Circles — JEE Main Previous Year Questions · PaperYodha

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Circles · JEE Main previous year questions

211 questions asked across 20 exam years, newest first

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2005 6 questions

Q612005 · 28 Apr 2005 · Shift 1
A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is :
1. A.an ellipse
2. B.a circle
3. C.a hyperbola
4. D.a parabola
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Answer: D
Q722005 · 28 Apr 2005 · Shift 1
The plane $x + 2 y - z = 4$ cuts the sphere $x^{2} + y^{2} + z^{2} - x + z - 2 = 0$ in a circle of radius
1. A. $3$
2. B. $1$
3. C. $2$
4. D. $2$
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Answer: B

2004 4 questions

Q172004 · 24 Apr 2004 · Shift 1
If a circle passes through the point (a, b) and cuts the circle $x^{2} + y^{2} = 4$ orthogonally, then the locus of its centre is :
1. A. $2 a x - 2 b y - (a^{2} + b^{2} + 4) = 0$
2. B. $2 a x + 2 b y - (a^{2} + b^{2} + 4) = 0$
3. C. $2 a x - 2 b y + (a^{2} + b^{2} + 4) = 0$
4. D. $2 a x + 2 b y + (a^{2} + b^{2} + 4) = 0$
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Answer: B
Q182004 · 24 Apr 2004 · Shift 1
If the lines $2 x + 3 y + 1 = 0$ and $3 x - y - 4 = 0$ lie along diameters of a circle of circumference $10 π$ , then the equation of the circle is :
1. A. $x^{2} + y^{2} + 2 x - 2 y - 23 = 0$
2. B. $x^{2} + y^{2} - 2 x - 2 y - 23 = 0$
3. C. $x^{2} + y^{2} + 2 x + 2 y - 23 = 0$
4. D. $x^{2} + y^{2} - 2 x + 2 y - 23 = 0$
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Answer: D
Q192004 · 24 Apr 2004 · Shift 1
Intercept on the line y = x by the circle $x^{2} + y^{2} - 2 x = 0$ is AB. Equation of the circle on AB as a diameter is :
1. A. $x^{2} + y^{2} + x - y = 0$
2. B. $x^{2} + y^{2} - x + y = 0$
3. C. $x^{2} + y^{2} + x + y = 0$
4. D. $x^{2} + y^{2} - x - y = 0$
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Answer: D
Q572004 · 24 Apr 2004 · Shift 1
A variable circle passes through the fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter through A is :
1. A. $(y - q)^{2} = 4 p x$
2. B. $(x - q)^{2} = 4 p y$
3. C. $(y - p)^{2} = 4 q x$
4. D. $(x - p)^{2} = 4 q y$
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Answer: D

2002 5 questions

Q212002 · 27 Apr 2002 · Shift 1
If the chord y = mx + 1 of the circle $x^{2} + y^{2} = 1$ subtends an angle of measure $x^{2} + y^{2} = 9 a^{2}$ at the major segment of the circle then value of m is :
1. A. $2 \pm 2$
2. B. $- 2 \pm 2$
3. C. $- 1 \pm 2$
4. D.none of these
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Answer: D
Q222002 · 27 Apr 2002 · Shift 1
The equation of a circle with origin as a center and passing through an equilateral triangle whose median is of length $3 a$ is :
1. A. $x^{2} + y^{2} = 9 a^{2}$
2. B. $x^{2} + y^{2} = 16 a^{2}$
3. C. $x^{2} + y^{2} = 4 a^{2}$
4. D. $x^{2} + y^{2} = a^{2}$
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Answer: C
Q602002 · 27 Apr 2002 · Shift 1
The centres of a set of circles, each of radius 3, lie on the circle $x^{2} + y^{2} = 25$ . The locus of any point in the set is :
1. A. $4 \leq x^{2} + y^{2} \leq 64$
2. B. $x^{2} + y^{2} \leq 25$
3. C. $x^{2} + y^{2} \geq 25$
4. D. $3 \leq x^{2} + y^{2} \leq 9$
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Answer: A
Q612002 · 27 Apr 2002 · Shift 1
The centre of the circle passing through (0, 0) and (1, 0) and touching the circle $x^{2} + y^{2} = 9$ is :
1. A. $(\frac{1}{2}, \frac{1}{2})$
2. B. $(\frac{1}{2}, - 2)$
3. C. $(\frac{3}{2}, \frac{1}{2})$
4. D. $(\frac{1}{2}, \frac{3}{2})$
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Answer: B
Q622002 · 27 Apr 2002 · Shift 1
Two common tangents to the circle $x^{2} + y^{2} = 2 a^{2}$ and parabola $y^{2} = 8 a x$ are :
1. A. $x = \pm (y + 2 a)$
2. B. $y = \pm (x + 2 a)$
3. C. $x = \pm (y + a)$
4. D. $y = \pm (x + a)$
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Answer: B