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ICSE Class X Prelims 2025 : Mathematics (Bhaktivedanta Swami Mission School (BSMS), Mumbai) Prelim 2

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Srikant Uchil
Ryan International School ICSE (RIS), Malad, Mumbai

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Bhaktivedanta Swami Mission School PRELIMINARY EXAMINATION (2024 - 2025) MATHEMATICS Std: X Maximum Marks: 80 Date: 06/01/2025 Time allowed: 3 hrs Answers tothis Paper must be writen on thepaper provided separately. Youwill not be allowed towrite 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 from Section Aand any four guestions from Section B. All workng, including rough work, must be clearly shown and must be done on the same 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 [I. 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.) Rishi invests 61, 600 in buying shares of nominal value 80 at 10 % () premium. The dividend on shares is 15% per annum then no. of shares he buys: (a) 600 (b) 650 (c) 750 (d) 700 (ii) If on dividing f(x) = 2x' + 6x'- (2k - 7)x + 5by (x +3), the remainder is (k- 1), then the value of k is: (a) -3 (b) -2 (c) 3 (d) 2 Page 1 of 11 The quadratic equation 4x*- 12x + 9=0 has: (a) Real, Rational and distinct roots (iii) (b) No real roots (c) Real, irrational and distinct roots (d) Real and two equal roots (iv) Jayesh has a recurring deposit account in a bank for two years at the rate of 8?% per annum simple interest. If at the time of maturity Jayesh receives 2000 as interest then the monthly installment is: (a) 1200 (b) 600 (c) 1600 (d) 1000 (v) A solid consisting of a right circular cone of height 'h' and radius 'r standing on a hemisphere of radius 'r' is placed upright in a right circular cylinder full of water such that it touches the bottom. Which of the following are true? Statement 1: Volume of cone is rh 3 Statement 2: Volume of Hemisphere is r3 Statement 3: The volume of water displaced out of the cylinder is -nr (h + 2r) (a) Both land 2 (b) Both 2 and 3 (c) Both 1and 3 (d) All 1, 2 and 3 (vi) The Arithmetic Progression is 57, 54, 51, 48, ......21. Assertion (A): The value of the 9h term is 38. Reason (R): The common difference is -3and the nth term for the above A.P, series is calculated by t, = 60- 3n (a) Both A and R are true, and R is the correct explanation. (b) Both A and R are true, but R is not the correct explanation. (c) A is false, but R is true. (d) Both A & R are false. Page 2 of 11 (vi) With reference to the diagram, the height of the mobile phone tower is: (a) 200 m (b) 0.18 m (c) 180 m h? (d) 18 m 1.8m 6m 60m (viii) The point of intersection of altitudes of a triangle is: (a) Orthocentre (b) Incentre (c) Circumcentre (d) Centroid (ix) F*+2y 4x then the value of (x - y) is: (a) -3 (b) 1 (c) 3 (d) 5 (x) The GST paid by a customer to the shopkeeper for an article which is priced at 1050 is 73.50. The rate of SGSTcharged is: (a) 1.5% (b) 3.5 %o (c) 7% (d) 3% (xi) In the given figure, O is the centre of the circle, PA is tangent and PBC is secant. If LABC= 65 , LAPC is: (a) 30 (b) 20 B (c) 115 (d) 40 Page 3 of 11 (xii) Point (-5, 3) divides the line segment joining (-3, -1) and (-8, -9)in the ratio of: (a) 2:3 (b) 3:2 (c) 1:1 (d) 4:11 (xiii) If AB| CD and makes an inclination of 0 and a respectively with x- axis. B Ot A Assertion (A) : The slope of lines AB and CD are equal. Reason (R): tan e= tan a (a) Both Aand R are true, and R is the correct explanation. (b) Both A and R are true, but R is not the correct explanation. (c) A is false, but R is true. (d) Both A & R are false. (xiv) When a dice is cast with bullets on its faces, as shown, the ratio of the probability of getting a multiples of 2 or 3 to the probability of getting a prime number is: (a) 3 : 4 (b) 4:3 (c) 1:3 (d) 2 : 1 (xv) The solution set for the given inequation is: -15 < 5x < 10, and x E N (a) (-3, -2, -1, 0, 1,2) (b) {1,2) (c) (0, 1,2) (d) {1} Page 4 of 11 Question 2. correct to three Solve the following quadratic equation for x and give your answer () significant figures: 4r'- 5x-3 = 0 [4] (Use mathematical tables if necessary) of the circle. In the given figure, Ois the centre (ii) intersect each other at pointP. The tangents at B and D LABC = 55 , find: If AB is parallel to CD and (4] (a) ZBOD (b) ZBPD (c) ZPBD [4] Prove that: (ii) sin'0 cos0 1- tan 0 Question 3. (1) sin Cos 9 = 1+sin cos 0 parallel to they -axis. In the given figure ABC isa triangle and BC is ABand AC intersect the y- axis at P and Q respectively. (a) Write the co-ordinates of the A. (b) Find the equation of the line perpendicular to AB and passing through A. B(2,3) (4] 3 P xe 3 A 0 -2 C2,4) y Page 5 of 11 2 3 (ii) A spherical copper shell of external diameter 18 cm is melted and recasted into a solid cone of base radius is 14 cm and height 4cm. Find the inner diameter of the shell. (ii) 14] For this