Circles · JEE Main previous year questions

211 questions asked across 20 exam years, newest first

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2018 6 questions

Q232018 · 8 Apr 2018 · Shift 1
If the tangent at (1, 7) to the curve $x^{2} = y - 6$ touches the circle $x^{2} + y^{2} + 16 x + 12 y + c = 0$ , then the value of c is :
1. A. $95$
2. B. $195$
3. C. $185$
4. D. $85$
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Answer: A
Q252018 · 8 Apr 2018 · Shift 1
Tangent and normal are drawn at P(16, 16) on the parabola $y^{2} = 16 x$ , which intersect the axis of the parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and $∠ CPB = θ$ , then a value of $tan θ$ is :
1. A. $\frac{4}{3}$
2. B. $\frac{1}{2}$
3. C. $2$
4. D. $3$
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Answer: C

2017 5 questions

Q32017 · 9 Apr 2017 · Shift 1
The equation $Im (\frac{i z - 2}{z - i}) + 1 = 0$ , $z \in C$ , $z \neq = i$ represents a part of a circle having radius equal to :
1. A. $2$
2. B. $1$
3. C. $\frac{3}{4}$
4. D. $\frac{1}{2}$
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Answer: C
Q152017 · 9 Apr 2017 · Shift 1
A line drawn through the point $P (4, 7)$ cuts the circle $x^{2} + y^{2} = 9$ at the points A and B. Then $PA \cdot PB$ is equal to :
1. A. $53$
2. B. $56$
3. C. $74$
4. D. $65$
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Answer: B
Q112017 · 8 Apr 2017 · Shift 1
If a point P has co-ordinates $(0, - 2)$ and Q is any point on the circle, $x^{2} + y^{2} - 5 x - y + 5 = 0$ , then the maximum value of $(PQ)^{2}$ is :
1. A. $\frac{25 + 6}{2}$
2. B. $14 + 53$
3. C. $\frac{47 + 10 6}{2}$
4. D. $8 + 53$
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Answer: B
Q172017 · 8 Apr 2017 · Shift 1
If two parallel chords of a circle, having diameter 4units, lie on the opposite sides of the center and subtend angles $cos^{- 1} (\frac{1}{7})$ and $sec^{- 1} (7)$ at the center respectivey, then the distance between these chords, is :
1. A. $\frac{4}{7}$
2. B. $\frac{8}{7}$
3. C. $\frac{8}{7}$
4. D. $\frac{16}{7}$
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Answer: B
Q272017 · 8 Apr 2017 · Shift 1
If the common tangents to the parabola, $x^{2} = 4 y$ and the circle, $x^{2} + y^{2} = 4$ intersect at the point P, then the distance of P from the origin, is :
1. A. $2 + 1$
2. B. $2 (3 + 22)$
3. C. $2 (2 + 1)$
4. D. $3 + 22$
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Answer: C

2016 4 questions

Q62016 · 3 Apr 2016 · Shift 1
If one of the diameters of the circle, given by the equation, $x^{2} + y^{2} - 4 x + 6 y - 12 = 0$ , is a chord of a circle $S$ , whose centre is at $(- 3, 2)$ , then the radius of $S$ is :
1. A. $5$
2. B. $10$
3. C. $52$
4. D. $53$
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Answer: D
Q82016 · 3 Apr 2016 · Shift 1
A wire of length 2 units is cut into two parts which are bent respectively to form a square of side $= x$ units and a circle of radius $= r$ units. If the sum of the areas of the square and the circle so formed is minimum, then:
1. A. $x = 2 r$
2. B. $2 x = r$
3. C. $2 x = (π + 4) r$
4. D. $(4 - π) x = π r$
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Answer: A
Q222016 · 3 Apr 2016 · Shift 1
The centres of those circles which touch the circle, $x^{2} + y^{2} - 8 x - 8 y - 4 = 0$ , externally and also touch the $x$ -axis, lie on :
1. A.a circle
2. B.an ellipse which is not a circle
3. C.a hyperbola
4. D.a parabola
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Answer: D
Q232016 · 3 Apr 2016 · Shift 1
Let $P$ be the point on the parabola, $y^{2} = 8 x$ which is at a minimum distance from the centre $C$ of the circle, $x^{2} + (y + 6)^{2} = 1$ . Then the equation of the circle, passing through $C$ and having its centre at $P$ is:
1. A. $x^{2} + y^{2} - \frac{x}{4} + 2 y - 24 = 0$
2. B. $x^{2} + y^{2} - 4 x + 9 y + 18 = 0$
3. C. $x^{2} + y^{2} - 4 x + 8 y + 12 = 0$
4. D. $x^{2} + y^{2} - x + 4 y - 12 = 0$
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Answer: C

