Marks ::Correct Answers ::Remarks !Wrong Answers ::AnsAnsAns

Question : If a cicrcle passes through the points of intersection of the lines 2x-y
+1=0 and x+λy-3=0, with the axes of reference then the value of λ is : 1/2. 1. -1 -2

Question : Two circles, each of radius 5, have a common tangent at (1, 1) whose equation is 3x+34y-7+0. Then their
center are (4, -5), (-2, 3) (4, 5), (-2, 5) (4, 5), (-2, -3) None of these

Question : The number of points an the circles 2x^{2}+2y^{2}-3x=0 which area at a distance 2 from the point
(-2, 1) is : 2 1 0 None

Question : If (2, 4) is a point interior to the circle x^{2}+y^{2}-6x+10y+λ=0 and the circle
does not cut the axes at any point then λ belongs to the interval (25, 32) (9, 32) (3, + ф None

Question : Two distinct chords drawn from the point (p, q) on the circle x2+y2=px+qy, where pq is not equal
0 are bisected bu the x-axis. Then |p|= |q| p^{2}=8q^{2} p^{2}<8q^{2} p^{2}>8q^{2}

Question : There are two circles whose equations are x^{2}+y^{2}-8x-6y+n^{2}=0, nεZ. If
the circles have exactly two common tangents then the number of possible values of n is : 2 8 9 None of these

Question : The number of common tangents to the circles x^{2}+y^{2}-6x-14y+48=0 and
x^{2}+y^{2-6x=0 is } 1 2 0 4

Question : The chords of contact of the pair of tangents to the circle x^{2}+y^{2}=1 drawn from any point on the line
2x+y=4 pass through the point: (1/2, 1/4) (1/4, 1/2) (1, 1/2) (1/2, 1)

Question : The number of feet of normal from the point (7,-4) to the circle
x^{2}+y^{2}=5 is 1 2 3 4

Question : Aline meets the coordinate axes in A and B. A circle is circumscirbed about the triangle OAB. If
the distances from A and B of the tangent to the circle at the origin be m and n, then the diameter of the
circle is: m(m+n) m+n n(m+n) m^{2}+n^{2}

Question : If the common chord of the circles x^{2}+(y-λ)^{2}=16 subtend a right
angle at the origin then λ is equal to 4 4(2)^{1/2} +-4(2)^{1/2} 8

Question : The common chord of the circle x^{2}+y^{2}+6x+8y-7=0 and a circle passing
through the origin ang touching the line y=x, always passes through the point: (-1/2, 1/2) (1, 1) (1/2, 1/2) None

Question : Two tangents to the circle x^{2}+y^{2}=4 at the points A and B meet at
P(-4, 0). The area of the quadrilateral PAOB, where O is the origin is 4 6(2)^{1/2} 4(3)^{1/2} None of these.

Question : A foot of the normal from the point (4, 3) to a circle is (2, 1) and a diameter of the circle is (2, 1)
and a diameter of the circle has the equation 2x-y=7. Then the equation of the circle is : x^{2}+y^{2}+2x-1=0 x^{2}+y^{2}-2x-1=0 x^{2}+y^{2}-2y-1=0 None

Question : The locus of the middle points of the chords of the circles x^{2}+y^{2}= 4a^{2}
which substains a right angle at the centre of the circle is : x+y =2a x^{2}+y^{2}=a^{2} x^{2}+y^{2}=2a^{2} x^{2}+y^{2}=x+y

Question : The angle between a pair of tangents drawn from a point P to the curve x^{2}+y^{2}+4x-6y
+9sin^{2}Ө+13cos^{2}Ө=0 is 2Ө. The locus of P is x^{2}+y^{2}+4x-6y+4 =0 x^{2}+y^{2}+4x-6y-9 =0 x^{2}+y^{2}+4x-6y-4 =0 x^{2}+y^{2}+4x-6y+9 =0

Question : The locus of the centres of the circles for which one end of diameter is (1, 1) while the other end
is on the line x+y=3 is x+y=1 2(x-y)=5 2x+2y=5 None of these.

Question : The locus of the centres of the circles paasing through the intersection of the circles
x^{2}+y^{2}=1 and x^{2}+y^{2}-2x+y+0 is A line whose eq. is x+2y=0 A line whose eq. is 2x-y=1 A circle A pair of lines

Question : The equation of the circle of radius 2(2)^{1/2} whose centre lies on the line x-y=0
and which touches the line x+y=4 and whose centres co-ordinates satisfies the inequality x+y>4 is x^{2}+y^{2}-8x-8y+24=0 x^{2}+y^{2}=8 x^{2}+y^{2}-8x+8y=24 None.

Question : If (x, 3) and (3, 5) are the extremities of a diameter of a circle with centre at (2x, y)
then the values of x and y are x=1, y=4 x=4, y=1 x=8, y=2 None of these.

Question : The point (1,4) lies inside the circle x^{2}+y^{2}-6x-10y+b=0 which
does not touch or interest the coordinate axes, then: 0

25

9

9

Question : An equilateral triangle is inscribed in the circle x^{2}+y^{2}=a^{2}
with the vertex at (a,o). The equation of the side opposite to this vertex is: 2x-a=0 x+a=0 2x+a=0 3x-2a=0

Question : An isoceles right angled triangle is inscribed in the circle x^{2}+y^{2}=r^{2}
. If the coordinates of an end of the hypotenuse are (a, b) the coordinates of the vertex are (-a, -b) (b, -a) (b, a) (-b, -a)

Question : If the polar of a point P with respect to the circle x^{2}+y^{2}
=a^{2} touches the circle (x-a)^{2}+y^{2}=a^{2}, then P lies on y^{2}-2ax=a^{2} y^{2}+2ax=a^{2} x^{2}-2ay=a^{2} x^{2}-2ay=a^{2}

Question : The equation of the normal at the point (2, 3) to the circles x^{2}+y^{2}
-2x-2y-3=0 is 2x+y-7=0 x+2y-3=0 2x-y-1=0 x-2y+1=0

Question : A line is drawn through the point P(3, 11) to cut the circles x^{2}
+y^{2}=9 at A and B. Then PA.PB is equal to 9 121 205 139

Question : The line 9x+y-28=0 is the chord of contact of the point P(h,k) with respect to the circle
2x^{2}+2y^{2}-3x+5y-7=0, for P(3, -1) P(3, 1) P(-3, 1) No value of P.

Question : The two circles x^{2}+y^{2}+2ax+c=0 and x^{2}+y^{2}
+2by+c=0 touching each other 1/a^{2}+1/b^{2}=1/c^{2} a^{2}+b^{2}=c^{2} 1/a^{2}-1/b^{2}=1/c^{2}) None.

Question : If the circles x^{2}+y^{2}+2x+2ky+6=0 and x^{2}+y^{2}
+2x+2ky+k=0 intersect orthogonally, then k is 2 or -3/2 -2 or -3 2 or 3/2 -2 or 3/2

Question : AThe circle x^{2}+y^{2}+4x-6y+9=0 undergoes the following transformation 3f(x, y)
-f(x+1, y)+f(x,y +1)=0 then the ratio of areas of the new circle is to original circle is: 1:2 2:1 1:1 None