Sample Paper : II (2013-14) Std. : X Q:1 (a) (b) Q:2 (c) (a) (b) (c) Q : 3. (a) (b) (c) Q:4 Q:5 ( Two and Half hours ) Sub. : Mathematics SECTION : A (40 Marks) Answer all questions. Mr Ashok borrows Rs 50,000 from Bank of India at 10% p.a. compound interest. He repays Rs. 20,500 at the end of first year and Rs. 23,850 at the end of the second year. Find the amount outstanding at the beginning of the third year. (03) A dice is thrown once. What is the probability that (i) the number is odd, (ii) the number is greater than 3 ? (03) 2 Solve : 2x – 5x – 4 = 0 and give your answer correct to one decimal place. (04) Find x and y, if (03) 2x x 3 25 y 3y 2 26 What least number must be added to each of the numbers 5, 9, 11 and 19 so that they are in proportion? Given that x + 2 and x + 4 are factors of 3x2 + ax2 – 6x – b. Determine the values of a and b. Solve the inequation and represent the solution set on the number line 8x 11 –4+x< +1< + 2x, where x I. 3 3 Find the value of k for which the lines 2x + 3y – 7 = 0 and 4y – kx – 12 = 0 are perpendicular to each other. In the given figure, O is the centre of circle, BAD = 70° and chord BC = chord CD. Find : (i) BOC (ii) OBD (iii) BCD (a) Find the mean, median and mode of the following distribution: 15, 17, 12, 16, 10, 7, 16, 12, 19, 14, 16 (b) Without using trigonometric tables, evaluate the following : sec 27 tan 58 + cos2 54° + cos2 36° cos ec 63 cot 32 (03) (04) (03) (03) (04) (03) (03) (c) AC and BD are two perpendicular diameters of a circle with centre O. If AC = 21 cm, 22 calculate the area and perimeter of shaded part. (Take = ) (04) 7 SECTION : B (40 Marks) Answer any four questions. (a) A shopkeeper bought a T.V. at a discount of 30% of the listed price of Rs. 48,000. The shopkeeper offers a discount of 10% of the listed price to his customer. If the V.A.T. is 10%, find : (03) (i) the amount paid by the customer. (ii) the V.A.T. to be paid by the shopkeeper. (b) Without solving, examine the nature of roots of equation : (c) Use graph paper to answer the following questions: (i) Plot the points P(4, 6) and Q (1, 2). (ii) P' is the image of P when reflected in X-axis. (iii) Q' is the image of Q when Q is reflected in the line PP'. (iv) Give the geometrical name for the figure PQP'Q'. 3X2 – 5x + 2 = 0. (03) (04) Q:6 (a) In the given figure, ABC and CEF are two triangles where BA is parallel to CE and AF : FC = 5 : 9. (04) (i) Prove that ADF ~ CEF. (ii) Find AD if CE = 8 cm. (iii) If DF is parallel to BC, find area of ADF : area of ABC. (b) Prove the following identity : sin A 1 cos A = 2 cosec A. 1 cos A sin A (03) (c) The following table gives the wages of workers in a factory: Wages (in `) No. of workers 45 - 50 5 50 - 55 8 55 - 60 60 - 65 65 - 70 70 - 75 30 25 14 12 75 - 80 6 Calculate the mean by the short cut method. (03) Q : 7. (a) Mr Khanna invests Rs 54,000 in buying Rs 100 shares at Rs.20 premium. The dividend is 15% p.a. Find : (i) the number of shares he buys, (ii) his yearly dividend, (iii) the percentage return on his investment. (03) (b) What sum of money will amount to Rs 9,261 in 3 years at 5% p.a. compound interest? (03) (c) Mr Gupta has a savings bank account in Bank of Baroda. His passbook entries are as follows: (04) Withdrawals Deposits Balance Date Particulars (in Rs) (in Rs) (in Rs) Jan. 4, 2008 By cash — 10,000.00 10,000.00 Jan. 11, 2008 By cheque — 3,000.00 13,000.00 Feb. 3, 2008 By cash — 2,500.00 15,500.00 Feb. 7, 2008 To cheque 2,000.00 — 13,500.00 Mar. 3, 2008 By cash — 5,000.00 18,500.00 May 25, 2008 By cash — 2,000.00 20,500.00 June 10, 2008 To cheque 3,500.00 — 17,000.00 Aug. 29, 2008 To cheque 1,000.00 — 16,000.00 Rate of interest paid by the bank is 6% p.a. If Mr Gupta closes his account on 30th Oct. 2008, find the interest he receives. Q:8 a3 + 3ab2 63 (a) Given that 3 Using Componendo and Dividendo, find a : b b + 3a2b 62 (b) In the given figure, AB = 14 cm and BC = 18 cm. (i) Prove that ACD – DCB. (ii) Find the length of CD. (03) (03) (c) The given figure represents a hemisphere surmounted by a conical block of wood. The diameter of their bases is 10 cm each and the slant height of the cone is 13 cm. Calculate: (i) the height of the cone. (ii) the volume of the solid. Q:9 (04) (a) Find the ratio and point on y-axis which divide the line joining the points (–2, 5) and (1, –9). (03) (b) From two points P and Q on the same side of a building, the angles of elevation of the top of the building are 30° and 60° respectively. If the height of the building is 25 m, find the distance between P and Q correct to two decimal places. (03) (c) Marks obtained by 200 students in an examination are given below : Marks 0-10 No. of students 5 (04) 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 10 14 21 25 34 36 27 16 12 Draw an ogive for the given distribution taking 2 cm = 10 marks on one axis and 2 cm = 20 students on the other axis. From the graph, find: (i) the median, (ii) the upper quartile, (iii) number of students scoring above 75 marks, (iv) if 20 students qualify for merit scholarship, find the minimum marks required to qualify. Q : 10 (a) Mrs Nair deposits Rs 500 every month in a recurring deposit account for 3 years at 8% p.a. interest. Find the maturity value. (03) (b) Find the equation of a line with X-intercept = 6 and passing through the point (4, –7). (03) (c) In a school the weekly pocket money of 50 students is as follows: (04) Weekly pocket money (in `) No. of students 40-50 50-60 60-70 70-80 80-90 90-100 2 8 12 14 8 6 Draw a histogram and find the mode. Q : 11 (a) The model of a building is constructed with scale factor 1 : 50. (03) (i) If the height of the model is 60 cm, find the actual height of building in metres. (ii) If the actual area of a tank at the top of the building is 25 m2, find the area of the tank on the top of the model. (b) The speed of an express train is x km/hr and the speed of an ordinary tram is 8 km/hr less than that of express train. If the ordinary train takes two hours longer than the express train to cover a distance of 480 km, find the speed of express train. (03) (c) Using ruler and compass only, construct (i) a triangle ABC in which AB = 6 cm, BC = 4 cm and AC = 5 cm. (ii) the locus of points equidistant from A and C. (iii) a circle touching AB at A and passing through C. (04)

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