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CBSE Class 10 Pre Board 2018 : Mathematics (St Xavier's Sr. Sec. School, Delhi) : Set 1

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ST. XAVIER'S SENIOR SECONDARY SCHOOL, DELHI - 110054 Pre-Board Examination 2018 in MATHEMATICS Set 1 Std. 10 18-01-2018 Max. Marks : 80 Time : 3 hrs. General Instructions: i) All questions are compulsory. ii) The question paper consists of 30 questions divided into four sections A, B, C and D. iii) Section A contains 6 questions of 1 mark each. Section B contains 6 questions of 2 marks each. Section C contains 10 questions of 3 marks each. Section D contains 8 questions of 4 marks each. iv) There is no overall choice. However, an internal choice has been provided in four questions of 3 marks each and three questions of 4 marks each. You have to attempt only one of the alternatives in all such questions. v) Use of calculators is not permitted. SECTION : A 2 45 3 20 1. Write whether 2. If the sum of the roots of the equation 3x - (3k - 2)x - (k - 6) = 0 is equal to the product of its roots, find the value of k. 3. Find the 20th term from the end of the A.P. 6, 10, 14, 18 ..174. 4. Write the coordinates of the reflections of the point (3, 5) along x and y axes. 5. In the given figure, PQ||BC and AP:PB = 1 : 2. 2 5 on simplification gives a rational or irrational number. 2 Find Ar.( APQ) . Ar.( ABC) A P B 6. If A+B = 900 and tan A = 3 4 Q C what is cot B? SECTION : B 7. Find the least number of square tiles required to pave the ceiling of a room 15m17cm long and 9m2cm broad, without any cutting of the tiles. 8. For what value of k will the following pair of linear equations have infinitely many solutions. 2x - 3y = 7 (k + 1)x + (1 - 2k)y = 5k - 4. 9. The sum of n terms of an A.P. is 10. If the vertices of a triangle are (1, -3), (4, p) and (-9, 7) and its area is 15sq. units, find the value of p. 11. Find the probability of getting 53 Fridays in an ordinary year. 5n2 3n . Find its 30th term. 2 2 12. 50 cards are made by writing numbers 0, 1, 2, 3 on it. If a card is drawn at random, find the probability that the number on the drawn card is a) a multiple of 5 or 10. b) a perfect square. Std. 10 -2- MATHEMATICS (Set - 1) SECTION : C 13. Prove that 5 is irrational. 14. What must be added to 4x + 2x - 2x + x - 1 so that the resulting polynomial is 2 divisible by x + 2x - 3. 15. Points A and B are 90 km apart from each other on a highway. A car starts from A and another from B at the same time. If they go in the same direction they meet in 9 hours 9 and if they go in opposite directions they meet in hours. Find their speeds. 7 16. In what ratio is the line segment joining the points (-2, -3) and (3, 7) divided by the y-axis? Also, find the coordinates of the point of division. (OR) A(1, -2), B(3, 6), C(5, 10) and D(3, 2) are the vertices of a parallelogram. Find the height of the parallelogram taking AB as the base. 4 3 2 B 17. BL and CM are medians of a triangle ABC right angled at A. 2 2 2 Prove that 4(BL + CM ) = 5BC (OR) C M A L ABC is right angled at B and D is the midpoint of BC. 2 2 2 Prove that AC = 4AD - 3AB A B C D 18. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle. 19. Without using trigonometric tables, evaluate, 2 2 5 cos ec2 58 cot 58 tan32 tan1337 tan 45 tan53 tan77 3 3 3 (OR) m2 1 sin . If sec tan m, prove that m2 1 20. In the given figure, ABC is a right angled triangle, B = 90o, AB = 28cm and BC = 21cm. With AC as diameter a semicircle is drawn and with BC as radius a quarter circle is drawn. Find the area of the shaded region correct to two decimal places. A 21. B C A right triangle, whose sides are 15cm and 20cm is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (use = 3.14) (OR) A cylindrical tub of radius 5cm and length 9.8cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed into the tub. If the radius of the hemisphere is 3.5cm and the height of the conical part is 5cm, find the volume of the water left in the tub. Std. 10 22. -3- MATHEMATICS (Set - 1) Find the mean of the following : Class Frequency 0 - 20 15 20 - 40 18 40 - 60 21 60 - 80 29 80 - 100 17 SECTION - D 23. A peacock is sitting on the top of a pillar, which is 9m high. From a point 27m away from the bottom of the pillar, a snake is coming to its hole at the base of the pillar. Seeing the snake the peacock pounces on it. If their speeds are equal, at what distance from the hole the snake caught? (OR) Find the discriminant of the equation 9x2 - 15x + 6 = 0 and hence write the nature of its roots. Find them, if they are real using the method of completing the square. 24. The sum of the first six terms of an arithmetic progression is 42. The ratio of its 10th term to its 30th term is 1:3. Calculate the first and 13th term of this A.P. 25. State and prove basic proportionality theorem. (OR) Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. 26. Draw a right triangle ABC in which AC = AB = 4.5cm and A = 90o. Draw a triangle 5 similar to ABC with its sides equal to th of the corresponding sides of ABC. 4 27. Prove that 28. A man standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 600. When he moves 40m away from the bank, he finds the angle of elevation to be 300. Find the height of the tree and the width of the river. 29. Jay Prakash, a juice seller has set-up his juice shop. He has two types of glasses of inner diameter 7cm to serve the customers. Type A : glass with a plane bottom & Type B: glass with hemispherical raised base of same radius. The height of both types of glasses is 10cm. He decided to serve the customers in type A of glasses. a) Find the volume of both type of glasses. b) By choosing a glass of type A, which value is depicted by the juice seller? 30. The mean of the following frequency distribution is 62.8 sin cos 1 1 . sin cos 1 sec tan Class Frequency 40 - 60 60 - 80 80 - 100 100 - 120 f 12 7 8 (OR) From the following frequency distribution, prepare the more than ogive: Score No. of 0 - 20 5 Find the missing frequency f. 400 - 450 20 20 - 40 8 450 - 500 35 500 - 550 40 550 - 600 32 600 - 650 24 650 - 700 27 candidates Also find the median from the ogive. -x-x-x-x-x-x-

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