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CTZ3MEM SUMMATIVE ASSESSMENT – I, 2014 MATHEMATICS Class – X Time Allowed: 3 hours Maximum Marks: 90 General Instructions: 1. 2. 3. 4. All questions are compulsory. The question paper consists of 31 questions divided into four sections A, B, C and D. Section-A comprises of 4 questions of 1 mark each; Section-B comprises of 6 questions of 2 marks each; Section-C comprises of 10 questions of 3 marks each and Section-D comprises of 11 questions of 4 marks each. There is no overall choice in this question paper. Use of calculator is not permitted. SECTION-A Question numbers 1 to 4 carry one mark each 1 In PQR, if B and C are points on the sides PR and QR respectively such that RB10 cm, 1 PR18 cm, RC15 cm and CQ12 cm, then find whether BC is parallel to QR or not. 2 Evaluate : sin 30 cos 60 1 3 Express cosec 48 tan 88 in terms of t – ratios of angles between 0 and 45. 1 4 For a certain distribution mode and median were found to be 1000 and 1250 respectively. Find 1 mean for this distribution using an empirical relation. SECTION-B Question numbers 5 to 10 carry two marks each. 5 Page 1 of 5 Find the smallest natural number by which 1200 should be multiplied so that the square root of 2 the product is a rational number. 6 What is the decimal expansion of the rational number 201 250 2 ? 7 Check whether x34x23x2 is divisible by x2. 2 8 In the figure, EFAC, BC10 cm ,AB13 cm and EC2 cm, find AF. 2 9 Prove that : 2 sec4 sec2 tan4 tan2 10 Given below is the distribution of monthly salary of workers in a factory. Calculate the modal 2 salary. Salary (inRs.) 4000 to 6000 Number of 21 workers 6000 to 8000 8000 to 1000 0 1000 0 to 1200 0 1200 0 to 1400 0 1400 0 to 1600 0 1600 18000 0 to to 1800 20000 0 43 72 230 185 110 85 35 SECTION-C Question numbers 11 to 20 carry three marks each. 11 Find HCF of the numbers 1405, 1465 and 1530 by Euclid’s division algorithm. 12 The perimeter of a rectangular garden, whose length is 4 m more than its width, is 40 m. Find 3 the dimensions of the rectangle. 13 Determine 2x7y14 10x35y35 has Page 2 of 5 graphically whether the following pair of linear 3 equations 3 (i) a unique solution, (ii) infinitely many solutions or (iii) no solution 14 2 Find the zeroes of the quadratic polynomial 3x 2 and verify the relationship between the 3 zeroes and the coefficients. 15 In a quadrilateral ABCD, if ACDB90, then prove that AD AB CD BC 16 The perimeters of similar triangles ABC and PQR are 180 cm and 50 cm respectively. If QR5 3 cm, then find BC. 17 Prove that : 2 2 2 2 3 3 (1cot cosec ). (1tan )2 18 If 2 sin A : 3 cos A 3 : 4, then find the values of tan A, cosec A and cos A. 3 19 Find the median age of the life of bulbs from the following data : 3 20 Life time 0-250 (in hours) 250500 500750 7501000 10001250 12501500 Number of bulbs 10 11 15 10 5 6 In a hospital, age record of diabetic patients was recorded as follows : Age (in years) 0-15 15-30 30-45 45-60 60-75 Number of patients 5 20 40 50 25 Find median age. Page 3 of 5 3 SECTION-D Question numbers 21 to 31 carry four marks each. 21 Is square root of every non-square number always irrational? Find the smallest natural number 4 which divides 2205 to make its square root a rational number. 22 Rahul donated some money and books to a school for poor children. Money and books can be 4 represented by the zeroes (i.e. , ) of the polynomial p(x)x2x2. Akash who is friend of Rahul, also got inspired by him and donated the money and books in the form of a polynomial whose zeroes are 12 and 12.Find the polynomial represented by Akash’sdonation ? Why Akash got inspired by Rahul ? 23 If a polynomial 2x43x36x23x2 is divided by another polynomial 2x23x4, then 4 remainder is pxq. Find the value of p and q. 24 Solve the following system of linear equations graphically : 4 5x 7y 50 5x 7y 20 Also write the coordinates of the points where they meet x-axis. Shade the triangular region. 25 In ABC, AD BC and D lies on BC such that 4 DBCD, then 4 prove that 5 AB25 AC23 BC2 26 In ABC, B90, BDAC, are (ABC)A and BCa, then prove that BD 2 4 A 1 a 27 In PQR, if PQ : QR : PR 8 : 15 : 17, then evaluate. (i) (ii) Page 4 of 5 cosP. cosRsinP. sinR ta n P 2 ta n R 1 1 ta n P . ta n R 4 2 A a 4 4 28 29 If sin(AB)1 and tan(AB) (i) tanAcotB (ii) secAcosecB. 3 4 , find the value of Prove that : c o tA 1 s in A c o tA 2 s in A 30 1 4 1 2 co sA 1 secA 1 1 co sA 2 secA For one term, absentee record of students is given. If mean is 15.5, find the missing 4 frequencies x and y. Number of days Number of students 31 0-5 5-10 15 16 10- 15- 20- 25- 30- 35- 15 20 25 30 35 40 x 8 y 8 6 4 70 Pocket money of 100 students is given in the following frequency distribution : Pocket money 0-20 (in `) 20-40 40-60 60-80 80-100 100-120 120-140 Number students 6 10 20 30 20 10 of 4 Draw a ‘less than’ ogive and ‘a more than’ ogive for the above data. -o0o0o0o- Page 5 of 5 Total 4