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MARBLE ARCH SCHOOL ARCH PRELIMINARY EXAMINATION MATHEMATICS MAX.MARKS: 80 STD: 10 TIME:3 HOURS DATE: 13/01/2025 Total No of Pages: 5 Answers to this Paper must be written on the paper provided separateiy. You will not be allowed to write during the first 15 minutes. This time is spent in reading the question paper. answers. The time given at the head of this Paper is the time allowed for writing the Attempt all questions from Section Aand any four questions from Section B. be done on the same All working including rough work must be clearly shown, and must sheet as the rest of the answers. Omission of essential working willresult in loss of marks. The intended marks for questions or parts of questions are given in brackets [] 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 question. Write the correct answer only. [16] this results in the increase of A solid metallic sphere is cut into equal hemispheres, surface area by .. C. 2TT sq. units Sq. units a. TIr2 d. none of the options b. 3 Trr2 sq. units i. negative slope. Assertion: (A) Aline has positive x and y intercepts, and and the positive direction of the x axis, Reason :(R) As the angle between theline i. measured anti clockwise direction is obtuse a. Both AandR incorrect b. Both A and R correct iii. C. only A is correct d. only R is correct the major segment of a circle Statement 1. If an acute angle ABC is in circle is in the minor segment of the same Statement 2. Then the obtuse angle ADC correct C. only statement 1is wrong a. Both statements 1&2 are d. only statement 2 is correct are correct b. Both statements 1 &2 iv. observed to the top of a ground an angle of elevation is levelled a on A point the height From a base of the tower is 30 m, then the from A of distance the If tower to be 60. of the tower iS.... MAS: Page 1 of 5 Std 10 Mathematics ARCH MARBLE ARCH SCHOOL SC a. 60 m. C. 30 m. b. 303 m. d. 60 V3 m. A customer pays Rs 9600 for an article he bought from a retailer at the price inclusive of 20 % GST.The tax received by the central government formprinted this sale is ... a. Rs. 800 V. b. vi. C. Rs. 400 d. Rs. 960 Rs. 1600 If 200, Rs. 100 shares were bought at 10 % discount, paying 18 % dividend, then the yield % on the investrment is a. 24 % C. 25 % d. 22 % b. 20 % With reference to question (vi) the annual inCome earned is ...... vii. a. 3600 C. 3200 d. 2240 b. 2200 vii. Asolid metallic cylinder of radius 2 'r and height 3 'h', is melted and recast into cones of radius 'r and height 'h'.The number of cones recast is.... a. 42 b. 12 ix. C. 36 d. none of the options. The interest earned on a RD scheme for 2 years is three times its monthly deposit , then the rate of interest on this RD is C. 24 % pa a. 20 % pa b. 12 % pa d. none of th options Find the equation of aline passingpoints (-4,0) and (0,8). X. a. b. xi. C. 2y = 4x + 16 y =2%- 4 d. -y = -4x - 8 y=4x Assertion : (A) Reason: (R) The curved surface area of a cone is greater than the area of its base. As the slant height of the cone is greater than its base radius a. Both A and R are correct b. Both A and R are incorrect xii. is 12.5 %, The market The rate of return on a Rs 500 share paying 20% dividend value of the share is a. Rs 400 b. Rs, 800 xiii. C. only A is correct d. onlyR is correct c. Rs 200 d. none of the options are supplementary. Statement 1. Diagonally opposite angles of a cyclic quadrilateral passes the center of the circle Statement 2. Diagonal of the cyclic quadrilateral always statement 1is correct a. Both statement 1 and 2 are correct b. Both statement 1and 2 are incorrect Std 10 Mathematics C. only d. only statement 2 is correct MAS: Page 2 of 5 ARGH MARBLE ARCH SCHOOL xiv, The median of 5,10,15, a. 33.5 20,25,30,35,40,45,50, 55. 