New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Circle

29 questions · Mathematics · JEE Advanced

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Advanced
Mathematics
Circle

Circle

29 questions · Mathematics · JEE Advanced

Let the straight line $y = 2 x$ touch a circle with center $(0, α), α > 0$ , and radius $r$ at a point $A_{1}$ . Let $B_{1}$ be the point on the circle such that the line segment $A_{1} B_{1}$ is a diameter of the circle. Let $α + r = 5 + 5$ … Includes table2024 · Shift 1 · Q32 · MCQ
Let $A_{1}, A_{2}, A_{3}, \dots, A_{8}$ be the vertices of a regular octagon that lie on a circle of radius 2 . Let $P$ be a point on the circle and let $P A_{i}$ denote the distance between the points $P$ and $A_{i}$ for $i = 1, 2, \dots, 8$ . If $P$ …2023 · Shift 2 · Q28 · Numerical
Let $C_{1}$ be the circle of radius 1 with center at the origin. Let $C_{2}$ be the circle of radius $r$ with center at the point $A = (4, 1)$ , where $1 < r < 3$ . Two distinct common tangents $P Q$ and $S T$ of $C_{1}$ and $C_{2}$ are drawn. The…2023 · Shift 2 · Q30 · Numerical
Let $A B C$ be the triangle with $A B = 1, A C = 3$ and $∠ B A C = \frac{π}{2}$ . If a circle of radius $r > 0$ touches the sides $A B, A C$ and also touches internally the circumcircle of the triangle $A B C$ , then the value of $r$ is …2022 · Shift 1 · Q26 · Numerical
Let $G$ be a circle of radius $R > 0$ . Let $G_{1}, G_{2}, \dots, G_{n}$ be $n$ circles of equal radius $r > 0$ . Suppose each of the $n$ circles $G_{1}, G_{2}, \dots, G_{n}$ touches the circle $G$ externally. Also, for $i = 1, 2, \dots, n - 1$ …2022 · Shift 2 · Q30 · Multiple correct
Consider a triangle $Δ$ whose two sides lie on the x-axis and the line x + y + 1 = 0. If the orthocenter of $Δ$ is (1, 1), then the equation of the circle passing through the vertices of the triangle $Δ$ is2021 · Shift 1 · Q20 · MCQ
Consider the region R = {(x, y) $\in$ R $\times$ R : x $\geq$ 0 and y2 $\leq$ 4 $-$ x}. Let F be the family of all circles that are contained in R and have centers on the x-axis. Let C be the circle that has largest radius among the circles…2021 · Shift 2 · Q26 · Numerical
Consider the region R = {(x, y) $\in$ R $\times$ R : x $\geq$ 0 and y2 $\leq$ 4 $-$ x}. Let F be the family of all circles that are contained in R and have centers on the x-axis. Let C be the circle that has largest radius among the circles…2021 · Shift 2 · Q27 · Numerical
Let $M = {(x, y) \in R \times R : x^{2} + y^{2} \leq r^{2}}$ , where r > 0. Consider the geometric progression $a_{n} = \frac{1}{2 ^{n - 1}}$ , n = 1, 2, 3, ...... . Let S0 = 0 and for n $\geq$ 1, let Sn denote the sum of the first n…2021 · Shift 2 · Q32 · MCQ
Let $M = {(x, y) \in R \times R : x^{2} + y^{2} \leq r^{2}}$ , where r > 0. Consider the geometric progression $a_{n} = \frac{1}{2 ^{n - 1}}$ , n = 1, 2, 3, ...... . Let S0 = 0 and for n $\geq$ 1, let Sn denote the sum of the first n…2021 · Shift 2 · Q33 · MCQ
Let O be the centre of the circle x2 + y2 = r2, where $r > \frac{5}{2}$ . Suppose PQ is a chord of this circle and the equation of the line passing through P and Q is 2x + 4y = 5. If the centre of the circumcircle of the triangle…2020 · Shift 2 · Q21 · Numerical
