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CARMEL SCHOOL DHANBAD FIRST TERM EXAMINATION 2020 CLASS: X TIME: 2 HRS SUB: MATHEMATICS FM: 80 NAME: ___________________________CLASS_________SECTION: ________ ROLL NO.:_______ NOTE: 1. Send your Answer Sheet on this number only 7209851449 2. Don t send multiple pdf. files. (Only 1 pdf allowed for 1 student) 3. Don t send text messages and photos. 4. Write correct question no. and answer your exams. ________________________________________________________________________________ Note: Attempt all questions in Section A and any FOUR questions in section B. All workings including rough work must be clearly shown. Section A (40 marks) Q 1. a) Mr. X has a recurring deposit Account in a bank for 3 years at 7.5% p.a. If he gets Rs. 8325/- as interest at time of maturity, find i) monthly installment and ii) the amount of maturity. (3) b) Solve using Quadratic formula and give your answer correct to one decimal place. (3) 4 + c) If = [ 0 0 ] 2 6 + 13 = 0 0 , = [ ] 1 0 = [ 1 1 ] 1 1 and BA = M 2 , find the values of a and b. (4) Q2. a) The mid point of the line segment AB , as shown in diagram is C( 4, -3). Write down the Co-ordinates of A and B. (3) b) A, B and C are in the same town. A sells an article to B for Rs 50000/- and B sells the same to C at a profit of Rs 6000/- If G.S.T is 12% find :(i) SGST paid by B. (ii) total tax received by the central government (CGST). (iii) How much does C pay for the article? c) Find the values of p and q so that the polynomial 3 + p 3 + qx 45 has ( x 1) and (x + 5) as its factors. With the values of p and q , factories the given polynomial completely. (4) Q3 a) Find the sum of all natural numbers between 250 and 1000 which are divisible by 9. (4) b) If a, b and c are in continued proportion , prove that 2 + + 2 2 + + 2 = (3) c) In what ratio is the join of A(4, 3) and B(2 , -6) divided by the x axis? Also find the co-ordinates of point of intersection? (4) Q4 a) Solve the inequation and represent the solution set on the number line. 4x 19 < 3 5 -2 - 2 5 + x, (3) x belongs to Real number. b) Using ruler and compasses only draw a circle of diameter 8cm mark a point P' outside the circle such that OP = 7cm where O' is the centre of a circle. Construct two tangents from P to the circle measure and record the length of the tangents. (4) c) In the given figure AC = 10cm, AP = 15cm and PM = 12cm. Prove that C M A i) ABC ~ B P AMP ii) Find AB and BC given angle B = angle M= 90 (3) Section B (40 marks) Answer only four questions:Q5 a) If x = + 1 + 1 + 1 1 using properties of proportion show that x2 - 2bx + 1 = 0 (4) b) The age of a father is twice the square of age of his son. Eight years hence , the age of the father will be 4 years more than three times the age of the son. Find their present ages. (4) c) Form the quadratic equation whose solution set is {-2 , 3}. (2) Q6 a) In a single throw of two dice , find the probability of i) a doublet ii) a number less than 3 on each dice. iii) an odd number as a sum. b) Given X = [ 2 0 ] 1 7 and I = [ 1 0 ] 0 1 (3) and X2 = 9X + k .I Find the constant k. (3) c) If the third and ninth terms of an arithmetic progression are 4 and -8 respectively, which term of it is zero? (4) Q7a) T' is a point on the side QR of PR = 6cm and TR = 3cm. i) ii) iii) PQR such that angle PTR = angle QPR. If PQ = 8cm, (4) Prove that PQR ~ TPR Find the length of QR and PT. Find area of PQR area of SPR P 8cm Q b) ABC is a triangle and G(4,3) is the centroid of the C =(a, 1) find a and b. 6cm . T 3cm . If A = (1,3) , B = (4, 6) and c) What must be subtracted from 16x3 - 8x2 + 4x +7 so that resulting expression has (2x +1) as a factor? Q8 a) Find the value of m' for which the roots of the following equation are real and equal. m2x2 - 2(2m 1)x + 4 = 0 R (3) (3) (3) b) Find x if (2x + 3) : (5x 38) is the duplicate ratio of 5 : 6. (3) c) Mr.Raj has a Recurring Deposit account of Rs.1000/- per month at 10% per annum. If she gets Rs 5550 as interest at the time of maturity, find the total time for which the account was held. (4) Q9 a) Using ruler and compass construct a ABC in which BC = 5.5cm , AB = 6cm and ABC = 120 . Also construct a circle circumscribing the Measure and record the radius of a circle. ABC. (3) b) The line joining the points A(-3, -10) and B(-2,6) is divided by the point P such that 1 = Find the co-ordinates of P. 5 (3) c) Attempt this question in a graph-sheet. (4) i) Plot the points A(3,5) and B(-2,-4). ii) Reflect A(3,5) about the line y=0 to get the image C. iii) Reflect B(-2,- 4) about the line x=0 to get the image D. iv)Plot the points C and D on a graph-sheet. v) Write down the geometrical name of the figure ACBD. ****************************************************************************************** SUPPORT TIMING: 08:00 A.M. to 11:00 A.M.
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