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HIRANANDANIFOUNDATION SCHOOL, THANE Second Preliminary Examination - January, 2024 Subject: Mathematies Std: X Time: 2 Hrs Date:08-01-2024 Max. Marks: 80 Answers to this Paper must be written on the paper provided separately. Youwill not be allowed to write during first 10 minutes. This time is to be spent in reading the question paper, The t me given at the head of this Paper is the time allowed for writing the answers. Attempt allquestions from Section A and any four questions from Section B. All working including rough work,must be clearly shown, and must be done on the same sheet as the rest of the answer. Omission of essential working willresult in loss of marks. The intended marks for questions or parts of questions are given in [] This Question paper consists of 6pages. Mathematical tables are provided. SECTIONA (Attempt all questions from this section) Question 1 Choose the correct answer to the questions from the given options. (Do not copy the questions, write the correct answer only) i) An article is marked at 1000. Adealer sells it at a profit of 5%. If the rate of GST is 18%, then the total amount paid by aconsumer to buy it, is a) 1324 b) 1239 c) Z1120 d) 1180 i ) If 3x2 - 6x + k= 0 has real and distinct roots, the the value of kis a) k<3 c) k>3 b) k = 3 ) k<3 ii ) The diameter of a sphere is 6 cm. It is melted and drawn into wire of d ameter 2mm, then the length of the wire is a) 12m b)18m c) 36m d) 66m iv) If anumber xis chosen from numbers 1,2,3 and number y is chosen from 1,4,9 then the probability that xy <9 is a) 3 b) 4 v) If polynomial4p - 4p + 2 is divided by p-1 then the remainder is a) 0 b) -1 c) 2 d) -2 recejNe vi) Aman deposited 1000 per month for 24 months and27000 as the maturity value. The interest received by him a) 3000 b) Z6000 c) 3500 d) <5000 v) In what ratio is the line joining (2, -3) and ( 5, 6) divided by x axis. a) 1:2 b) 3:2 c) 2:1 d) 2 :3 1 [15j vii) If nth term of an A.P. is 13-4n then the 20th term is a) -67 b) 67 d)-76 c) 76 ix) The solution set for 5x < 23 when x E N is a) {1,2, 3,4 } b) {1, 2, 3, 4, 5} c) {1, 2, 3} d) Allof theabove x) 4sin Asec A-1= a) 3sec?A b) 4 sin Atan A c) cotA d) 4tan'A Xi) In the given figure, PQ is a chord of a circle with center O and PT is the tangent at P such that e QPT = 60 , then the value of ZPRQ is a) 120 b) 160 c) 130 d) 150 xii) Ify intercept and inclination of a line is 6 and 4S respectively then the line is a) x-y +6=0 b) equation of the -x-y+6=0 c)y-x+ 6=0 d)x+y+6=0 Xiii) Which of the following equations has 2 as a root a) x'- 4x +5 =0 b) x +3x - 12 = 0 c) x + 5x - 14 = 0 xiv) If 9 0 d) 3x2 6x-2 = 0 -then the value of a) 4 b) +4 x -yis c) 5 a d) 8 xv) Assertion (A): The ratio of areas of two similar triangles is equal to square of the ratio of their proportionate sides. Reason (R): The sides of two similar triangles are in the ratio of 4:25, then the ratio of the areas of triangles is 2: 5. a) A is false, R is true c) A is true, R is false b) Both are true d) Both are false Question 2 i) Salman opened a recurring deposit account in a bank and deposited 900 per month for 2 year. If he receives 29000 at the time of maturity then find the rate of interest per annum. (4] i) Using the properties of proportion solve the following equation for x. x'+3x 3x2+1 341 [4) 91 ii) Use the graph paper to answer the following question. a) Plot the points A(-4,0), B(-3,2), C (0,4), D(4,1) and E(7,3) b)Reflect the points B, C, D and E on x- axis and name them as B',C',D' and E' respectively. 2 c) Join the points A, B, C,D, E, E, D,C,B' and Ainorder. d) Name the geometrical figure formed (4] Question 3 i) Prove that (cos A- sin A) (1+ tanA) 2cos A-1 secA I1) Solve the following inequation and represent the [41 solution on the number line where x ER -4+x <* +1<+2x, 3 i) Study the graph and answer the following questions: a) Name the curve plotted. b) The median marks 80% marks in the examination. c) The number of students whoscored more than is 35%. d) The number of students who did not pass, if the pass percentage e) The interquartile range. 