2015 1 question

Q232015 · 4 Apr 2015 · Shift 1
The number of common tangents to the circles $x^{2} + y^{2} - 4 x - 6 y - 12 = 0$ and $x^{2} + y^{2} + 6 x + 18 y + 26 = 0$ , is :
1. A. $3$
2. B. $4$
3. C. $1$
4. D. $2$
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Answer: A

2014 1 question

Q242014 · 6 Apr 2014 · Shift 1
Let $C$ be the circle with centre at $(1, 1)$ and $radius = 1$ . If $T$ is the circle centred at $(0, y)$ , passing through origin and touching the circle $C$ externally, then the radius of $T$ is equal to :
1. A. $\frac{1}{2}$
2. B. $\frac{1}{4}$
3. C. $\frac{3}{2}$
4. D. $\frac{3}{2}$
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Answer: B

2012 3 questions

Q242012 · 26 May 2012 · Shift 1
The number of common tangents of the circles given by $x^{2} + y^{2} - 8 x - 2 y + 1 = 0$ and $x^{2} + y^{2} + 6 x + 8 y = 0$ is
1. A.one
2. B.four
3. C.two
4. D.three
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Answer: C
Q192012 · 7 May 2012 · Shift 1
The parabola $y^{2} = x$ divides the circle $x^{2} + y^{2} = 2$ into two parts whose areas are in the ratio
1. A. $9 π + 2 : 3 π - 2$
2. B. $9 π - 2 : 3 π + 2$
3. C. $7 π - 2 : 2 π - 3$
4. D. $7 π + 2 : 3 π + 2$
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Answer: B
Q242012 · 7 May 2012 · Shift 1
The equation of the circle passing through the point $(1, 2)$ and through the points of intersection of $x^{2} + y^{2} - 4 x - 6 y - 21 = 0$ and $3 x + 4 y + 5 = 0$ is given by
1. A. $x^{2} + y^{2} + 2 x + 2 y + 11 = 0$
2. B. $x^{2} + y^{2} - 2 x + 2 y - 7 = 0$
3. C. $x^{2} + y^{2} + 2 x - 2 y - 3 = 0$
4. D. $x^{2} + y^{2} + 2 x + 2 y - 11 = 0$
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Answer: D

2010 2 questions

Q72010 · 25 Apr 2010 · Shift 1
The circle $x^{2} + y^{2} = 4 x + 8 y + 5$ intersects the line $3 x - 4 y = m$ at two distinct points if :
1. A. $- 35 < m < 15$
2. B. $15 < m < 65$
3. C. $35 < m < 85$
4. D. $- 85 < m < - 35$
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Answer: A
Q262010 · 25 Apr 2010 · Shift 1
For a regular polygon, let $r$ and $R$ be the radii of the inscribed and the circumscribed circles. A false statement among the following is :
1. A.There is a regular polygon with $\frac{r}{R} = \frac{1}{2}$
2. B.There is a regular polygon with $\frac{r}{R} = \frac{2}{3}$
3. C.There is a regular polygon with $\frac{r}{R} = \frac{3}{2}$
4. D.There is a regular polygon with $\frac{r}{R} = \frac{1}{2}$
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Answer: B

