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PAWAR PUBLIC SCHOOL, KANDIVALI FIRST PRELIMINARY EXAMINATION (2023-2024) SUBJECT: MATHEMATICS GRADE: 10 MARKS: 80 DATE: 21/11/2023 TIME: 2 HOURS Answers to this paper must be written on the answer script provided by the school. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of the paper is the time allowed for writing the answers. Attempt all questions from Section A and any four questions from Section B The intended marks for questions or parts of questions are given in brackets []. This paper consists of 7 printed pages. SECTION A (Attempt all questions from this section) Question 1 Choose the correct answers to the questions from the given options: [15] (i) If a dealer supplies goods worth 30000 to another dealer with a rate of GST 28%, then the tax levied under CGST is (a) 3600 (b) 4200 (c) 2100 (d) 8400 3 4 1 1 (a) Unit matrix (ii) If 2 is: (b) Negative of the unit matrix (c) Zero matrix (d) Twice of unit matrix. (iii) The value of (a) 2 (b) 1 1 for which the roots of 0 are real and equal is : (c) 0 2 (d) (iv) If : 5: 3 then : is: (a) 17: 8 (b) 15: 7 (c) 8: 17 PPSK 23-24 /10 / MATHEMATICS Pg 1 of 7 (d) 7: 15 2 (v) The remainder when 5 7 is divided by 3 : 17 (a) (b) 17 (c) 55 55 (d) (vi)Assertion: ABC~ DEF such that area ( ABC 49cm then, AB: DE 36cm and area DEF 6: 7. Reason: If 56~ 789, =>C :;<: =>? @AC :;<: @AB >?C ABC =?C @BC : (a) A is true and R is false. (b) A is false and R is true. (c) Both A and R are true. (d) Both A and R are false. D DFE DF E (vii) The common difference of the AP , E E , E , . (a) 1 1 (b) (c) D E D (d) E (viii) The coordinates of the point of intersection of the medians of AOB in the adjoining figure are: (a) 2,3 J (b)I2, K (c) 3,2 (d)I4, K (ix) A bag contains 5 red balls, 7 white balls and 3 black balls. The probability that a ball drawn from the bag is neither white nor black is (a) (b) D L DM (c) PPSK 23-24 /10 / MATHEMATICS Pg 2 of 7 (d) D M (x) How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm? (a) 24 (b) 12 (c) 64 (d) 512 (xi) NO N Q (a) NO Q RSTU O: 1 (b) 1 (c) T Q (d) Q (xii) Assertion: Total investment to purchase 400 shares, 12 shares at a premium of 1 is 5200 Reason: Sum invested the number of shares bought _ N. V of 1 share. (a) A is true and R is false. (b) A is false and R is true (c) Both A and R are true. (d) Both A and R are false. (xiii)If the angle of depression of an object from a 75m high tower is 30b , then the distance of the object from the tower is: (a) 25 3 (b) 50 3 (c) 75 3 (d) 150 (xiv) The median of number 10, 8, 2, 7, 3, 8, 5, 1 is . If 10 is replaced by 1, then the new median is d, the value of (a) d is: 1.5 (b) 0 (c) 1 (d) 2 PPSK 23-24 /10 / MATHEMATICS Pg 3 of 7 (xv) ABCD is a rhombus with coordinates 3, 1 T f 6 5,6 . The slope of diagonal BD is: F (a) L FL (b) (c) M (d) L Question 2 (i) From a circular cylinder of diameter 10N and height 12cm, a conical cavity of the same radius and of the same height is hollowed out. Find the volume and the whole surface area of the remaining solid. (g (ii) In the given figure 78 56, 7: 75 3.14 [4] 5: 4 [4] A Find : (a) 78: 56 D (b) If AE=2.5cm, find AC. (c) A ADE : A DBCE (iii) Prove that: jkl m DFnopm qrpm DFstnm B E C NO [4] Question 3 (i) From the top of a tower of height 60m, the angle of depression of the top and bottom of a pole are 30 and 45 . Find [4] (a) How far the pole is from the bottom of the tower. (b) The length of the pole. (ii) Draw a regular hexagon of side 4cm. Construct its incircle. Measure the radius. (iii) Draw an ogive for the following distribution. [4] [5] Take Scale on one axis, 2 cm = 100 and on the other axis, 2 cm = 50 employees Monthly 6007008009001000income 700 800 900 1000 1100 No. of 40 68 96 120 90 employee Determine: (a) The median income. (b) The percentage of employees whose income exceeds 1180 (c) The interquartile range. PPSK 23-24/ 10 / MATHEMATICS 11001200 40 12001300 26 Pg 4 of 7 SECTION B (Attempt any four questions from this section) Question 4 (i) If Find: 5 3 ,5 1 26 4 T f7 5 6 ,6 1 47 2 2 [3] (ii) The model of a building is constructed with the scale factor 1:30. (a) If the height of the model is 80cm, find the height of building in meters. (b)If actual volume of the building is 27 , find the volume of the model in cm3 [3] (iii) Solve the quadratic equation and give the answer correct to two significant figures. 