question, use a graph paper. (5] Scale: 2cm=2 units along both xand y - axis. Plot the points A(10,-2) and B(2,6) in the graph and answer the following: (a) Reflect point Bin line y = -2 to point Dand write the co-ordinates of points D. (b) Reflect point A in the line BD topoint C and write the co-ordinates of point C. (c) Find a point P on BC which is invariant under reflection in y =0, and write its co-ordinates. (d) Write the geometrical name of the closed figure ABCD. SECTION B (Attempt any four questions from this Section) Question 4. A child's game has 8 triangles of which 4 are blue and rest are red, and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a: [3] (a) Triangle (b) Square of blue colour (c) Triangle of red colour () Find the sum of all natural numbers between I and 100, which are divisible by 3. [3] Page 6 of 11 (ii) Mr. Sumeet Narayan invested 8000 in 7% of 100 shares at 80. After a year he sold these shares at 75 each and invested the proceeds (including his dividend) in 18% for {25 shares at 41. Find: [4] (a) His dividend for the first year. (b) Sale proceeds. (c) His annual income in the second year. Question 5. () If (x- 2) is a factor of the expression 2x3 - x - px - 2. |3] (a) Find the value of p. (b) Also, factorise the above expression completely. (i) Using a graph paper, draw a histogram for the given distribution showing the number of runs scored by 50 batsmen. Runs scored 30 - 40 [3| 40 -S0 50 60 60-70 70- 80 80 - 90 90 -100 4 6 (in 100 runs) No. of batsmen 4 18 2 Estimate the mode of the data. (iii) Construct a triangle ABC with the following data: [4] AB=5 cm, BC = 6 cm and LABC =90 . (a) Find the point R and S which is equidistant from B and C and is 4 cm from A. Measure SR. (b) Construct acircle circumscribing the triangle ABC. Page 7 of 11 Question 6. () IfA= find the value of A - 5A+ 71, -1 [3] where I is the unit matrix of order 2 x 2. 3 (ii) How many terms of the Geometric Progression (G.P.) : 3, ; the sum (iii) 3 are needed to give 3069 [3] 512 B In the given figure, 14| AB =9 cm, PA =7.5 cm and PC = 5 cm. D Chords AD and BC intersect at P. (a) Prove that APAB ~ APCD. 7-5 cm (b) Find the length of CD. (c) Find the area of APAB:area of APCD. A Question 7. (i) The difference of squares of two natural numbers is 180. The square of the smaller number is 8 times the larger number. Find the two natural numbers. (3] (i ) Using the properties of proportion, solve the following equation for x: x3 + 3x 3x2 + 1 (ii) (3] 341 91 The following bills shows the GST rate and the marked price of articles: 14] Morris Clothings and Accessories S. No. Item Marked Quantity Discount Rate of GST Price 1. Jeans 2500 02 8% 28% 2. A pair of shoes 12000 01 10% 12% Find the total amount to be paid (including GST) for the above bill. Page 8 of 11 Questio)n8. Utkarsh has a recurring deposit account of ? 1000 per month at 10% per annum. If he gets 5550 as interest at the time of maturity, find the total time in years for which the account was held. 3] (i) The vertices of atriangle are A(-5,3),B(p,-1)and C (6,q). (a) Find the values of p and q if the (b) The midpoint of AC (ii) A boy [3) centroid of the triangle ABC is the point (1, -1). standing on the ground finds a bird flying at a distance of 100 m from him at an elevation of 30 . A girl standing on the roof of 20 m high building finds the angle of elevation of the same bird to be 45 , The boy and the girl are on opposite sides of the bird. Find the distance of the bird from the girl. (Give your answer correct to the nearest metre.) (4] Question 9. In the given figure, (i) (S] O is the centre of the circle. PSTUand PQTS are the cyclic quadrilateral. If ZSPQ=45 and ZPOT = 150 , find the measures of: (a) ZPUT (b) LPST (c) 2QTR (d) LQRT T 150 P Page 9 of 11 45 R (ii) The class mark and frequency of a data in the graph. 11 - 25 35 55 65 75 Age (in years) From the graph, find: (a) The table showing the class interval and frequwency. (b) Find the average (mean) number of patients attending the hospital by using Step deviation method. Take the assumed mean as 45. Question 10. (1) Prove that: [3] (cosec 6- sin 0)(sec 6 - cos ) (tan 6 + cot 0) = 1 Page 10 of 11 (ii) Solve the following inequation write the line. 5 solution set and represent it on the real number |3] 1 <2, xE W (ii) Use a graph sheet to answer the following questions: The following data represents the distribution of marks gained by a group of 400 students in an examination: Marks less than 14) Number of students 10 20 30 10 30 40 60 105 180 270 355 390 400 60 70 80 90 100 Use 2 cm = 10marks and2cm =50studnets along x- axis and y- axis respectively. (a) Represent the above distribution by a smooth ogive. (b) Find the median marks from the graph drawn. (c) If 25 students qualify for merit scholarship, find the minimum marks required. Page 11 of 11

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