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Kapol Vidyanidhi lnternationalSchool(1CSE) Temple Of Knowledge `td:X 10-01-25 H4730 PRELIMINARY EXAMINATION Duratior MATHEMATICS Set A 3hours Answers to this paper must be written on the paper provided separately. You will not be allowed to write during first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this paper is the time allowed for writing the answers. Attempt all questions fromSection Aand any four questions from Section B. Allworking, includingrough work, must be clearly shown,and must be done on the same sheet asthe restoj the anSWer. Omission of essential working will result in loss of marks. The intended marks for questions or parts of questions are given in brackets [] Mathematical tables are provided. SECTION-A (40 Marks ] Answer all questions from this section. Question 1 Choose the correct answers to thequestions from the given options. (Do not copy the questions, write the correct answers only.) i) [15] ? 50 per month is deposited for 20 months in a recurring deposit account. If the rate of interest is 10% the maturity value is (a) 187.50 (b) (b) 87.50 (c) (c)*2175 (d) (d)?1087.50 i) Inthe given diagram, RT is a tangent touching the circle at S. If ZPST= 30 and zSPQ= 60 then ZPSQ is equal to: (a) 40 (b) 30 (c)60 (d) 90 iii) 60*1 R (1 + sin A)(1 - sin A) is equal to : (a) cosec2 A (b) sin' A (c) sec' A (d) cos A o iv) The cost of certain servicesis t 10,000,excluding GST =*1800 the rate of GST is (a) 12% (b) 5% (c)18% (d)28% v) 3 What must be subtracted from the polvnomialy + x2 2x + 1, so that the result is exactly divisible by (x-3) ? (a)-31 (b)-30 (C) 30 (a)31 vi) 3 2x 2 3 where xER Assertion (A): the largest value of xis 9 Reason (R):When the sign of both the sides of inequality are changed the sign of inequality reverses (a) Ais true ,Ris false (b)A is false,R is true (c) Both A and R are true and R is the correct reason for A (d) Both A and Rare true and Ris the incorrect reason for A vii) If the quadratic equation kx' + kx + 1= 0 as real and equal roots the value ofk is (c) 0and 4 (d)0 or 4 (b)4 (a)0 60 and quoted at 70 is; viii) The money requiredto buy 80 shares each of (d)R4200 (c)780 x 60 x 70 (b)74800 (a)75600 ix) Ifa matric A=|and matrix B= P then which of the following is possible: (a) A+B (b)A-B (c) AB (d) BA x)|In an AP if a=-36 d=18 and | =36 then n is: (c) 15 (b)5 a) 10 xi) What is the 6th term of the GP (a) 3 64 (b) 3 32 3 3 (d)20 3 2 '4 '8 3 (c) 128 (a), 256 xi) Theimage of thepoint (x, y) in the line x=0 is (-2,7). The point (x, y) is: (a)(-2,-7) (b)(2,-7) (c) (2, 7) (d)(-2,7) ki) If the lines 4x +3y =84 and 3x +ky +7 = 0are perpendicular to each other: Then the value of k is (a)4 (a) (b)-4 A Xiv In figure MN BC and AM:MB=1:2 then what is area(AMN) area(DABC) (a)9:1 (b)1:9 (c) 3:1 (a)1:3 MA B are written, are mixed thoroughly and then a XV. 20tickets, on which numbers 1 to 20 the probability that the number on ticket is drawn at random out of them. What is the drawn ticket is a multiple of 3 or 7?3 (a); (b) (c) 4 Question 2 of the polynomial 3x3 +x- ax factor a is x-a 'a'if of value the Find i) 81 (4) which pays interest at the rate bank a in account deposit recurring ii) Raghuram has a 78638,as the maturity value after 3 h gets he If years. Yh 3 for annum per of 9.5% account {41 tangent at point Aand PBD is astraight line. ii) In the given figure, QAP is the 42 , find: [4] years,how much money should he deposit every month in this If ZACB = 36 and LAPB = (a) BAP (b)ZABD (c) QAD (d)zBCD Question 3: seventh term and the last term of a geometric progression are i) Thefourth term,the term, common ratio and number of 10, 80 and 2560respectively. Find its first (4] terms. ii) Ahemispherical and a conical hole is scooped out of asolid wooden cylinder:. Find the volume of the remaining solid where the measurements are as follows the height of the solidcylinder is 7cm, radius of each of hemisphere, cone and cylinder is 3 cm Height of cone is 3cm.Give your answer correct to the nearest whole number. [Take 1. 