2 + x + 3y = 0
C
x2 + y2 + 2y $$-$$ 1 = 0
D
x2 + y2 + x + y = 0
4
JEE Advanced 2019 Paper 1 Offline
+3
-1
A line y = mx + 1 intersects the circle $${(x - 3)^2} + {(y + 2)^2}$$ = 25 at the points P and Q. If the midpoint of the line segment PQ has x-coordinate $$- {3 \over 5}$$, then which one of the following options is correct?
A
6 $$\le$$ m < 8
B
$$-$$3 $$\le$$ m < $$-$$1
C
4 $$\le$$ m < 6
D
2 $$\le$$ m < 4
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