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Std.X Walsingham House School PRELIMINARY EXAM MATHEMATICS Date 9/12/2019 Time 2 hrs M.M. 80 Answer to this paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this paper is the time allowed for writing the answers. Attempt all questions from section A and any four questions from section B. All working including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer. Omission of essential working will result in the loss of marks. The intended marks for questions or parts of the questions are given in brackets [ ]. Mathematics tables are provided. Section A ( 40 marks) ( Attempt all questions from this section ) Question 1. (a) Solve the following inequation and represent the solution set on a real number line. -2 + 10x 13x + 10 < 24 + 10x, x Z. [3] (b) A man invests ` 22,500 in `50 shares available at 10 % discount. If the dividend paid by the company is12 %. Calculate : (i) the number of shares purchased (ii) the annual dividend received (iii) the rate of return on his investment. [3] (c) The Printed price of an article is ` 60,000. The manufacturer of Nagpur allows a discount of 25% on the printed price to the wholesaler of Mumbai. The wholesaler sells it to retailer in Pune at a discount of 15 % on the printed price. The retailer sells it to the customer at printed price. If the rate of GST for all the sales is 18%, Find : (i) The price of the article paid by the wholesaler inclusive of the tax (under GST) (ii) The price of the article paid by the retailer inclusive of the tax (under GST) (iii) the amount of tax (under GST) paid by the wholesaler to the central government (iv) the amount of tax (under GST) paid by the retailer to the state government. [4] Question 2 (a) Use the factor theorem to factorise : f(x) = x3 + x2 4x 4. (b) Prove that: sin A (1 + tan A) + cos A (1 + cot A) = sec A + cosec A [3] [3] Cont. 2..
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