Question
Sat December 31, 2011

# answer the following: (1)From each corner of a square of side 4cm a quadrant ofa circle of radius 1cm is cut and also a circle of diameter 2m is cut .find the remaining portion of the square. (2)The base radius and height of a right circular solid cone are 2cm and 8cm respectively.It is melted and recast into spheres of diameter 2cm each.Find the number of spheres so formed. (3)For what value of k the poimts A(1,5),B(k,1) and C(4,11) are collinear? (4)All cards of ace,jacks and queen are removed from a deck of playing cards.One card is drawn at random from the remaining cards.Find the probability that the card drawn is [a]a face card [b]not a face card. (5)Prove that no matter what the real numbers a&b are,the sequence with nth term a+nb is always A.P.What is the common difference?What is sum of the first 20 terms?

Sun January 01, 2012
(1) Area of square  = 42 = 16 cm2
Area of 4 quadrants of radius 1 cm = area of 1 circle of radius 1 cm = pi(1)2 = pi
Also, area of 1 circle of radius 1 cm = pi(1)2 = pi
Area of remaining part = 16 - 2(pi) = 16 - 2(3.14) = 9.72 cm2

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