Circles · JEE Main previous year questions

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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
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