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Bhaktivedanta Swami Mission School Pre-Preliminary Examination (2023-24) Mathematics MM: 80 Class: XAB Time: 2Hr. 2 Date: 11.12.23 Answers to this Paper must be written on the paper provided minutes. separately. You will not be allowed to write during first 15 This time is to be spent in reading the question paper. writing the answers. The time given at the head of this Paper is the timne allowed for Section B. Attempt all questions from Section A and any four questions from on the same must be done Allworking, including rough work, must be clearly shOWn, and sheet as the rest of 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 (Attempt all questions from this Section.) Question 1 Choose the correct answers to the questions from the given options [15] (Do not copy the question, write the correct answers only.) () A retailer buys an article for 750 and sells it to a customer for some fixed profit. If the customer paid GST of 150to the retailer, the SGST paid by the customer is and to the final purchase price paid by the customer is (ii) (a) 150, 7900 (b) }150, 2750 (c) 75, Z825 (d) 75,1000 Thepoint (3,0) is invariant under reflection in: (a) (iii) The origin (b) X-axis (c) y-axis (d) both x and y axes A lighthouse is 80m height. The angle of elevation of its top from a point 80m away from its foot along the same horizontal line is: (a)60 (b) 45 (c) 30 Page 1 of 9 (d) 90 line is: The solution sct representing the following number (iv) -3 (a) (x:xE R, -3<x<2} (b) {x:xE R, -3 <x< 2} {x:xE R, -3 <x< 2} {x:xE R, -3 <x< 2} (c) (d) 3 1 -1 -2 Which of the following is/are an Arithmetic Progression (A.P.)? (v) 1. 1, 4,9, 16,......... 2. Vs, 2V5,3N5, 4V5.. 3. 8, 6, 4, 2,....... (a) only 1. (vi) (b) only 2. (c) only 2. and 3. In the given diagram, A ABC ~ A PQR and AD PS (d) all 1., 2. and 3. 7 =. The value of AB:PQ is: 2 P A C (a) 7:2 (vi ) R (b) 2:5 (c) 2:7 (d) 5:7 The radius of aroller 100 cm long is 14 cm. The curved surface area of the roller is: (Take - 22/7) (a) 13200 cm' (b) 15400 cm' (c)4400 cm? (d) 8800 cm? Page 2 of 9 (viii) For two matrices P and ) Assertion (A): P yields anullmatrix Reason(R) always Null P and O are not (ix) (a) A is true. R is false (b) (c) A is false. R is true (d) matrices A is true,R is true Ais false. R is false west tomorrow. Event A: The sun will set in the Event B:It willrain on Tuesday. Event C: An hour has 60 minutes. probability Which of theabove event(s) has equal to 1? (a) allevents A, B and C (b) both events A and B (c) both events B and C (d) both events A and C (x) (x) intersect The point where three angle bisectors (c)circumcentre (b)incentre (a) orthocentre between two parallel tangents is equal to: In a circle with radius R. the shortest distance (b)2R (a) R (xii) (d) centroid (d) R (c) 2uR Evaluate: (cosec A - sin A) (sec A - cos A): (a) (cos A + sin A) (b)(cos A- sin A) (c) cos A sin A (d) sec A equation of line L is: (xiii) A point P(6,0). when reflected in line L,gives P'(0,0). The (a) x=6 (b) X+6=0 (c) y=3 (d) x=3 Page 3 of 9 distribution, find the modal class: (xiv) From the following 10 Class 20 16 Frequency () 50 - 60 10 40 - 50 26 (c) 40 - 50 (b) 30 - 40 (a) 10 - 20 40 30 22 20 -30 (d) 50 60 is produced to point E. In the given figure. AD isextended to point F and AB LCDF =? C 106 (a) 1000 (b) 40 (c) 60 (d) 80 Question 2 Trisha gets 2400 as interest at the end of 2vears in a recurring deposit account at 8% i) Find the monthly instalment. i ) the amount at the time of maturity. The first term of an A.P is (-5) and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms andcommon difterence. Page 4of 9 [4] (Use graph paper for this question) (c () Plot points A(4. 