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10th I.C.S.E. Kewal Sir & Dhaval Sir Rudra s Academy Mathematics Preliminary Exam [Time: 2.5 hrs] [Marks: 80] [Set - 3] Section I All Questions are Compulsory Q.1) a] Show that 2 x 3 is a factor of 2 x3 19 x2 38x 21 .Hence factorise 2 x3 19 x2 38x 21 b] Two isosceles triangles have equal vertical angles and their areas are in the ratio 16:25. Find the ratio of their corresponding heights. c] Following toy is made by joining the three solid parts, a cone, a cylinder and a hemisphere. Mr. Pranit initially completely painted all three parts individually and then joined them as shown in the figure. If the cost of painting is Rs 19/- per sq.mm then how much could he save by first joining and then painting. [3] [3] [4] Q.2) a] In circle with center O, find x. [3] b] Mr. Vansh owns a tractor whose diameter of a fore wheel is 1.26 m, and diameter of the rare wheel is double the diameter of fore wheel. How far he would travels in 500 revolutions of rear wheel? How many revolutions are made by fore wheel during the journey? c] A x : 7 x 3 18x 51, x I and B x : 25 2 x 8x 19, x R . Find the range set A B & A B and represent it on a number line. Q.3) a] Mrs. Krishna has an account with The Bank of India. The following entries are from her pas book: Withdrawals Deposits Balance Date Particulars Rs P Rs P Rs P 08.02.06 B/F 8500.00 11.02.06 NEFT 6000.00 -------18.02.06 To Self 14000.00 -------12.04.06 By Online 2638.00 -------19.05.06 To LIC 941.00 -------31.05.06 LIC Maturity 11247.50 -------15.06.06 To Self 5000.00 -------08.08.06 By Cash 6000.00 -------Complete the above page of her pass book and calculate the interest for the six months, from February 2006 at 4.5%p.a. b] Socks of Mr. Darshil are observed from two points A and B 120 m apart on the either side of the tree. The sine of the angle of elevation from points A and B are 0.707 and 0.5 respectively. Find the height at which his socks are hanging. c] Find the co-ordinate of circumcenter of a triangle with vertices ( 2, 0), (2, 0) and (0, 2 3 ). ****Best of Luck**** Kewal Sir & Dhaval Sir [3] [4] [3] [3] [4] Page 1
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