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ST MARYrssCHOOL, PUNE 2024-2025 EXAMINATION PRELIMINARY 10minutes 3 Hours Reading Time: X Class Witing Time: Mathematics Subject Maximum Marks 80 Instructions: loss of marks. will resut in Omission of essential steps on the answer script to be done work working, including the rough All Section Answer all itsef A (40marks) from this section questions 1 Question (15) Choose the OG) s() -2(). the Which of equally should (c) inclined 2x-2y =3 2500 (b) (c) 2x+7*-4x the polynomial then equal If to-2, one 7 of -14 completely the values of a is (d) 3x-2y is given 30-40 4 40-50 Frequency Assertion( A)The difference between the median class is 0. Reason (R) Modal (a)both A and R (c) A true but 60-70 70-80 5 2 limit class and median class are always of the modal dass and the upper same for a frequency distribution. A and R are false (b)both Ris false (d) A is false but Ris true S the given diagram, railway stations P, Q, R, and T are connected by straight tracks. Track ST is parallel 24 km QR The time taken bya train travelling at a speed of 72km/ hr to reach Q from P by the shortest route is 30km (a) 75 minutes (b) 60 minutes (c) 45minutes 90km 41-minutes Page 1 of6 is (d)-9 3 are true (vi)in quotient 50-60 8 the upper 2040 -1 n, then the fourth tem of the (c)- 39 (v) to track =2 () by S,=n-16 (b) 48 C.I. (d) by (2x-a) and the (c) 1 n terms of an A.P. (a) -21 2020 divisible (b) -7 (v) If the sum of first series is (G) axes? to 2400 is to the for 2years paying 6% p.a opena RD. account for 2000 per month annum. How much to 5% per interest the rate of interest The bank reduced the same.? remains her interest so that Smita deposit monthiy for 2 years intended simple (a) lines (b) y=-3 (D Smita ()-23 (C) 23 equations represent the following (a) x=3 (N) x - yis value of b) -11 (a) 11 (a) questions from the given options. cored answersto the limit of : Mathematics X Class sS:X 7 A paint mixture is created by mixing 3 parts of blue pigment with pats of the base. Using the infomation in the following table, determine the values of x, y and z to (vii) 3 7 blue pigment of Parts Parts of base (a) x=14,ym4.5, z the mixture. ratio in the correct maintain y 6 21 24 (b)x=14, y=9, z=21 (c)X= 10.5,y =4.5, z=28 (d) x=14, A person standing on a boat that (ix) is moving towards a y ciff is = 3, z=10 observing the top of the cif. Over a period of 15minutes, the angle of elevation from the boat changes from to . Which of the following is true? 0 (a) (x) <0 (b) > (c) if O the centre is theciff = (b)x +x -6 =0 (d) 4x?- 5x -6 =0 +5x-6=0 fiqure, of and 2 x-5x-6=0 (a) (x) In the top 3 Form the quadratic equation whose roots are (c)4x 8 to the of circle and zBOC tocteou = 110 , then LADC = 1100 D B (a)55o (b) 70 Find the difference between (xii) (c) 35 the (d) 25 maximum and minimum values of x that the satisfy inequality: s -1 (a) -5 Which (xii) 3+ 4x < of the following (c) 6 points is (a) (-3, -2) invariant A (d) 4 with respect to the (b) (3,-2) dealer buys an article for consumerat a profit of 25%. dealer to the state (xiv) xZ 23, (b) 5 line (-1,-3) (c) y =-3? (d) (1,3) 16000from If a wholesaler. He sells the the rate of GST is 5%,the tax (under government is 100 (a) (b) (xv)The volumes (a) 5:4 200 (c) two spheres are of (b) 4 in the ? 400 (d) 125:64.The ratio (c) 16: 25 ratio :5 article toa GST) paid 800 of their surface areas (d) 25:16 Question2 (0) If4 x21 is a factor (a) find the value (b) factorise of m m x- 12 x-x+n,then n using remainder and factor theorem. the given polynomial completely. of and ()A(6, - 2), B(3, 3)and C(-1, 5)are the vertices of a (a) median throughA (b) altitude through B. Page 2of 6 triangle. by the Find the equation of the is Mathematics o) In figure, BD is a diameter Find: (a) 2BAC and (b) ZACB CE (c) a tangent at C. is ZADC BCE ACD =75": 25 , (d) zDBC D (4,4,4) ) 3 Question An A.P. consists Find (a)the ( ) The ratio of 29th 50 terms of which (b) the sum tem. the radius and the height melted and (a) diameter made into of cone a solid term is 12 and the last term 3rd of of of first a (c) Find the perimeter of the quadrilateral Name the geometrical figure POP'O. Find the area of the figure POP'0'. (c) (d) (e) right circular 20cm Question ()In figure, AT is a tangent at T, (b) (c) Find area 4 :1. This is and POP'O' (4, 4, 5) section) AB = 8cm, AT=12 cm A ABT andA ACT are Prove that Find the length (a) is (Take1cm = 1 unit on both axes) O'is the image of O(origin) when Section B(40 marks) four questions from this any (Answer 4 cylinder and height 12cm. Find : height of cylinder. question. following the (i) Use a graph paper to answer The point P(3, 4) is reflected to P' in the x-axis in the line PP' reflected co-ordinates of P' and O'. (a) Write down the Find the length of segments PP'and O0'. (b) metallic height cone of slant 106. 