4); B(4,-6) &C(8, 0). (i) B&C Retlect ABCon the x-0 andname it A'. Write down the co-ordinates of A'. B.C'. AAC'BBC. Write the geometric name of the figure (ii) (iv) Question3 (a) circle. Tangents at Aand B meet at C. If In the given figure Ois the centre of the LACO =30 . find (i) APB (ii) LAOB () BCO B b Prove the following identity (sin A +cosec A)t(cos A +sec A)P= 5+ sec-A.cOsec*A Find the mean of the given frequency distribution using step dev iation method. Correct to two decimal. Agein !5-19 20-24 23-29 30-34 35-39 20 38 24 10 Yrs No of children Pzge 5 of9 40-44 SECTION B (Attemptany 4 questions from this Section.) Question 4: (a) (b) The model of abuilding is constructed with scale factor I :30. building in metres. () fthe height of the model is 80 cm, find the actual height of the find the volume of (i) lf the actual volume of atank at the top of the building is 27m', [3] the tank on the top of the model. A and B are two points on the x-axis and y-axis respectively. P (2, -3) is the midpoint [3] of AB. Find the (c) (i) Coordinates ofA and B. (ii) Slope of line AB. (iii) Equation of line AB. A /P (2,-3) B Using ruler and compasses construct () (ii) (iii) atriangle ABCin which AB = 5.5 cm, BC =3.4 cm and CA = 4.9 cm. the locus of points equidistant from A and C. a circle touching the lineAB at A and passing through C. ohestion 5 (aj In the figure AB =7 cm and BC -9cm. i) Prove AACD ~ADCB (ii) Findthe length ofCD Page 6 of9 [4| buying 100 shares at Amit Kuimar invests 36.000 in (b) 15% per annum.Find: (i) The number of shares he buys on (111)The percentage return (ii) Hisyearly dividend his investment. correct to the nearest Giveyour answer [31 whole number. and graph the solution Solve the given inequation (c) 20 premium. The dividend is on the number line. [3| 2y- 3<y+1<4y+7; y R. ghestion 6 Attempt this question on graph paper. (a) Marks obtained by 200 students in Marks 0-10 10-20 No. of 5 10 examination are given below: 20-30 30-40 40-50 14 21 50-60 60-70 70-80 80-90 90-100 34 36 27 16 12 25 2 cm=10 marks on one axis and Draw an Ogive for the given distribution taking the graph find: 2 cm =20 students on the other axis. From (i) (i) (iv) (b) the Median Number of students scoring above 65 marks. minimum marks required to If 10students qualify for merit scholarship, find the (6] qualify. elevation of the From two points A and B on the same side of a building, the angles of top of the building are 30 and 60 respectively. If the height of the building is 10m, [4| find the distance between A and B correct to two decimal places. Page 7 of9 LQrtestion 7 (a) When divided by N-3the polynomials x'-px' txt6 and 2x'-x-(p+3) x- 6 leave the same remainder. Find the value of 'p'. (b, (3| In AABC. AP :PB-2:3. PO is parallel to BC and is extended to Q so that C is parallel to BA. Find: (i) AAPO~AABC (ii) Area AAPO: area AABC. A [3| (c) A shopkeeper bought an article with market price 1200 from the wholesaler at a discount of 10%. The shopkeeper sells this article to the customer on the market price printed on it. If the rate of GST is 6%, then find: (i)GST paid by the wholesaler. (ii) Amount paid by the customer to buy the item. [4| aestion (a) If an office works for 5 days in a week (Monday to Friday) and if two employees of office remain absent in the same week, what is the probability that it is (i) the same day (ii) Consecutive days ? (i) different days (3| (b) Find A--A iB0 Ahemisphcrical bowlofinternal radius 9em is full of liquid. The liquid is to be illed into cy lindrical shaped s1mall botles, cach of diameter Bem and height 4cm. How nany botles arc herded to enpty the bowl? Page 8 of 9 [3| Question 9 B(3,6) is Calculatethe ratio inwhich theline segment joiningA(-4,2) and (a) divided by [3] point P(x,3). Also find x. surnnounted by a conical block of wood. hcmisphere a represents figure given TIhe (b) the slant bcight of the cone is 5 cm. The diancterof thcir bases is 6 cm cnch and Caleulatc: (i)the height of the cone. [4| (ii)thevolume of he solid. (c) 2. Findthc number Sum of nterms of GPis 381. Its first term is3 andcomnon ratio is |3| of terms and the 7h term. Question 10 (a) A nanon the top of the tower observes a car mnoving at a uniforrn spccdtOwards it. If it 1akes 12 minutes for the angle of depression to change from 3(' to 45,how s0on will [4| thecar reach the tower? Give your answer to ncarest sccond. (b) Comdructah ABCith 3C6.5 cm, AB 5,5 cIn, C 5 cn, CoStruct thc incirclc of the triangle. Measure and recordtheradius of the incircle. [31 The sm of thre numbers in an AP is -12 andtheir product is 36. tind the nunbers
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