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MATNENATICS TUNNE S s+SWis. Raasg Time t e sse stet st e r t e sAe. rt strats Qtissiacfessertel waris x Natenetica Log aes reprovice SECTIONA(QARKS) (Ansaer al he questors roa tis Seton) Questont Caocse tte coret anses to te questos om ea e ctors 2-(2k-7) x+5ty (x+3 Eereander isk-1 Fn civicing en e vee of ks b) -4 c) D) 3 custame o Aretaler buIsan aride frem te widesaler far &Z50and selstio the 79000 f tne retailer gays GST cf 5to e govemTent, herate of CGST iS: a) 5e b) 7.5% c) 10% This paper consists of 1f printed sides and 1blank page. iii) The surface area of a sphere is 5544cm , then the diameter of the sphere is a) 21cm b) 42 cm c) 10.9cm d) iv) 21.8cm If matrix C= [1 -4] and D =Then matrix DC is a) Null matrix b matrix multilplication is not possible c) [4 -4) d) V) Amit invested acertain sum of money in F100 shares paving a 7.5% dividend. The rate or returnon his investment is 10%. The money invested by Amit to purchase 10 shares is a)75 b) 750 c) 2900 d) 71100 vi) The roots of the quadratic equation x + m + (2x m-1)+2=0 are equal. Then the value of m is a) 3 b) 2 c) 1 d) -1 vii) If (y +z . y then it can be concluded that: (z + x )2 X a) x , y .z are in proportion b) x,y ,z are in continued proportion c) x,z y are not in proportion d) x,z y in propotion vii) Given that sum of the squares of the first 7 natural numbers is 140, then their mean is: a) 20 b) 70 c) 280 d) 980 2 ix) In triangle ABC, AB = 5cm,BC= 12cm and ABC= 900 the radius of the circle is a) 2cm A b) 5cm c) 3cm 5 cm d) 1cm B 12 cm C grouped calculated by plotting a less than ogive for a X) ASSERTION (A):Mode can be frequency distribution. REASON(R): A less than ogive is constructed on the in ascending order . a) A is true, R is false basis of cumulative frequencies being b) A is false, R is true c) Both Aand R are true d) Both A and R are false xi) 7 is If xe W. then the solution set of equation - x> a) {8,9,10 --* b) {0,1,2,3,4,5,6} c) {0,1,2,3 ---+ d) (} first term and the common difference xii) If the sum of n terms of an AP is 3n+ n,then the 342 is: a) 4,14 b) 14, 4 c) 6,4 d) 4,6 laboratory model of The approximate volume of a human eye is 6.5 cm. The volume of a the human eye is 1404 cm'. The value of k is a) 6 b) 1/6 c) 216 d) 1/216 3 x0v) tne given figure O is the centre of the circle and m B= 550 The angle ZAIS equal tc 55 B a) 550 b) 350 c) 450 25 d) 50 XV) Which of the following equation represent aline passing through origin and parallel to the line 3y- 2x +5 =0 (a) 3x -2y + 5= 0 (b) 2x -3y = 0 (c) 3x - 2y =0 (d) y=-5 Question 2 i) In the given diagram, O is the centre of the circle. PQ is the tangent to the circle at T. Chord AB produced meets the tangent at P. If AB=9cm, BP = 16cm , ZPTB = 500 and ZOBA = 450 , find: a) length of PT b) Z BAT c) Z BOT d) ABT i) Using remainder and factor theorem factorise the following polynomial completely 2x3 + 3x?- 11x -6. 4 [4] [4] (4) i) From the diagram given below find: B7,12) 2y+ kz= 45 A (-2, 6) X C a) The value ofk b) Coordinates of point C c) Equation of line AB Question 3 i) 10,40 and 640. If the The4,6h and the last term term of ageometric progression are Commonratio is positive find: [4] a) First term b) Common ratio c) Number of terms d) Sum of the terms A specially designed thick wooden cylindrical pencil has a sharpened conical tip, as shown in the given diagram. The length and the diameter of the pencil is 18 cm and 1.4 cm respectively and length of the conical tip is 1.5 cm. It has coating of alternate red and black colours. (Use T as 22/7) Find a. The volume of conical tip of the pencil. b. the cost of coating the curved surface of cylindrical part( excluding the conical part) at the rate of {0.30 per cm . Give your answer corrected to the nearest whole number. 