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CENTRAL MODERN SCHOOL Pre-Board Examination for ICSE - 2021 MATHEMATICS Class -X F.M. 8 0 Time 2 hrs. 30 min. [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. Attempt all questions from Section-A and any four questions from SectionB. All working including rough work must be clearly shown and must be done on the same sheet as the rest of the answers. The intended marks for questions or parts of questions are given in brackets [] [10X4=40] SECTION-A 1. a) If x 4V6 =2 + b) b) IfA = Xt2/2 find the value of x-2 2 B C . x+23 x-2 3 [ _ and 5A +2B = C find the values of a, b, c. c) c) AB is a diameter of the circle with centre O and CD|| BA. If LCAB=24 find the value of: i) 2COBii) 2DOC ii) 2DAC iv) ADC [3+3+4=10] D 24 A 2. a) The sum of the first 3 terms of an A.P is 33. If the product of the first and the third terms exceeds the second term by 29, find the A.P b) Solve c) 2a+b+2x L+2+ 2x 2a A girl of height 90cm is walking away from the base of a lamp post at a speed of 1.2 m/sec. f the lamp is 3.6m above the ground, find the length of her shadow after 4 seconds. [3+3+410] 3. a) A shopkeeper buys an article whose list price is Rs. 4500 at some rate of discount from a wnolesaler. He sells the article to a Page 1 of 4 consumer at the list price and charges GST at the rate of 12%. If the sales are intrastate and the shopkeeper has to pay tax (under GST) of Rs. 27, to the State Government, find the rate of discount at which he bought the article from the wholesaler. b) The sum of the radius and the height of a cylinder is 37 cm and the total surface area of the cylinder is 1628 cm. Find the height and volume of the cylinder. Cote+Cosec0-1 1+Cos C) Prove that: ) Cote-Cosec 0+1 Sin 6 1 i0) Sec A+Tan A Cos A Sec A-Tan A Cos A [3+3+4=10] n u m w u s 4. a) A gameisofdrawn members has cards with 11,12........ A Card at random. Findmarked t h e probability that the number , 440. 0 on the card drawn is (i) A perfect Square (i) Divisible by 7. b) A(2, 3), B(0, 4) and C(0, -5) are the vertices of triangle in the Cartesian plane () VWrite the c0ordinates of A1, the reflection of A in the x axis and Az, the reflection of A in the origin (i) Write down the coordinates of B,, the image of B by reflection in the y axis (ii) Name 2 pts which are invariant under reflection in the y axis. c) eu The following table gives the marks scored by students in an examination. AMakes No. of Students 0-5 5-10 3 7 10-15 15-20 20-25 25-30 30-35 35-40 15 24 8 16 5 2 Calculate the mean marks correct to 2 decimal places. 3+3+4=10 SECTION-B [10X4=40] (Attempt any four questions ) 5. a) Mrs. Mirza deposits Rs. 1500 per month in a bank for 1 year 6 months under the recurring Deposit Scheme. If the maturity value is Rs. 30,420. Find the rate of interest per annum. D)(X-2) is a factor of x'+ax+bx+6. When this expression is divided it leaves the remainder 3. Find the values of a & b. An aeroplane at an altitude of 1500 metres finds that 2 ships by x-3) c) are sailing towards it in the same direction. The angles of depression as observed from the aeroplane are 45 and 30"respectively, find the distance between the 2 6 [3+3+410] ships. a) Solve the following inequation, write the solution set and represent it on the numberline -3(x-7)215-7x>* xER Page 2 of 4 b) Find the equation of a straight line passing through the origin and through the point of intersection of the lines 5x+7y=3 and 2x-3y=7 c) Using step deviation method calculate the mean marks of the following distribution. Class intervals Frequency 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 5 20 10 10 9 6 12 8 [3+3+4-10] 7. a) Given12x -Y*27Using componendo and dividendo findx :y 6x2+8 9y2+27 b) In the adjoining figure medians AD and BE of AABC meet at the point G and DF is drawn parallel to BE. Prove that i) EF=FC i) AG:GD =2:1 c)Use graph paperfor this question. Plot the points O(0, 0), A(4,4) B(-3, 0) and C(0, -3) i) Reflect points A and B on the y axis and name them A' and B respectively. Write down their coordinates i) Name the figure OABCB'A'. [3+3+410] 8. a) Solve the equation 3x-x-7=0 using formula and give your answer correct to 2 decimal places. b) Three consecutive vertices of a parallelogram ABCD are A(1, 2), B(1,0) and C(4, 0). Find the fourth vertex D c) In the adjoining figure AD is a diameter, O is the centre of the circle, AD is parallel to BC 2CBD=32" find: i) 20BD, i) LAOB, ii) zBED, iv) 2OAB. (3+3+4 10] 32 Page 3 of 4 9 a) A card is drawn from a well shuffled deck of 52 cards. Find the probability that the card drawn is ()An ace, (i) Neither a king nor a queen (ii) a card of spade or an ace. b) The daily wages of 80 workers in a project are given below No. of workers Wages (Rs.) 450 500 2 6 500 550 12 550 600 18 600 650 24 650 7000 13 400 450 700 750 5 Use a graph paper to draw an Ogive for the above distribution. Use your Ogive to estimate: (i) the median wage (i) the lower quartile wage of workers (i) number of workers who earn more 4+(2+4)10] than Rs. 625 daily. 10. a) An aeroplane flying with a wind of 30 km/hr takes 40 minutes less to fly 3600km, than what it ould have taken to fly against the same wind. Find the plane's speed of flying in still air. b) Prove that: 2 sec6- sect0 2 cosec 0 + cosecte = cotta - tante c)Find the sum of integers between 100 and 200 that a c) in) not divisible by 9. i)divisible by 9 11.) A-2.B [ .c 2 3+3+4-10] find A+AC-5B b) Show that (2x+7) is a factor of 2x*+5x-11x-14. Hence factorise the given expression completely using factor theorem. c) The height of a cone is 30cm. A small cone is cut off at the tip by a plane parallel to its base. If .s volume beof the volume of the given cone, at what height above the base is the section cut? 3+3+4 10] --- X -----. Page 4 of 4
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