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MCQ (More than One Correct Answer)
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Twenty metres of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of t...
WB JEE 2022
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Let P be a variable point on a circle C and Q be a fixed point outside C. If R is the midpoint of the line segment PQ, t...
WB JEE 2021
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MCQ (Single Correct Answer)
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A straight line meets the co-ordinate axes at A and B. A circle is circumscribed about the triangle OAB, O being the ori...
WB JEE 2022
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Two circles $${S_1} = p{x^2} + p{y^2} + 2g'x + 2f'y + d = 0$$ and $${S_2} = {x^2} + {y^2} + 2gx + 2fy + d' = 0$$ have a ...
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The side AB of $$\Delta$$ABC is fixed and is of length 2a unit. The vertex moves in the plane such that the vertical ang...
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If the equation of one tangent to the circle with centre at (2, $$-$$1) from the origin is 3x + y = 0, then the equation...
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A curve passes through the point (3, 2) for which the segment of the tangent line contained between the co-ordinate axes...
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Two tangents to the circle x2 + y2 = 4 at the points A and B meet at M($$-$$4, 0). The area of the quadrilateral MAOB, w...
WB JEE 2021
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The equation of circle of radius $$\sqrt {17} $$ unit, with centre on the positive side of X-axis and through the point ...
WB JEE 2020
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The locus of the centre of the circles which touch both the circles x2 + y2 = a2 and x2 + y2 = 4ax externally is...
WB JEE 2020
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If P(0, 0), Q(1, 0) and R$$\left( {{1 \over 2},{{\sqrt 3 } \over 2}} \right)$$ are three given points, then the centre o...
WB JEE 2019
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A variable circle passes through the fixed point A(p, q) and touches X-axis. The locus of the other end of the diameter ...
WB JEE 2019
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Let A be the centre of the circle $${x^2} + {y^2} - 2x - 4y - 20 = 0$$. Let B(1, 7) and D(4, $$-$$2) be two points on th...
WB JEE 2018
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A chord AB is drawn from the point A(0, 3) on the circle x2 + 4x + (y $$-$$ 3)2 = 0, and is extended to M such that AM =...
WB JEE 2018
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If one of the diameter of the circle, given by the equation x2 + y2 + 4x + 6y $$-$$ 12 = 0, is a chord of a circle S, wh...
WB JEE 2018
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The angle between a pair of tangents drawn from a point P to the circle x2 + y2 + 4x $$-$$ 6y + 9sin2$$\alpha$$ + 13cos2...
WB JEE 2018
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Without changing the direction of the axes, the origin is transferred to the point (2, 3). Then the equation x2 + y2 $$-...
WB JEE 2018
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If one of the diameters of the curve x2 + y2 $$-$$ 4x $$-$$ 6y + 9 = 0 is a chord of a circle with centre (1, 1), the ra...
WB JEE 2017
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The locus of the mid-points of the chords of the circle $${x^2} + {y^2} + 2x - 2y - 2 = 0$$, which make an angle of 90$$...
WB JEE 2017
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The common chord of the circles $${x^2} + {y^2} - 4x - 4y = 0$$ and $$2{x^2} + 2{y^2} = 32$$ subtends at the origin an ...
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If the coordinates of one end of a diameter of the circle $${x^2} + {y^2} + 4x - 8y + 5 = 0$$ is (2, 1), the coordinates...
WB JEE 2011
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The intercept on the line y = x by the circle x2 + y2 $$-$$ 2x = 0 is AB. Equation of the circle with AB as diameter is...
WB JEE 2011
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The locus of the centre of a circle which passes through two variable points (a, 0), ($$-$$a, 0) is
WB JEE 2011
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If the straight line y = mx lies outside of the circle x2 + y2 $$-$$ 20y + 90 = 0, then the value of m will satisfy...
WB JEE 2011
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The straight line x + y $$-$$ 1 = 0 meets the circle x2 + y2 $$-$$ 6x $$-$$ 8y = 0 at A and B. Then the equation of the ...
WB JEE 2010
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For the two circles x2 + y2 = 16 and x2 + y2 $$-$$ 2y = 0 there is/are...
WB JEE 2009
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The circles x2 + y2 $$-$$ 10x + 16 = 0 and x2 + y2 = a2 intersect at two distinct points if...
WB JEE 2009
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The equation of the chord of he circle $${x^2} + {y^2} - 4x = 0$$ whose midpoint is (1, 0) is
WB JEE 2009
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The locus of the centres of the circles which touch both the axes is given by
WB JEE 2008
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The circles $${x^2} + {y^2} + 6x + 6y = 0$$ and $${x^2} + {y^2} - 12x - 12y = 0$$
WB JEE 2008
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The equation $$(x - {x_1})(x - {x_2}) + (y - {y_1})(y - {y_2}) = 0$$ represents a circle whose centre is
WB JEE 2008
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The equation of the circle which passes through the points of intersection of the circles $${x^2} + {y^2} - 6x = 0$$ and...
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