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CBSE Pre Board Class 10 2019 : Mathematics (St Xavier's Sr. Sec. School, Delhi) : Set 2

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Pre Board Examination 2019 Std. 10 15-01-2019 Set 2 MATHEMATICS Max. Marks : 80 Time : 3 hrs. General Instructions: i) All the questions are compulsory. ii) The questions paper consists of 30 questions divided into 4 sections A, B, C and D. iii) Section A comprises of 6 questions of 1 mark each. Section B comprises of 6 questions of 2marks each. Section C comprises of 10 questions of 3 marks each. Section D comprises of 8questions of 4 marks each. iv) There is no overall choice. However, an internal choice has been provided in two questions of 1mark each, two questions of 2 marks each, four questions of 3 marks each and three questionsof 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 (1 6 = 6 marks) 1. 14587 The decimal expansion of the rational number, of decimals? 1250 will terminate after how many places 2. If one of the zeros of the quadratic polynomial p(x) = (k 1)x2 + kx + 1 is -3, find the value of k. 3. Find the value of p for whichthe equation px(x 6) + 6 = 0 has equal roots. 4. Find the 9th term from the end of the arithmetic progression 5, 9, 13, .... 185. 5. If sin + cosec = 5, evaluate sin2 + cosec2 . (OR) What happens to the value of cos when increases from 00 to 900? 6. If ABC ~ QRP, 9 = 4, AB = 18 cm, BC = 15 cm, find the length of PR. (OR) If the corresponding medians of 2 similar triangles are in the ratio 5:7, find the ratio of the corresponding sides. Section - B (2 6 = 12 marks) 7. The HCF and LCM of two numbers are 6 and 3024 respectively. If one number is 54, find the other number. (OR) Show that 3 + 7 is irrational given that 7 is irrational. 8. If seven times seventh term of an AP is equal to eleven times of its eleventh term, find its 18th term. (OR) Find the number of all 3 digit natural numbers which are divisible by 9. 9. For what value of p, will the following pair linear equation have infinitely many solutions? (p 3) x + 3y = p px + py = 12 10. Find the coordinates of the point P which divides the join of A( 2,5) and B(3,5) in the ratio 2:3. 11. Find the zeroes of the quadratic polynomial 3x2 75 and verify the relationship between its zeros and coefficients. 12. Prove that sin 3 + cos 3 sin +cos = 1 sin cos . MATHEMATICS (Set 2) Page 2 Std. 10 Section - C (3 10 = 30 marks) 13. By using Euclid s division algorithm find the largest number which divides 650 and 1170. (OR) In a school there are two sections of class10. There are 48 and60 students in section A and B respectively. Determine the least number of books required for the library of the school so that the books can be distributed equally among all the students of each section. 14. Prove that : = (OR) Prove that sin 2 3 2 cos 3 cos 2 2 1 sin cos . = tan . 15. Two different dice are rolled together. Find the probability of getting a) Even number on both dice b) Product of numbers on the both dice is a prime number. 16. Construct triangle ABC with sides 6cm, 8cm, 9cm and then construct a triangle similar to it whose sides are 3 5 of the corresponding sides of triangle ABC. 17. Find the area of minor segment of a circle of radius 42cm if the length of corresponding arc is 44cm. 18. Find mean for the following frequency distribution table: MARKS: No.of students: 19. 0 10 8 10 20 22 20 30 12 30 40 10 40 50 5 50 60 3 In a cuboidal solid metallic block of dimensions 15cm 10cm 5cm a cylindrical hole of diameter 7cm is drilled out. Find the surface area of the remaining block. (OR) From the top of a solid cone of height 12cm and base radius 6cm a cone of height 4cm is removed by a plane parallel to its base.Find the lateral surface area of the remaining solid. 22 (use = 7 , 5 = 2.236) 20. A person on tour has Rs 4200 for his expense, if he extends his tour for 3 days he has to cut down his daily expense by Rs 70.Find the original duration of the tour. 21. Prove that the area of an equilateral triangle described on one side of a square is equal to half of the area of equilateral triangle described on one of its diagonal. (OR) State and prove converse of Pythagoras theorem. 22. From the top of a 7m high building angle of elevation of the top of a cable tower is 60o and angle of depression of its foot is 45o. Determine the height of the tower. SECTION - D (4 8 = 32 marks) 23. Solve the following pair of linear equation graphically. Shade the region bounded by these lines and Y axis. x + 3y = 6 2x 3y = 12 24. A train takes 2 hours less for a journey of 300km. If its speed is increased by 5km/hr from its usual speed, find the usual speed of the train. (OR) Solve for x : 1 + + 1 1 = + 1 + . MATHEMATICS (Set 2) 25. Page 3 Std. 10 State the theorem of the relationship between the ratio of areas of similar triangles and their sides. If in ABC, XY || BC and it divides ABC into 2 parts of equal area. Using the above theorem prove that = 2 1 2 . 26. Draw a pair of tangents to a circle of radius 5cm, which inclined to each other at an angle of 750. 27. A bucket of height 8cm made up of copper sheet is in the form of a frustum of a right circular cone with radii of its lower and upper ends are 3 cm and 9 cm respectively. Calculate : a) Volume of bucket. b) Area of copper sheet required to make a bucket in terms of . 28. During the medical check up of 35 students of a class their weight were recorded as follows: WEIGHT in kg. NO. OF STUDENTS 38 40 40 42 42 44 44 46 46 48 48 50 50 52 3 2 4 5 14 4 3 Draw a less than type ogive from the given data. Hence obtain the median weight from the graph. 29. The coordinates of A, B, C and D are (6, 3), (-3, 5), (4, 2) and (k, 3k) respectively. If 1 = 2, find k. (OR) If the point P(k 1, 2) is equidistant from the points A(3, k) and B(k, 5); find the value of k. 30. The angles of depression from the top of 60 m high building to the base and top of a tower are 600 and 450 respectively. Find the height of the tower. (OR) Angles of elevation of the top of a tower from 2 points at a distance 9 m and 16 m from the base of the tower in the same side and same straight line are complementary. Find the height of the tower. -x-x-x-x-x-x-

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