**LEVEL – I **

1. If the straight line mx – y = 1 + 2x intersects the circle x^{2} + y^{2} = 1 at least at one point, then the set of values of m is

(A) (-4/3 , 0)

(B) (-4/3 , 4/3)

(C) (0 , 4/3)

(D) all of these

2. Circles are drawn having the sides of triangle ABC as their diameters. Radical centre of the circles is the

(A) Circumcentre of triangle ABC

(B) In centre of triangle ABC

(C) Orthocentre of triangle ABC

(D) Centroid of triangle ABC

3. The circle described on the line joining the points (0, 1), (a, b) as diameter cuts the x-axis at points whose abscissae are roots of the equation

(A) x^{2} + ax + b = 0

(B) x^{2} – ax + b = 0

(C) x^{2} + ax – b = 0

(D) x^{2} – ax – b = 0

4. The straight line y = mx + c cuts the circle x^{2} + y^{2} = a^{2} at real points if

(A) √[a^{2}(1+m^{2})] ≤|c|

(B) √[a^{2}(1-m^{2})] ≤|c|

(C) √[a^{2}(1+m^{2})] ≥|c|

(D) √[a^{2}(1-m^{2})] ≥|c|

5. The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x^{2} + y^{2} = 9 is

(A) (3/2 , 1/2)

(B) (1/2 , 3/2)

(C) (1/2 ,1/2)

(D) (1/2 , -√2)

6. If circles are drawn on the sides of the triangle formed by the lines x = 0, y = 0 and x + y = 2, as diameters, then the radical centre of three circles is

(A) (0, 0)

(B) (1, 1)

(C) (√2 , 1)

(D) None of these

7. The length of the chord cut off by y = 2x + 1 from the circle x^{2} + y^{2} = 2 is

(A) 5/6

(B) 6/5

(C) 6/√5

(D) √5/6

8. The coordinates of middle point of the chord 2x – 5y + 18 = 0 cut off by the circle x^{2} + y^{2} – 6x + 2y – 54 = 0 is

(A) (1, 4)

(B) (–4, 2)

(C) (4, 1)

(D) (6, 6) 9. The locus of the point, such that tangents drawn from it to the circle x^{2} + y^{2} – 6x – 8y = 0 are perpendicular to each other, is

(A) x^{2} + y^{2} – 6x – 8y –25 = 0

(B) x^{2} + y^{2} + 6x – 8y – 25 = 0

(C) x^{2} + y^{2} – 6x – 8y + 25 = 0

(D) none of these

10. The equation of circle touching the line 2x + 3y + 1 = 0 at the point (1, -1) and passing through the focus of the parabola y^{2} = 4x is

(A) 3x^{2} + 3y^{2} – 8x + 3y + 5 = 0

(B) 3x^{2} + 3y^{2} + 8x – 3y + 5 = 0

(C) x^{2} + y^{2} – 3x + y + 6 = 0

(D) none of these

### ANSWER :

1. D 2. C 3. B 4. C 5. D 6. A 7. C 8. A 9. A 10. A