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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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# a cylindrical vessel having diameter equal to its height is full of water which is poured into two identicle cylinderical vessel of diameter 42 cm and height 21 cm which are filled completely . find the diameter of cylindrical vessel

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