4 7 2 0 [4] Question 5 (i) A mathematics aptitude test of 50 students was recorded as follows: [3] Marks 50-60 60-70 70-80 80-90 90-100 No of 4 8 14 19 5 Students Draw a histogram for the above data using a graph paper and locate the mode. Take Scale: on x axis 2cm 10units, on y axis, 2cm 2units (ii) Mr. Rahul goes to a shop to buy a leather coat which costs 885(list price). The rate of GST is 18%. He tells the shopkeeper to reduce the price to such an extent that he has to pay 885 inclusive of GST. Find the reduction needed in the price of the coat. (iii) [3] Shobha has a recurring deposit account in a bank for 3years at 7.5% p.a. simple interest. if he gets 8325 as interest at the time of maturity, find [4] (a) The monthly installment. (b) The amount of maturity. Question 6 (i) In a GP, if the third term is 72 and the sixth term is 1944, find the nth term. [3] (ii) A hollow sphere of internal and external radii 6cm and 8cm respectively is melted and recast into small cones of base radius 2cm and height 8cm. Find the number of cones formed. PPSK 23-24 /10 / MATHEMATICS [3] Pg 5 of 7 (iii)Construct a triangle ABC in which 5 5N , 5 60 , 45 [4] (a) Construct the locus of the point equidistant from the sides BC and AB (b)Construct the locus of a point at a fixed distance 3cm from the point C. (c) Two loci intersect at P and P '. Measure and record PP '. Question 7 (i) If the sum of the first 7 terms of an AP is 119, and that of the first 17 terms is 714. Find the sum of first n terms & the 10th term. [5] (ii)The weights of 50 apples were recorded is given below. Calculate the mean weight, to the nearest gram, by step deviation method. wt in [5] 80-85 85-90 90-95 95-100 100-105 105-110 110-115 5 8 10 12 8 4 3 grams. No of apples Question 8 (i) Solve the following in equation. Find the solution set and represent it on a number line {|D 7 z (ii) Prove that: z 11, D|qrpm DFqrpm ~ T [3] N [3] (iii) A straight line passes through P (2, 1) and cuts the axes in points A on x-axis and B on yaxis. If 5 : 3: 1 Find: (a) The coordinates of A and B (b)The equation of the line AB. [4] Question 9 (i) Using properties of proportion solve for x: L{ | J{F L{F J{F (ii) Without using Pythagoras theorem, prove that the points 6 [3] 1,3 , 5 3, 1 and 5, 5 are the vertices of a right triangle. (iii) The speed of an express train is 12 6 [3] / d and the speed of the ordinary train is / d less than that of the express train. If ordinary train takes one hour longer than the express train to cover a distance of 240km, find the speed of the express train. PPSK 23-24 /10 / MATHEMATICS [4] Pg 6 of 7 Question 10 (i) The polynomials T divided by 3 13 and 2 5 T leave the same remainder when 2. Find a. [3] (ii) There are 25 discs numbered to 25. They are put in a closed box and shaken thoroughly. A disc is drawn at random from the box. Find the probability that the number on the disc is: [3] a. An odd number b. Divisible by 2 or 3 c. A number less than 16 (iii) Use graph paper to solve this question. Take 2cm 1 Unit on both axes. [4] a. Plot A ( 4, 2) and B (2,4) on the graph paper. b. A' is the image of A when reflected in the y- axis. Plot it on the graph paper write the coordinates of A'. c. B is the image of B when reflected in the line AA'. Write the coordinates of B'. d. Write down the geometrical name of the figure ABA'B'. PPSK 23-24 /10 / MATHEMATICS Pg 7 of 7
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