1.5 cm 1.4 cm 18 cm 5 (4) Use graph paper to answer the following questons [Use scae 2cm 1 unit on both axes) (a) Piot quadrilateral OABC where O(0 0) A(1 3) B(3.3)and C (3 0) (0) Reiect quadrilateral OABC through the ongin as OPQR and write down thet coordinates (C)Reflect quadrilateral OABC on xaxs as OA'B'Cand wnte down ther coordinates (d) Name 2points which are invariant when OABCIS refected on the Aaxs SECTIONB (Attempt any fout Questions rom ths section) Question 4 ) ) Aman rvests 22500 in 50 shares avalatile at the comparies is 12% caicu ate a) No of shares b) the t0%dscount If the divdendpand by purchased annual drvidend recevved c) the rate of retutn he gets on his itvestant Gve you answe correct to the whole number ) ) Solve the tolowng nequation arte he sOter set and reposent it or a numbe lne Sx-21< (3) Prove the tolowirng identty 4) Question 6 ) Priyanka has a recurring depost accout of t430 pe morth at t0% per annum lf she gets 30100at the time of ahurty fnd the tota time for wtich the account was held. in the given tigure BC is parallel to EF.CD is caralel to FG AE EB= 2:3 ZBAD =70" ZACB 105, ZADC= 40 and AC is bisecto of z BAD 8 a) Prove that AAEF ~ AAGF. b) Find AG: AD. area ofA ACB. c) Find area of quadrilateral ABCD: families are given I) The daily expenditure of 100 expenditure is Z188. expenditure 140 160 160 180 No of families daily below. Calculate f; and f2. if the mean 180-200 200-220 220 240 5 f 25 Question 6 electrical goods. i) Sanjay goes toa shop selling [3] he buys the following items. Discount GST % item Quantity Rate per piece 1 Rs 4000 20% 18% Wall Fan 10 Rs 300 NIL 12% LED bulbs Find a) Discounted price of wall fan. b) Total GST paid on 2 items c) Total bill amount including GST. 7 \720 A(a )8(,$) ax C8,8) re the vetioes of atnange ABC bnt Dis on BC ) quaton of ne passing thugh and pepeicular to80 Question 7 i)) Sum of frst thrse tems of an anthmatic progession is tS.5and the product of t andthwd temmis t4. Find: (3) (a) the commen ditfarenas (b) first tem (c) sum of first 21tems of this progression, ) Sove the following quadratic equation and give your answer to 2 sgniticant tigures (x-1 -3x +4 = 0 (3) i) [4) is a tangent to the circle at b In tne givenfigure O is the centre of the circle and AB R B A If ZPQB= 550, find: a) The values of x ,y and z PQ b) Prove that RB is parallel to Question 8 i) squares of [31 blue and rest are red and 10 are 3 which of triangles Achild's game has 8 probability that piece is lost at random. Find the One red. are rest and blue are which 6 it is a a) triangle b) square c) triangle of red colour. ii) ii) 3ab )(62) = (b + 3a b )(63). Using properties of propotion, find a: b if (a+ (3] [4] cylindrical vessel, partly sphere of diameter 12 cm is dropped into aright circular A submerged in water, the water level in the filled with water, If the sphere is completely 5 vessel. cylindrical rises byy 3- cm. Find the diameter of the cylindrical Question 9 i) either side of the road, P 2 lamp posts AB and CD each of height 100 metres are on of the is a point on the road between the lamp posts. The angles of elevation of the top lamp post from the point P are 60 and 40 . Find the distance between the two lamp posts .Give your answer to the nearest metre. [5] i) The following graph represents weightof 100 lemons. The lemons weighing above the average weight are termed as juicy lemons and the ones weighing below 42 grams as raw lemons. 100 90 LEMONS NUMBEROF 30 40 50 60 70 80 90 WEIGHT (in gms) Study the graph carefully and answer the foliowing a) Form a frequency distribution table for the above ogive and use it to find the median class. b) medianweight of the lemons c) lower quartile value. d) if the average weight of lemons is 58 grams, find the number of juicy lemons. e) The percentage of raw lemons. f) Findthe cost of raw lemons at the rate of 26 lemons for 750. 10 (5) ion10 and B= find the matrix M6uch that M A- 44+ AB an educational tr1p The travel ager planned school a of teacher geography Ihe ") trip was certain number of days. Later,the quoted a price of 4800 per student for a the agent not to charge any extra extended by 2 more days. Teacher requested unchanged.the travelagent reduced the amount. To keep the totalexpenditure orginally What was the durat on of the trip expenses of each student by80 per day. ii) Use ruler and compass for this question. AB=7em,CAB = 75 and AC=5cm wh ch in ABC triangle a) construct a points equidistant from AB and AC all of locus the construct b) points equ distant from AB and BC c) construct the locus of all internally touching the three sides of the triangle d) Hence construct the circle and measure the radius of the circle. 11 (41
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