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MATHEMATICS (Two hours and a half) 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 reading the question paper. The time given at the head of this paper is the time allowed for writing the answers. Attempt all the questions in Section A and any 4 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 loss of marks. The intended marks for questions is given in the brackets [ ]. Mathematical tables will be provided. SECTION A (40 marks) Attempt all the questions from this section Question 1 (a) A shopkeeper in Delhi buys an article at the printed price of 24,000 from a wholesaler in Mumbai. The shopkeeper sells the article to a consumer on Delhi at a profit of 15% on the basic cost price. If the rate of GST is 12%, find: (i) The price inclusive of tax (under GST) at which the wholesaler bought the article. (ii) The amount which the consumer pays for the article. (iii) The amount of tax (under GST) received by the state government of Delhi. (iv) The amount of tax (under GST) received by the Central government. (b) The midpoint of the line segment joining A (i) +1 2 , 2 [4] and B (x + 1, y 3) is C (5, -2). Find the value of x and y. (ii) The co-ordinates of the point D that divides the line segment AB in the ratio 2 : 5. [3] (c) (3x + 5) is a factor of the polynomial (a 1)x3 + (a + 1)x2 (2a + 1)x 15. Find the value of a . For this value of a , factorize the given polynomial completely. [3] 1 Turn Over
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