Single correct1 the value of a for which one root of eqn is twice of other is (A)-2/3 (B)1/3 (c)-1/3 (D)2/32 A regular 12-gon is inscribed in a circle of radius 1 unit. The sum of all possible distinct lengths of sides and diagonals can be written in form where and are positive integers, then is Note: If two lengths are same, consider it only once.(A) 11 (B) 4 (C) 6 (D) 73.f(x) is a polynomial of least degree such that , . Then f(10)=(A)1 (B)1/2 (C)1/10 (D)1/54. let have roots , ,then the value of =(A)3 (B)4 (C)7 (D)10

5. it is given that the polynomial has three distinct positive integer roots andP(14)=231. Let . It is also given that the polynomial P(Q(x)) has no real zeros,then |a|=(A)21 (B)43 (c)67 (D)916.evaluate where (A)50 (B)51 (C)100 (D)1027.number of positive real number x satisfying the

is k then =___? Where [.] is greatest integer function(A)0 (B)1 (C)2 (D)38. let S= the G.M. of the G.M’s of all non empty subsets of S is

(D)

9. In acute triangle ABC c > a > b the line IO (I: incentre, O: circumcentre) intersects the line segments(A) AB & AC (B) AC & BC (C) AB & BC (D) None of theseMulticorrect 10.two parabolas P1 : and P2: intersects at P &Q, tangent to at P to P1 and P2 intersects the axis of parabola at M and N respectively, then which of the following is/are true?(A)if MN=18, then radius of circum circle of tri.MPN is 9(B) distance b/w directrix of parabolas is 8(C) if cntre of circumcircle of tri MPN is (a,b) then |a|+|b|=7(D) FP,FN and FM are in H.P., where F is the focus of P2

11.the eqn has all its roots positive and real then(A) (B) (C) (D)

PSGA parabola touches both the axes and its focus is (3, 4). Then answer the following. 12. Equation of axis of this parabola is(A) 3x – 4y + 7 = 0 (B) 3x – 4y = 0 (C) 4x – 3y = 0 (D) None of these13. Length of its latus rectum is

(A) (B) (C) (D) 4814. The point where it touches the y – axis is

(A) (B) (C) (D)

PSG###in the fugure ABCD is a rectangle AB=4 and AD=3 units. Where AP,DP , BQ,CQ are the angular bisector of angle CAD, angle CDA, angle ABC, angle BCA respectively. PR and QS are the normal on diagonal AC , then15.the length of PR is(A)3/2 (B)2 (C)1 (D)none of these16.the length of RS is(A)1 (B)2 (C)3/2 (D) none of these

Integer type17. A point P moves in x – y plane such that maximum if the area of region bounded by point P is , then values of k is(Where points A, B & C are (0, 0), (1, 0), (2, 0) respectively)18. The vertices of ∆ ABC right angled at A are and

. If circumcentre of ∆ABC coincides with origin, then value of is 19 .From a point P tangents PA & PB are drawn to a circle S as shown. M is a point (any) on minor arc (AB). If perpendicular distances of M from PA & PB are 3 and 12 respectively. Then perpendicular distance of M from AB is