4 SMARK [4 SECTION B (Attempt any four questions from this section) Question 4 ) USing ruler and compass only, construct a 4ABC such that BC= Scm and AB =6.5cm and ZABC = 1200. a) Construct a circumcircle of 4ABC. b) Construct a cyclic quadrilateral ABCD, such that D is equidistant from AB and BC. ii) Let R1 and R be remainders when polynomial x3 2x-5ax -7 and x*+ ax?-12x + 6 are divided by x + 1 and x-2 respectively. If 2R +R2 =6, find the value of a. 1i) A man invests 22500 in 50 shares available at a discount of 10%. If the by the company is 12%, calculate (3] [3] dividend paid a) the number of shares purchased. b) the annual dividend received. c) the rate of return he gets on his whole number. investment. Give your answer correct to the nearest [41 Question 5 i)A straight line passes through the points A (-5, 2) and B (3, -6). It intersect the coordinate axis at points C and D as shown in the figure. Mis the point on AB (3] which divides CD in the ratio1:2. Find a) the equation of line AB. b) the coordinates of the points C and D. c) the coordinates of the point M B(3, -6) i)) Each of the letters of the word 'AUTHORIZES' is written on identical circular discs and put in a bag. They are well shufled. If the discs are drawn at random from the bag, what is the probability that the letter is a) a vowel? b) one of the first 9 letters of English alphabet which appear in the given word. c) one of the last 9letters of English alphabet which appear in the given word. [3] ii) A solid is made of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and the radius of each hemispherical end is 7 cm, then find the cost of polishing the surface at the rate of 2 per dm?. (4] Question 6 i)The 8 term of an A.P, is 37 and the 15th term is 15 more than the 12h term, find the A. P. ii) The numerator of afraction is 3less than the denominator. If 2is added to both numerator and denominator. then the sum of the new fraction and the original fraction is 29 20 (3) Find the original fraction. 11) In the given figure, 4ABC and 4AMP are right angled at B and Mrespectively. Given, AC= 10cm, AP = 15cm and PM = 12cm. a) Prove that 4ABC ~ AAMP [41 b) Find AB and BC Question 7 affected due to floods and i) 1500tents are set up by 50 schools to help homeless people of the tent the whole expenditure will be shared equally by the schools. The lower part of the same part upper conical with 3.5m, is cylindrical of base radius 2.8m and height base radius and height 2. 1m. Ifthe tarpaulin sed to make the tent costs 120 per sq.m, find the amount shared by each school. ships on ii) From the top of the lighthouse 100m high, the angle of depressions of the two distance Find the respectively. 36 and 48 are lighthouse the opposite sides of the between the ships to the nearest metre. [5] Question 8 i) Find the value ofk, so that the equation (3k + 1)x'+ 2(k+ 1)x+ 1=0 has real and equal roots. Also find the roots of the quadratic equation formed. [3] ) IfA = [3] - and A'=9A +ml , then fnd the value of'm'. ii) In the given figure, diameter AB an chord CD of the circle meet at P. PT is the tangent to the circle at T and CD =7.8cm, PD = Scm, PB = 4cm. Find a) the length of AB. 4] b) the length of tangent PT. Question 9 i) A(2, 5), B (-1,2) and C( 5, 8 ) are vertices of 4ABC, Mis the point on AB such that AM :MB = 1: 2. Find the coordinates of point Mand also find the coordinates of the centroid of AABC. [3] ii) A box contains some black balls and 30 white balls. If the probability of drawing a black ball is two-fifth the probability of drawing a white ball, find the number of black balls in the box. [3) 5 ii) The marked price of the goods is 26000 and the rate of GST is 18%.A shopkeeper buy the goods at a reduced price and sells it at markedprice. If the shopkeeper paid 153 as CGST tothe government, then find the amount (inclusive of GST) paid by [4) the shopkeeper. Question 10 1) Theweights of 50 mangoes was recorded as given below. Calculate the mean weight to the nearest gram, Weight in (3] 80- 85 85-90 90-9595-100 100-105 105-110| 110-115 grams Number of 5 10 12 4 3 mangoes ii) The second term of the G. P., is 18 and the 5th term is 486. Find: a) the first term b) the common ratio. [3] ii) In the given figure, AB | CD and O is the centre of the circle. If zADC= 25 , then find LAEB.Give reason to support your answer. 6 [4]
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