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ICSE Class X Mid-term 2025 : Mathematics

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JUBILEE INTERNATIONAL PUBLIC SCHOOL (Affiliated To CISCE, New Delhi) Papareddy Palya, Bangalore-72 Preparatory Examination -I 2023-24 SUBJECT : Mathematics CLASS -X Date: 11/ 12/ 23 Marks : 80 Time: 2 hours Answers to this paper must be written on the paper provided separately. 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 this paper is the time allowed for writing the answers. This paper comprises of two Sections; Section A and Section B. Attempt all the questions from Section A and Attempt four questions from Section B. The intended marks for questions or parts of questions are given in brackets [ ] SECTION - A (40 MARKS) (Attempt all the questions) Question 1 Choose the correct answers to the questions from the given options : [15] i. Seema went to a shop to buy a sewing machines worth 10,080. The rate of GST is 12%. He asked the shopkeeper to reduce the price of washing machine to an extent that she has to pay 10,080 inclusive GST. What is the reduced price of the machine ? (a) 9,250 ii. (b) 8,800 (c) 9,000 (d) 8,500 Which of the following is the better investment (I) 16%, 100 shares at 80 (II) 20%, 100 shares at 120? iii. (a) Only I (b) Both I and II have equal values (c) Only II (d) Can t be determined If the polynomial ax3 +3x2 - 9 and 2x3 + 4x + a leaves the same remainder when divided by x + 3 , then the value of a is______. (b) 3 (a) 3 iv. (d) 6 (c) 6 In the given figure PT is a tangent at T to the circle with centre O. if TPO = 250 then the value of x is (a) 250 (b) 650 (c) 1150 (d) 900 vi. A sphere is melted and half of the melted liquid is used to form 11 identical cubes, whereas the remaining half is used to form 7 identical smaller spheres. The ratio of the side of the cube to the radius of the new small sphere is (b) ( ) (a) vii. If sin = then the value of (1 + (a) (c) (d) 2 (c) (d) ) is (b) viii. x -axis divides the line segment joining A(2,- 3 ) and B (5, 6) in the ratio (a) 2 : 3 (b) 3 : 5 ix. Assertion : ABC (c) 1 : 2 (d) 2 : 1 DEF such that ar ( ABC ) = 36 cm2 and ar( DEF ) = 49 cm2 then, AB: DE = 6 : 7. Reason : If ABC DEF , then = = = (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanationof assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. x.The graph of the solution on number line of the inequality 3x 2 < 2x + 1 is xi.Out of one digit prime numbers, one number is selected at random. The probability of selecting an even number is (a) (b) (c) xii.The nature of roots of the quadratic equation 2 (d) - 3x +1 = 0, is: (a) two distinct real roots (b) two equal real roots (c) no real roots (d) more than 2 real roots xiii. Two chords AB and CD of a circle intersect at E such that AE = 2.4cm , BE= 3.2cm and CE = 1.6cm. The length of DE is (a) 1.6 cm (b) 3.2 cm xiv.Value of a if line (c) 4.8 cm and (a) 5/2 (d) 6.4 cm are parallel: (b) 2/5 (c) 10 (d) 2/5 xv. In the adjoining figure, O is the centre of a circle. If the length of chord PQ is equal to the radius of the circle ,then PQR is (a) 600 (b) 450 (c) 300 (d) 150 Question 2 a) A cylindrical tub, whose diameter is 12 cm and height 15 cm is full of ice-cream. The whole [4] ice- cream is to be divided into 10 children in equal ice-cream cones, with conical base surmounted by hemispherical top. If the height of conical portion is twice the diameter of base, find the diameter of conical part of ice-cream cones. b) Rohan has a recurring deposit account in Bandhan Bank. He deposited some amount every month [4] For 2 years at 6% per annum simple interest. If he gets ` 1800 as interest at the time of maturity, then find (i) the monthly installment. (ii) the amount of maturity. c) Prove that : [4] = Question 3 a) Given, x = Use componendo and dividendo to prove that b2 = b) In the given figure, PQ is a diameter, SR | | PQ and RPQ = 29 . [4] [4] Calculate: (i) PSR (ii) SPR c) The marks obtained by 100 students in a Mathematics test are given below: [5] Marks 0 -10 10 -20 20 -30 30 -40 40 -50 50 -60 60 -70 70 -80 80-90 90 -100 No. of 3 12 17 23 14 9 6 5 4 7 students Draw an ogive for the given distribution on a graph sheet. (Use a scale of 2 cm = 10 units on both axes). Use the ogive to estimate the: (i) median. (ii) lower