1
JEE Advanced 2021 Paper 2 Online
MCQ (Single Correct Answer)
+3
-1
Change Language
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
2
JEE Advanced 2021 Paper 1 Online
MCQ (Single Correct Answer)
+3
-1
Change Language
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
3
JEE Advanced 2019 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Change Language
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
4
IIT-JEE 2012 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1
A tangent PT is drawn to the circle $${x^2}\, + {y^2} = 4$$ at the point P $$\left( {\sqrt 3 ,1} \right)$$. A straight line L, perpendicular to PT is a tangent to the circle $${(x - 3)^2}$$ + $${y^2}$$ = 1.

A possible equation of L is

A
$${x - \sqrt 3 \,y = 1}$$
B
$${x + \sqrt 3 \,y = 1}$$
C
$${x - \sqrt 3 \,y = -1}$$
D
$${x + \sqrt 3 \,y = 5}$$
JEE Advanced Subjects
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12