**LEVEL – I **

11. If it is not possible to draw any tangent from the point (1/4, 1) to the parabola y^{2} = 4x cosθ + sin^{2}θ , then θ belongs to

(A) [-π/2 π/2]

(B) [-π/2 π/2] – {0}

(C) (-π/2 π/2) – {0}

(D) none of these

12. The number of focal chord(s) of length 4/7 in the parabola 7y^{2} = 8x is

(A) 1

(B) zero

(C) infinite

(D) none of these

13. The ends of line segment are P (1, 3) and Q (1, 1). R is a point on the line segment PQ such that PR : RQ = 1 : λ . If R is an interior point of parabola y^{2} = 4x, then

(A) λ ∈ (0, 1)

(B) λ ∈ (-3/5 , 1)

(C) λ ∈ (1/2 , 3/5)

(D) none of these

14. A set of parallel chords of the parabola y^{2} = 4ax have their mid points on

(A) any straight line through the vertex

(B) any straight line through the focus

(C) a straight line parallel to the axis

(D) another parabola

15. The equation of the line of the shortest distance between the parabola y^{2} = 4x and the circle x^{2} + y^{2} – 4x – 2y + 4 = 0 is

(A) x + y = 3

(B) x – y = 3

(C) 2x + y = 5

(D) none of these

16. If normals are drawn from the extremities of the latus rectum of a parabola then normals are

(A) parallel to each other

(B) perpendicular to each other

(C) intersect at the 450

(D) none of these

17. The triangle formed by the tangent to the parabola y = x^{2} at the point whose abscissa is k where k ∈ [1, 2] the y-axis and the straight line y = k^{2} has greatest area if k is equal to

(A) 1

(B) 3

(C) 2

(D) none of these

18. A parabola y^{2} = 4ax and x^{2} = 4by intersect at two points. A circle is passed through one of the intersection point of these parabola and touch the directrix of first parabola then the locus of the centre of the circle is

(A) straight line

(B) ellipse

(C) circle

(D) parabola

19. A circle with centre lying on the focus of the parabola y^{2} = 2px such that it touches the directrix of the parabola. Then a point of intersection of the circle and the parabola is

(A) (p/2 , p)

(B) (p/2 , 2p)

(C) (-p/2 , p)

(D) (-p/2 , -p)

20. The locus of a point divides a chord of slope 2 of the parabola y^{2} = 4x internally in the ratio 1 : 2 is

(A)

(B)

(C)

(D)

__ANSWER:__

**11. C 12. B 13. A 14. C 15. A 16. B 17. C 18. D 19. A 20. B **