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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 .

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