quartile. (iii) number of students who obtained more than 85% marks in the test. (iv) number of students who did not pass in the test if the pass percentage was 35. Section -B (Attempt any four questions from this section ) Question: 4 a) Find a matrix A such that A * +=* + and state the order of Matrix A. [3] b) Amit is proprietor of a firm registered under GST. He has paid GST of 28500 on purchase and collected 39000 on sale. What is the amount of ITC (Input Tax Credit) to be claimed ? What is the amount of GST payable. [3] c) [4] In the given figure, AB || CD || EF . If CD = 6 cm and AC : CE = 2: 3 , find (i) Shows that ECD EAB (ii) Shows that ACD AEF (iii) AB and EF (iv) area AECD : area EAB Question: 5 a) Sachin invests 8500 in 10% 100 shares at 170. He sells the shares when the price of each share rises by 30. He invests the proceeds in 12% 100 shares at 125. Find (i) the sale proceeds. (ii) the number of 125 shares he buys. (iii) the change in his annual income. [3] b) [3] In the given figure, O is the centre of the circle. PQ and PR are tangents and 0 QPR = 70 Calculate (i) QOR (ii) QSR c) Calculate the mean of the following distribution using step deviation method: [4] Marks 0 - 10 10 -20 20 -30 30 -40 40 -50 50 -60 No.of students 10 9 25 30 16 10 Question: 6 a) If 2x3 + ax2 11x + b leaves remainder 0 and 42 when divided by (x 2) and (x 3), respectively, [3] find the values of a and b and hence, factorise the given expression. [3] b) Three vertices of a parallelogram ABCD taken in order are A (3, 6), B (5, 10) and C (3, 2) Find: (i) the coordinates of the fourth vertex D. (ii) the length of diagonal BD. c) Draw histogram of the following fequency distribution and using it, calculate the mode. [4] C.I. 0 -10 10 -20 20 - 30 30 -40 40 -50 50 -60 Frequency 5 15 10 5 12 8 Question: 7 a) Use a graph paper for this question taking 1 cm = 1 unit along both the x and y axis: [5] (i) Plot the points A(0, 5), B(2, 5), C(5, 2), D(5, 2), E(2, 5) and F(0, 5). (ii) Reflect the points B, C, D and E on the y-axis and name them respectively as B , C , D and E . (iii) Write the coordinates of B , C , D and E . (iv) Name the figure formed by BCDEE D C B . b) The mean of the following distribution is 50 and the sum of all the frequencies is 120 . [5] Find the values of p and q. Class Intervals 0 - 20 20 -40 40 - 60 60 - 80 80 -100 Frequency 17 p 32 q 19 Question: 8 [3] a) Solving the following inequation, write the solution set and represent it on the number line -3(x 7) 15 7x > , x R [3] b) Given equation of line L1 is y = 4. (i) Write the slope of line L2 if L2 is the bisector of angle O.( = 450) (ii) Write the co-ordinates of point P. (iii) Find the equation of L2. c) In the given figure, ABCD is a cyclic quadrilateral, PQ is tangent to the circle at point C and BD is its diameter. If DCQ = 40o and ABD = 60o, find: [4] i) DBC ii) BCP iii) ADB Question: 9 a) Use ruler and compass draw a circle with centre O and radius 4 cm.and mark a point P, [3] such that OP = 7 cm. Construct the two tangents to the circle from P. Measure and record the length of one of the tangents. b) Solve for x c) ( )-4( )=3 [3] A toy is made in the form of hemisphere surmounted by a right circular cone whose base coincides exactly with the plane surface of hemisphere. The radius of the base of the cone is 3.5 m [4] and its volume is two third of the hemisphere. Calculate the height of the cone and the surface area of the toy, correct to two places of decimal. Question: 10 a) A game of chance consists of spinning an arrow which comes to rest pointing at one of the [3] Numbers 1, 2, 3, 4, 5, 6, 7, 8 (shown in the adjoining figure) and these are equally likely outcomes. What is the probability that it will point at (i) 8 ? (ii) an odd number ? (iii) a number greater than 2? (iv) a number less than 9? b) If b is the mean proportional between a and c, prove that (i) [3] = (ii) abc (a + b + c)3 = (ab + bc +ca )3 c) A cylindrical can of internal diameter 21 cm contains water. A solid sphere whose [4] diameter is 10.5 cm is lowered into the cylindrical can. The sphere is completely immersed in water. Calculate the rise in water level, assuming that no water overflows. ****************************************************************

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