(a) Find the probability that a player can get the bookmarks.
(b) If the game stall owner expects the probability of any player winning the bookmarks to be 1/3, what is the distance (in cm) between any two parallel lines should be
(c) In order to make the game more attractive, a player is allowed to throw another CD of diameter 6 cm but the distance between any two parallel lines is kept at 16m. If the CD of diameter 6 cm lies between two parallel lines, the player hets 3 bookmarks, otherwise he/she gets nothing. Nelson wants to get as many bookmarks as possible, which CD ( the one of the diameter 6 cm or that of diameter 12 cm ) should he choose to throw?
5(a)Show that the points (-1,0) and (1,0) are on the same side of the line y=x-3
(b)Find the equations of the two circles each passing through the points (-1,0) , (1,0) and
touching the line y=x+3
(c)Find the equation of the circle which passes through A(0,4) and B(8,0) and has its centre on the x-axis.If the point C lies on the circumference of the circle, find the greastest possible area of triangle ABC.
Q1:Find the equation of the common tangent to the circles x^2+y^2-6x-16=0 and x^2+y^2+6x-40=0
Q2:The circles C1:x^2+y^2-4x+2y+1=0 , C2:x^2+y^2-10x-4y+19=0
having a common chord AB.
P(x,y) is a variable pt such that
distance form P to centre of C1/distance from P to centre of C2=1/k (k>0)
Find the value of k if P lies on a st.line.
Q1Two fair dice are tossed. It is known that the sum of the two numbers obtained is an even number. Fing the probability that at least a '4' is obtained.
Q2Six balls A, B, C, D, E and F are put into six boxes numbered 1, 2, 3, 4, 5, and 6. If only one ball can be put into each box, what is the probability that ball A is not in box 1 and ball B is not in box 6?
A right circular cone is inscribed in a sphere of radius Rcm.Suppose r1cm,h1cm and V1cm^3 are radius ,height and volume of the circular cone respectively.
(a)Express r1 in terms of R and h1.Hence, show that V=1/3兀h1^2(2R-h1),where 0<2R
(b)Find h1, so that the cone has the maximum volume.
(c)Suppose the sphere is inscribed in another right circular cone with radius r2cm,height h2cm and volume V2cm^3.
(1) show that V2=1/3兀R^2(h2^2/(h2-2R)), where 2R<+infinite
consider 4 straight lines
L1:x+y-4=0 , L2:x-y-2=0 , L3:x+y-6=0 ,L4:x-y=0
let d1,d2,d3,d4 be the perpendicular distances from a moving pt P to lines
L1-L4 respectively.then the locus of P is x^2+y^2-6x-4y+14 =k (where k is real)
Find the value of k such that the circle touches the four given lines