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THE BISHOP S CO-ED. SCHOOL, KALYANI NAGAR - PUNE SECOND PRELIMINARY EXAMINATION (2019-2020) MATHEMATICS CLASS: 10 TOTAL MARKS: 80 READING TIME: 15 MINUTES WRITING TIME: 2 HOURS DATE: 02-12-2019 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 loss of marks. The intended marks for questions or parts of questions are given in brackets ( ). SECTION A (40 MARKS) Answer all questions from this section Question 1: (a) Solve the following inequation and represent it on a number line 1 1 2 2 -5 - x 1 - 3x 3 - x, x R (3) 2 (b) Amit deposits 1,600 per month in a bank for one and a half year in a recurring deposit account. If he gets 31,080 at the time of maturity, what is the rate of interest per annum? (3) (c) The mean of the following distribution is 49. Find the missing frequency 'a' (4) Class interval 0-20 20-40 40-60 60-80 Frequency 15 20 30 a 80-100 10 Question 2: (a) Find a if the polynomials ax3 + 3x2 - 9 and 2x3 + 4x + a, leave the same remainder when divided by x + 3. Hence find the remainder. (3) 2 2 2 2 (b) Prove that tan + cot + 2 = sec . cosec (3) (c) A manufacturer sells a TV to a dealer for 18,000 and the dealer sells it to a customer at a profit of 1,500.If the sales are intra-state and rate of GST is 12%,find: i) the amount of GST paid by the dealer to the State Government. ii) the amount of GST received by Central Government. iii)amount paid by the customer for purchasing the TV (4) Question 3: (a) For what value of n, are nth terms of two A.Ps 63,65,67,......and 3,10,17,.....are equal? Also find that term. (3) (b) Find the ratio in which the line joining (-2,5) and (-5,-6) is divided by the line y =-3. Hence find the point of intersection. (3) (c) Suresh invested equally in two companies A and B. 100 shares of company A are available at 10% premium and it pays 8% dividend whereas 50 shares of company B are available at 12% discount and it pays 7% dividend. If the total income from both the companies is 1340,find how much, in all does he invest? (4) Page 1 of 3
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