50 terms. solid (b) radius of cylinder is similar. of BC. (A ABT):area (4 TBC). B ( ) bank and deposited Mr. Amit had a recurring deposit account in a find: was 10% p.a., interest If the rate of years. the equivalent principal for one month. (a) (b) (c) the simple interest. value of this account. the maturity Page 3of 6 600 per month for 2% Mathematics Class :X ()The wages of daily workers 500 Class marks Wages)( (Daily were recorded asfollows: 900 800 700 a construction site in 600 1000 3) 8 No. of workers Fom a frequency distribution plotting a histogram. table and find class intervals with 5 12 18 15 the modal wage by (3,3,4) 5 Question (0) theidentity: Prove () 13750 man invests A on dividend the 15% p.a. shares he of he receives 0)= sec 0 +t cosec 0 50 at 10% premium. The Calculate: buys. ( )Solve and graph the solution -3 (x-7) 15-7x ) cot annually. he gets on rate of interest + cos 0) ( tan e buying shares of nominal value in shares is the (a)the number (b) the dividend (c) + (sin his money. on a number > line: ,x R (3,3,4) 6 Question the given figure, the line segment In respectively, such the co-ordinates Find AD is intercepted BC: CD=3:1. B is the mid- that A,B and C of by the point of X-axis and y-axis at B and AC. Y-axis X-axis D (1,-6) (ii) The sum of 3 numbers (ii)The following S. No bill Items 13 in isand their product 12 G.P. is -1. Find the numbers. shows the GST rate, marked price and discount given Ganesh super market Marked Price Quantity % of Discount for items: Rate of GST 80 per Rice 1 2 Wheat flour Soap Powder 3 kg 10kg 10% Z 50 per kg y Nil 120 kg per kg 5kg 5% X % 12% 18% Find: (b)the (c) total of value y, x, if GST on rice and soap powder is SGST paid for wheat flour is R 36. total if (a) the value the amount to be paid (including GST) for the 138.60 above bill. (3,3,4) Page 4 of 6 C Mathetatkos Question (0 awer prepaig while Fi (a) (b) nt pwesentatin PR PR x the enargenent (c)QR5 scale factor A FOR argex akv QR the skte o ANQR tk x. is QR () s APQR APQR PAstI yNr answex (e) ar (AFQR)= en,nd the art (AFQR) m 0 ()The maris a mathematics test are as given bekw 80 0-404050 50-6060-707080 n btaineN by t00 shudents Marks 10-20 2080 90 100 14 23 17 14 Number of 90 students on of 2em = 10 unita on a graph sheet, (Use a scale distribution the given or quartile. Draw an give b) the upper the median your ogive to estimate (a) (d)the number both the axes) Use marks in the test than 75% more students who obtanexd 35 s(c) the number was percentage not pass in the test, the pass (58) of students who dd of it QuestionS equation,find the value the following quadratic roots: equation has real and equal Q Without solving ()In + 2(m a tilted circular the adjoining diagram, base diameter 14m with cylindrical vessel the contains a liquid. When placed vertically, is the mean vessel in the height of the liquid two heights shownin the diagram. (a)volume of liquid in the vessel. the cylinder (b)area of wet surtace, when surface. a horzontal on vertically placad of m or which the given )x t (m+5)=0 - 2em of Scm Find ()The mean the following frequency is 50. Find the values of p and q. C.L. Frequency distribution of 0-20 7 is 20- 40 40-60 is 57.6 and the 60-80 10 sum 80-100 of all the frequencies 100-120 5 (3,3,4) Question 9 Va'+b+va-b Va'+b-Va'-b 2a x prove b that Page 5 of 6 using properties of proportion, Mathematics Class: X scored by The marks (0) 50students are given below. Number of students Marks scored 2 5 0-10 10-20 20-30 12 30-40 40-50 8 50-60 60-70 4 2 70-80 Find the the class is selected at random. Astudent in (a) less than 30. (b) below 60but (c) above has scored: 30 or more. number books that could be purchased and each book to be x, form an equation find measure its the cost per book was more. a certain numberof books of cost If 9600 would be 40 find the original of (3,3,4) x and regular for for Question 10 Construct a 29600. purchases Taking the original cost ofthe book. (ii) that the student 59. A shopkeeper 78 less, the (ii) probability = XA + y so that A hexagon of side 4 cm. where yl, l is Construct the a unit matrix. incircle of the hexagon and radius. observed from the top of a light house depression of two ships A andB as are on the opposite sides of the 50m high are 40 and 52 respectively. If the two ships to twO the ships. Give your answercorrect light house, find the distance between (ii) The angles of 2 significant figures. (3,3,4) Page 6 of 6
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