2009 1 question

Q242009 · 27 Apr 2009 · Shift 1
If $P$ and $Q$ are the points of intersection of the circles $x^{2} + y^{2} + 3 x + 7 y + 2 p - 5 = 0$ and $x^{2} + y^{2} + 2 x + 2 y - p^{2} = 0$ then there is a circle passing through $P, Q$ and $(1, 1)$ for :
1. A.all except one value of $p$
2. B.all except two values of $p$
3. C.exactly one value of $p$
4. D.all values of $p$
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Answer: A

2006 2 questions

Q132006 · 29 Apr 2006 · Shift 1
If the lines $3 x - 4 y - 7 = 0$ and $2 x - 3 y - 5 = 0$ are two diameters of a circle of area $49 π$ square units, the equation of the circle is :
1. A. $x^{2} + y^{2} + 2 x - 2 y - 47 = 0$
2. B. $x^{2} + y^{2} + 2 x - 2 y - 62 = 0$
3. C. $x^{2} + y^{2} - 2 x + 2 y - 62 = 0$
4. D. $x^{2} + y^{2} - 2 x + 2 y - 47 = 0$
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Answer: D
Q142006 · 29 Apr 2006 · Shift 1
Let $C$ be the circle with centre $(0, 0)$ and radius 3 units. The equation of the locus of the mid points of the chords of the circle $C$ that subtend an angle of $\frac{2 π}{3}$ at its center is :
1. A. $x^{2} + y^{2} = \frac{3}{2}$
2. B. $x^{2} + y^{2} = 1$
3. C. $x^{2} + y^{2} = \frac{27}{4}$
4. D. $x^{2} + y^{2} = \frac{9}{4}$
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Answer: D

2005 6 questions

Q132005 · 28 Apr 2005 · Shift 1
If the circles $x^{2} + y^{2} + 2 a x + cy + a = 0$ and $x^{2} + y^{2} - 3 a x + d y - 1 = 0$ intersect in two distinct points P and Q then the line 5x + by - a = 0 passes through P and Q for :
1. A.exactly one value of a
2. B.no value of a
3. C.infinitely many values of a
4. D.exactly two values of a
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Answer: B
Q142005 · 28 Apr 2005 · Shift 1
If a circle passes through the point (a, b) and cuts the circle $x^{2} + y^{2} = p^{2}$ orthogonally, then the equation of the locus of its centre is :
1. A. $x^{2} + y^{2} - 3 a x - 4 b y + (a^{2} + b^{2} - p^{2}) = 0$
2. B. $2 a x + 2 b y - (a^{2} - b^{2} + p^{2}) = 0$
3. C. $x^{2} + y^{2} - 2 a x - 3 b y + (a^{2} - b^{2} - p^{2}) = 0$
4. D. $2 a x + 2 b y - (a^{2} + b^{2} + p^{2}) = 0$
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Answer: D
Q152005 · 28 Apr 2005 · Shift 1
If the pair of lines $a x^{2} + 2 (a + b) x y + b y^{2} = 0$ lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then :
1. A. $3 a^{2} - 10 ab + 3 b^{2} = 0$
2. B. $3 a^{2} - 2 ab + 3 b^{2} = 0$
3. C. $3 a^{2} + 10 ab + 3 b^{2} = 0$
4. D. $3 a^{2} + 2 ab + 3 b^{2} = 0$
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Answer: D
Q232005 · 28 Apr 2005 · Shift 1
A spherical iron ball $10$ cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of $50 c m^{3}$ /min. When the thickness of ice is $5$ cm, then the rate at which the thickness of ice decreases is
1. A. $\frac{1}{36 π}$ cm/min
2. B. $\frac{1}{18 π}$ cm/min
3. C. $\frac{1}{54 π}$ cm/min
4. D. $\frac{5}{6 π}$ cm/min
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Answer: B