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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
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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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
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 ...
WB JEE 2022
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...
WB JEE 2022
If the equation of one tangent to the circle with centre at (2, $$-$$1) from the origin is 3x + y = 0, then the equation...
WB JEE 2022
A curve passes through the point (3, 2) for which the segment of the tangent line contained between the co-ordinate axes...
WB JEE 2022
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
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
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
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
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
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
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
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
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
Without changing the direction of the axes, the origin is transferred to the point (2, 3). Then the equation x2 + y2 $$-... WB JEE 2018 If one of the diameters of the curve x2 + y2$$-$$4x$$-$$6y + 9 = 0 is a chord of a circle with centre (1, 1), the ra... WB JEE 2017 The locus of the mid-points of the chords of the circle$${x^2} + {y^2} + 2x - 2y - 2 = 0$$, which make an angle of 90$$...
WB JEE 2017
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 ...
WB JEE 2017
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
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
The locus of the centre of a circle which passes through two variable points (a, 0), ($$-$$a, 0) is
WB JEE 2011
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
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
For the two circles x2 + y2 = 16 and x2 + y2 $$-$$ 2y = 0 there is/are...
WB JEE 2009
The circles x2 + y2 $$-$$ 10x + 16 = 0 and x2 + y2 = a2 intersect at two distinct points if...
WB JEE 2009
The equation of the chord of he circle $${x^2} + {y^2} - 4x = 0$$ whose midpoint is (1, 0) is
WB JEE 2009
The locus of the centres of the circles which touch both the axes is given by
WB JEE 2008
The circles $${x^2} + {y^2} + 6x + 6y = 0$$ and $${x^2} + {y^2} - 12x - 12y = 0$$
WB JEE 2008
The equation $$(x - {x_1})(x - {x_2}) + (y - {y_1})(y - {y_2}) = 0$$ represents a circle whose centre is
WB JEE 2008
The equation of the circle which passes through the points of intersection of the circles $${x^2} + {y^2} - 6x = 0$$ and...
WB JEE 2008

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