3 [4| ii) Study the graph and answer the questions that follow: -40 -35 -30 Number of studernts -25 20 15 10 X 120 130 140 150 160 170 Height (in cm) (a) Make a frequency table for the information provided in the graph. (b)The number of studentswhose height is less than 150cm. (c) The total number of students. (d) The modal height. (e)The difference in the modal height and the mean height, if the average height of the students is 145.5 cm. Section B(40 Marks) (Answer any four questions from this Section) Question 4: i) Aman invests *7,770in acompany paying 5% dividendwhen ashare of nominal [3] value of 100 sells at a premium of 5. Find: (a) the number of shares bought; (b) annual income; (c)percentage income. 1)| Solve the following inequation. Write downthe solution set and represent it on the [31 real number line. -5(x -9) 2 17-9x>x+ 2, xER. iii) Prove: tan A tan A (sec A 1) (secA + 1) = 2cosec A 4 [4] Question 5: [3] In the given figure, Ois the centre of the circle and AB is a tangent at B.IfAB= 15 cm and AC =7.5 cm. i) D Calculate the radius of the circle. i) Sampuran has a recurring deposit account in abank. He deposits ?2000 per month (3) andthe bank pays interest at the rate of 8% per annum. If he gets 1040 as interest at the timeof maturity,find in years total time for which the account was held. ii)Thedata on the number of patients attending a hospital in a month are given below. Find the average (mean) number of patients attending the hospital in a month by [4] using the shortcut method. Take the assumed mean as 45. Give your answer correct to 2 decimal places. Number of patients Number of days i) 20-30 2 10-20 5 30-40 40-50 7 50-60 2 60-70 5 Question 6: A(7,- 5), B(5, 3)and C(-9, 1) form atriangle Find the [3] )Slope Of BC. (ii) Equation of altitude through A. (iii) equation of median through ii)In APQR MN is parallel to QR and PM _2 MQ [3] 3 Mu MN ) Find QR (ii) Prove that A0MN and AORQ are similar. (ii) Find, Area of AOMN: Area of AORQ i) Swaroop went to a mobile selling shop. He bought the following items given in table: [4) Rate of GST Price Discount Sr No. Item 1 Mobile {24000 2 Memory Card 1000 3 Charger {1200 Find the: (a) Total GST paid. (b)Total bill amount including GST. 12% 18% 18% 10% 5% Ouestion 7: were recorded as answer this question. weights to paper school, graph Use 60 students in a During a medical checkup follows: Weight (in kg) 28-30 30-32 32-34 34-36 36-38 38-40 40-42 42-44 of Number of students 4 10 13 15 9 5 2 the other axis draw along students 10 one axis and 2 cmn = Taking 2 cm = 2 kg along graph to find the: an ogive. Use your (a) median (b)upper quartile whose weight is above 37 kg. students of number (c) 4] angle of depression of two the observes man a high, of tower 100 m 38 respectively. If the foot and ii) |From the top of a 45 as tower the of two sides the distance between shipsA and B, on opposite same horizontal line, find the tower and the ships are in metre. ships A and B tothe nearest and shuffled. A|[31 Question 8: o, p. They are put in a boX n, m, , ... c, b, a, as labelled probability that the card drawn 1) Sixteen cards are the is What box. the from boy is asked todraw acard is: (a) a vowel (b)a consonant word median? (C) none of the letters of the [3] V2a +1 +v2a -1 prove that x - 4ax +1 =0 Ifx = ii) V2a +1 - V2a-1 diameter [41 for 10tents conical in shape with base canvas donate to decided Ramniwas I11)| handicapped person's welfare. If the cost of 2 m 14 mandheight 24 m to a centre for amount by which Ramniwas helped the wide canvas is Rs. 40 per meter, find the centre. Question 9: 1)|Solve for x using the quadratic [3] ii)The sum of first 7 terms of an AP is 63 and sum of its 7 next terms is 161. Find 28th term of AP. [3] figures. (x-1)2 -3x +4 =0 formula. Write your answer correct to two significant 1) (a) The point P (2, -4) is reflected about the line x =0to get the image Q. Find the co-ordinates of Q. (b)The point Qis reflected about the line y = 0to get the image R. Find the co-ordinates or R. (c) Name the figure PQR. (d) Find the area of figure PQR. (4] Ouestion 10: i)|The denominator of a fraction is two more than its numerator. If the sum of the [31 34 |fraction and its reciprocal is i) If A= 3 ;and 15 find the fraction. then find A 5A+ 71 iii) | Using a ruler and a pair of compass only, construct a) A ABC, given AB = 4 cm, BC = 6 cm and ZABC = 90 (b) Draw a circle that passes through the point A, Band C and mark its centre as O All The Best [3] [4]
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