60. is ... C. 32.5 b. 35 The 10th term of a GP XV, a. 256 d. none of the options ,1,2,4.. is ... b. 1024 Xvi. C. 128 d. none of the options The 10th term of the AP 22,27,32 is ...... a. 96 b. 67 c. 69 d. 76 Question 2. a. From a point P' on levelled ground ,an angle of elevation of 60 is observed to the top point 'A' of a cliff.From the same point 'P' the angle of elevation to a point 'B' that is 30 mvertically below 'A' on the cliff , was observed to be 30 . Find the height of the cliff tothe nearest meter. Diagram required. (V3 = 1.732 ) [4 b. Given points A (-6,2) and B(8,10 ). Find the equation of line segment AC that is perpendicular to AB at A.Find the ratio in which AB is divided by the Yaxis (4) C. The 3rd and 6th terms of a GP are 27 and 729 resp. Find the 10h term and the sum of [4] the first 11terms of this GP. Question 3. a. At a given instance a pilot observes an angle of depression to the landing point 'P' on a runway to be 30 . If at the same instance the aircraft's altitude is 3 km.,find the time in seconds taken to touch down at point 'P'. Given speed of landing is 200 km/h. [4] b. Find the mean using the short - cut method,answer upto 3 s.f. 80 -100 100 - 120 120 -140 Class 40 - 60 60-80 25 20 15 12 Freq. (4) 140 - 160 10 p.a. dividend. If the C. A dividend of Rs. 4500was earned on Rs 200 shares paying 15% the rate of return on the shares were bought at a premium by investing Rs 36000, find along with investment.After all the shares were sold at 10% discount,the prOceeds find the dividend, paying 15 % annual income was invested in Rs 100 shares at par (4] change in the annual income of the investments. MAS: Page 3 of 5 Std 10 Mathematics ARCH MARBLE ARCHSCHOOL SECTION B (Answer any 4 questions from this section ) Question 4. a. Amodel of aship made to ascale of 1:800. Find the volume of the ship in m,if the volume of the model is 600cc. . Find the deck area on the model in sq.cm, ifthe deck [3) area on the ship is 500 sq m. (3] b. Solve :(upto 3 s.f ) 5x2-6x -9 =0 A 14] C. Given ABCD is a cyclic quadrilateral , O is center reflex angle BOD = 220 0,find angles x, y ,z.. B Question 5. a. B(4,4,) C(-6,0 ).Reflect points B Use agraph paper to plot points A(0,6) points A, B and B' in the line Yaxis to obtain points B' and C. Reflect and C in the B C'B" A'B"" CB' to obtain a closed y=-2to obtain A',B",B" resp. .Join A of points on the figure that are invariant geometrical figure, name the figure.List a pair [5] on reflection in the line y =0. a circle . Find the length of side 6.5 cm, that is inscribed in hexagon regular a Construct (5] b. of the diagonal of the hexagon. (6] Question 6. construct a cumulative frequency curve -70 a. Use the given datato 6060-6565 45 45 - 50 50 -55 55 - Weight Kg40 8 12 15 20 10 70 -75 4 7 pupils If 52 Kg is quartiles, find the inter quartile range. the and median the Estimate number of over weight pupils. considered to be the idealweight, find QR= 8cm. Findthe locus of cm, 6 PQ= Q, at angled PQR, right PQ and QR b. Construct triangle a point Y equidistant from of locus and R and Q P, [4] point X equidistant from and 2 cm from Q. Question 7. prove: (a+b): (c + d) = :b::c:d a If a. Va2 + b2 : Vc? + d2 whose squares is 84. is 16 and sum of sum whose AP in b. Find 4 numbers A C. Given: matr0X matrix C. and A2-5B = 5C. Find MAS: Page 4 of 5 Std 10 Mathematics (3) (3] [4) ARCH MARBLE ARCH SCHOOL A Question 8. In AABC, AB = 6. BD =8, BC = 10cm D angle ABD = ACB. Find AD and the ratios (3) of areas of the similar triangles x3 b. Factorize the given expression completely. (3] 19x-30 modal class for the given data C. Plot aHistogram and estimate the mode and Scale X- axis 2cm = 10 units,y- axis 1cm =1unit Weight Kg 21 - 29 pupils 31 -39 41 - 49 51 -59 12 15 7 (4] 61 - 69 |71- 79 3 Question 9. at random from 41 to 64. If acard is drawn out marked cards identical contains a. A bOx ii. amultiple of 2 and 3 a prime number i. find the probability of getting ii. aperfect square b. Prove: (3] [3] 1+ (sec A-tan A) _=2 tan A COsecA( secA-tan A) metal cylinder of height out from the ends of a solid drilled are hemispheres resulting solid,given C. Apair of volume and surface area of the the Find 30cm. radius and (4] 80 cm have equal radii. (TT =3.1) hemispheres and cylinder the discount on article he purchased at 25% an on tax input as Rs.1200 retailer at a profit of a. A trader pays manufacturer.The trader sells the article to a Question 10. marked price, from a If the rate of article from the retailer at marked price . the buys customer A 1000. retailer Rs. received by the central govt. from the GST is 20 %, find the amount of money (3] sale of the article and from the trader for the represent the solution on anumber line. b. Solve the inequation and 4x 19 <-2s+x (3] xER Find secant. Ois center of the circle. is a AE atC. circle the C. Given AB is atangent to similar. If angle COD is 100 , triangles of pair a proving by the length of the tangent ED= 12 cm x,y .Given AD = 4cm. find the measure of angle Bs C A (41 E +ttktkkkk MAS: Page 5 of 5 Std 10 Mathematics
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