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CBSE Pre Board Class 10 2019 : Mathematics (St Xavier's Sr. Sec. School, Delhi) : Set 1

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Pre Board Examination 2019 Std. 10 15-01-2019 Set 1 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. The decimal expansion ofa rational number is of decimals? 43 24 53 will terminate after how many places 2. If the sum of zeros of a quadratic polynomial p(x)=(k2 14)x2 2x 12is 1, find the value of k. 3. If the quadratic equation 2 2 5 + 15 = 0 has equal roots find the value of p. 4. For what value of k will + 9, 2 1, 2 + 1 are consecutive terms of an arithmetic progression. 5. A girl walks 500 km towards the east and then 1200km towards the north.Find her distance from the starting point. (OR) Is a triangle with sides 25m, 5cm and 24cm is a right triangle? Give reasons. 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 13 and 182 respectively.If one number is 26, find the other number. (OR) Show that 8 3is irrational given that 3is irrational. 8. If seven times seventh term of an AP is equal to eleven times of its eleventh term, find its 18th term. OR rd An AP consists 50 terms of which 3 term is 12 and last term is 106.Find the 29th term. 2 9. Find the zeroes of the quadratic polynomial 7x 175 and verify the relationship between zeros and coefficients. 10. For what value of p, will the following pair of linear equation have infinitely many solutions? (p 3) x + 3y = p px + py = 12 11. Find the coordinates of the point P which divides the join of A(-2,5) and B(3,5) in the ratio2:3. 12. Prove that: sin 3 + cos 3 sin +cos = 1 sin cos . MATHEMATICS (Set 1) Page 2 Std. 10 Section - C (3 10 = 30 marks) 13. Find mean for the following frequency distribution table: MARKS: No.of students: 14. 0 10 8 10 20 22 20 30 12 30 40 10 40 50 5 50 60 3 Construct triangle ABC with sides 6cm, 8cm, 9cm and then construct a triangle similar to it whose sides are 3 5 of the corresponding sidesof triangle ABC. 15. By using Euclid s divisionalgorithm 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. 16. In acubicalsolid metallic block of dimensions 15cm 10cm 5cm acylindrical hole of diameter 7cm is drilled out. Find thesurface area of the remaining block. (OR) From the top of a solid cone of height12cm and base radius 6cm a cone of height 4cm is removedby a plane parallel to its base.Find the lateral surface area of the remaining solid. 22 (use = , 5 = 2.236 ) 7 17. Prove that the area of an equilateral triangle described on one side of asquare is equal to half of thearea of equilateral triangle described on one of its diagonal. (OR) State and prove converse of Pythagoras theorem. 18. Prove that : = (OR) Prove that sin 2 3 2 cos 3 cos 2 2 1 sin cos . = tan . 19. From the top of a 7m high building angle of elevation of the top of a cable toweris 60o and angle of depression of its foot is 45o. Determine the height of the tower. 20. 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. 21. Find the area of minor segment of a circle of radius 42cm if the length of corresponding arc is 44cm. 22. 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. 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. Ifits speed is increased by 5km/hrfrom its usual speed, find the usual speed of the train. (OR) Solve for x : 1 + + 1 1 = + 1 + . MATHEMATICS (Set 1) 25. 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 26. Page 3 = 2 1 2 . 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. 27. 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. 28. Draw a pair of tangents to a circle of radius 5cm, which inclined to each other at an angle of 750. 29. 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 . 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 9m and 16m 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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