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ICSE Class X Prelims 2023 : Mathematics (Baldwin Boys High School (BBHS), Bangalore)

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Dikshit Rishi Jain
Baldwin Boys' High School (BBHS), Bangalore

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BALDWIN BOY'S HIGH SCHOOL MODEL EXAMINATION JANUARY 2023 MATHEMATICS Class:X Time:2Hours Date:1-01-20a3 Max. Marks : 80 General Instructions Intended for the question are given in the brackets Reading time for the paper is 15 minutes Section A (Attempt all questions from this section) Question 1. Choose the correct answers to the questions from the given options [15] i. A dealer in a city buys some goods worth Rs.6000 from the same city. Ifthe rate of GST is 18% find SGST paid a) Rs.1080 ii. b) Rs.540 d) Rs.6540 c)Rs.7080 When the roots of a quadratic equation are imaginary then the discriminant of the quadratic equation is a) equal to zero b) greater than zero c) less than zero d) infinity ii. Find the value of k for which x is equal to 2 is a root ofequation kx2 +2x -3 is equal to is equal to zero b) a) d) iv. A point P is reflected in the x-axis,co-ordinates of its image are (8, -7) find the co-ordinates of P a) (-8,7) b)(-8,-7) c) (-7,8) d) (8,7) v. In AABC, AB=4cm, BC=3cm, ZB=90 and In ADEF, DE-24cm, EF=18cm, 2E=90 then the triangles are similar by the axiom a) SSS b) SAS d) RHS c) AAA vi. Order of matrix A is 1x2 and order of B is 2x3 then the order ofmatrix AxB is a) 2x2 d) 2x3 c) 3x1 b) 1x3 vii. 5, 8, 11, 14...... . are in arithmeticprogression, the value of 1Oth term is a) 20 c)32 b) 23 d) 3 vii. The volume of a right circular cone with same base and radius and height as that of a right circular cylinder is 60 cm', the volume of the cylinder is a) 180 cm b) 20 cm c) 360 cm ix. The solution set for the given in equation is -2 <y<4 a) {1.2,3) b) {0,1.2,3 d) 90 cm xEN c)-1,0,1,2 d) (-2-1,0,1,2.3} X. In a single throw of a dice find the probability of getting a number less than or equal to 2 b) 1 d) 0 c) xi. In the given diagram AC is diameter of the circle and 2BAC=40", find zACB a) 60 B b) 90 c) 70 0 d) 50 XIL Calculate the coordinate ofthe point P which divides the line segment joining A (1,3) and B (5,9) in the ratio 1:2 a) (53) xii. Find the sum b) G.5) of 10 terms a) 55 xiv. The d) (3.) c) 120 d) 110 of an AP 2, 4, 6,... b) 220 weights of5 persons are 67, 65, 71, 57 and 45 find the Arithmetic mean of the weights a) 63Kg xV. )G.3) Curved surface b) 65 Kg area of a cylinder a) 40 cm c) 61 Kg d) 71 Kg cylinder is 4400 cm and circumstances of its base b) 44 cmn c) 11 cm is 110 cm find height of a d) 42 cm Question 2. i. Ashish deposits certain sum of money every month in a recurring month if the bank pays interest at the rate of 11% Pa and Ashish of this account, what sum of money did he pay every month? ii. Prove cos+tan A = secA deposit account for a period of 12 gets Rupees 12715 as a maturity value 4 4] 1. Using componendo and dividendo find the value of x 3x44 +3x-5 - 9 V3x+4- V3x-5 [4] Question3. i. The radius of the base and the height of a right circular cone are 7 cm and 24 cm respectively, find the volume and the total surface area of a cone, ii. In the given figure, line APB meets the x-axis at AP:PB=1:2 find the co-ordinates of A and B P [4 point A and y-axis at point B, P is the point (-4,2) and [4) 11. Using a graph paper, plot the points A(6,4) and B(0, 4) Reflect A and B in the origin to get the inmages A' and B b. State the coordinates of A' andB a. C. State the geometrical name for the figure AB A' B d. Find the perimeter Section B (Attempt any four questions from this section) Question 4. 1. Solve for x and give your answer correct to 2 decimal places x - 5x - 10= 0 (3] i. Find the amount of Bill for the following intra-state transaction of goods, the rate of GST is 12% MRP Rs.250 Rs.200 DISCOUNT 30% 40% ii. Draw a histogram for the given data using a graph paper, find the mode. Weekly Wages (in Rs.) No. of people 3000- 4000 4 4000 5000 9 5000 6000 18 6000- 7000 6 [4) 7000-8000 8000 9000 2 9000 10000 4 Question 5, i If A- and I- find A-5A +71 ii. In the given figure, given alongside PQ=QR, 4RQP=-68 , PC and QC are tangents to the circle with centre O. calculate the values of a) 2Q0P b) 2QCP [3] [31 [3] 111. Using the remainder theorem, factorise the expression 2x + x 2x - I completely [4] 12, 31 Question 6. i. Find the equation of the line whose X intercept ii. Prove thatanA t SecA-1 - 1+ sinA tanA-secA + 1 111. is 8 and Y intercept is 13] coSA Determine the AP, whose 3 is 16 and the 7th term exceeds the Sth term tem by 12 [41 Question7. i. A bag contains 16 coloured looking into the bag. a. balls, 6 green, 7 are red and 3 are probability that the ball chosen is Find the Red are white, A ball is chosen without 3 b. Not white C. Green or red ii. A Hollow metal cone sphere of intemal and external radii 2 cm and 4 cm respectively is melted into a cm, Find the height and slant height of the cone. of base radius 4 solid 3] A ii. In the given circle with Centre O, angle LABC=100 , 4ACD=40 and (4 CT is tangent to the circle at C. B Find 2ADC and 2DCT 100 Question8. i. Solve the O C T following inequation and represent the solution set on number line 7%, x I -8 < - -4x ii. Using the step deviation method calculate the Class Interval 50-55 given figure calculate AD nmarks of the 55-60 60-65 65-70 20 10 10 Frequency ii. In the mean AB and DE are following distribution 70-75 75-80 9 perpendiculars to BC, if AB 80-85 85-90 612 = 9 cm, 3 8 DE=3cm and AC=24 cm 4] D B C Question9. 1Some students planned a picnic. The budget for the food was Rs.480, as 8 ofthem failed to join the party, the cost ofthe food for each member increased by Rs.10, Find how many students went to the picnic? [4] 11. The marks obtained by 100 students in a Maths test are given below Marks 0-10 No. of students 3 10-20 20-30 7 12 30-40 40-50 50-60 17 23 14 [6] 60-70 70-80 80-90 96 90-100 4 Draw an ogive for the given distribution on a graph sheet. Scale 2cm = 10 units on both axes. Use ogive to estimate a. b. C. d. Median lower quartile number of students who obtained more than 85% marks in the test number of students failed if the past percentage was 35 Question 10. i. If Ba-5b 8c-5d 8css Provethat ii. Construct a regular hexagon of side 4cm. Construct a circle circumscribing the hexagon. [3] 13 ii. The angles of depression of two ships A and B as observed from the top of a light house 60m high, are 60 and 45 degree respectively, If the two ships are on the opposite side of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number [4]

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