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 $- \frac{3}{5}$ , then which one of the following options is correct?2019 · Shift 1 · Q21 · MCQ
Let the point B be the reflection of the point A(2, 3) with respect to the line $8 x - 6 y - 23 = 0$ . Let $Γ_{A}$ and $Γ_{B}$ be circles of radii 2 and 1 with centres A and B respectively. Let T be a common tangent to the circles $Γ_{A}$ …2019 · Shift 1 · Q32 · Numerical
Let S be the circle in the XY-plane defined the equation x2 + y2 = 4. Let E1E2 and F1F2 be the chords of S passing through the point P0 (1, 1) and parallel to the X-axis and the Y-axis, respectively. Let G1G2 be the chord of S passing…2018 · Shift 1 · Q33 · MCQ
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…2016 · Shift 1 · Q28 · Multiple correct
A circle S passes through the point (0, 1) and is orthogonal to the circles $(x - 1)^{2} + y^{2} = 16 an d x^{2} + y^{2} = 1$ . Then2014 · Shift 1 · Q22 · Multiple correct
Circle (s) touching x-axis at a distance 3 from the origin and having an intercept of length $27$ on y-axis is (are)2013 · Shift 2 · Q34 · Multiple correct
The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x - 5y = 20 to the circle $x^{2} + y^{2} = 9$ is2012 · Shift 1 · Q26 · MCQ
A tangent PT is drawn to the circle $x^{2} + y^{2} = 4$ at the point P $(3, 1)$ . A straight line L, perpendicular to PT is a tangent to the circle $(x - 3)^{2}$ + $y^{2}$ = 1 A common tangent of the two circles is2012 · Shift 2 · Q32 · MCQ
A tangent PT is drawn to the circle $x^{2} + y^{2} = 4$ at the point P $(3, 1)$ . A straight line L, perpendicular to PT is a tangent to the circle $(x - 3)^{2}$ + $y^{2}$ = 1. A possible equation of L is2012 · Shift 2 · Q33 · MCQ
The circle passing through the point (-1, 0) and touching the y-axis at (0, 2) also passes through the point.2011 · Shift 2 · Q24 · MCQ
The straight line 2x - 3y = 1 divides the circular region $x^{2} + y^{2} \leq 6$ into two parts. If $S = {(2, \frac{3}{4}), (\frac{5}{2}, \frac{3}{4}), (\frac{1}{4} - \frac{1}{4}), (\frac{1}{8}, \frac{1}{4})}$ …2011 · Shift 2 · Q25 · Numerical
Tangents drawn from the point P (1, 8) to the circle $x^{2} + y^{2} - 6 x - 4 y - 11 = 0$ touch the circle at the points A and B. The equation of the cirumcircle of the triangle PAB is2009 · Shift 1 · Q33 · MCQ
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 $C_{1}$ …2009 · Shift 2 · Q33 · Numerical
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 $3 x + y - 6 = 0$ and the point D is $(\frac{3 3}{2}, \frac{3}{2})$ …2008 · Shift 1 · Q38 · MCQ
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 $3 x + y - 6 = 0$ and the point D is $(\frac{3 3}{2}, \frac{3}{2})$ …2008 · Shift 1 · Q39 · MCQ
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 $3 x + y - 6 = 0$ and the point D is $(\frac{3 3}{2}, \frac{3}{2})$ …2008 · Shift 1 · Q40 · MCQ
Consider $L_{1} : 2 x + 3 y + p - 3 = 0 L_{2} : 2 x + 3 y + p + 3 = 0$ where p is a real number, and $C : x^{2} + y^{2} + 6 x - 10 y + 30 = 0$ STATEMENT-1 : If line $L_{1}$ is a…2008 · Shift 2 · Q37 · MCQ
Tangents are drawn from the point (17, 7) to the circle $x^{2} + y^{2} = 169$ . Statement 1 : The tangents are mutually perpendicular. Statement 2 : The locus of the points from which mutually perpendicular tangents can be drawn to the given circle…2007 · Shift 1 · Q33 · MCQ