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CBSE Class 10 Pre Board 2026 : Mathematics (Amity International School, Gurgaon) : Preboard

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PERIODIC TEST-3 (2025-26) SUBJECT: MATHEMATICS STANDARD CLASS : X MAX. MARKS : 80 DURATION : 3 HRS General Instruction: Read the following instructions carefully and follow them: 1. This question paper contains 38 questions. All Questions are compulsory. 2. This Question Paper is divided into 5 Sections A, B, C, D and E. 3. In Section A, Question numbers 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion- Reason based questions of 1 mark each. 4. In Section B, Question numbers 21-25 are very short answer (VSA) type questions, carrying 02 marks each. 5. In Section C, Question numbers 26-31 are short answer (SA) type questions, carrying 03 marks each. 6. In Section D, Question numbers 32-35 are long answer (LA) type questions, carrying 05 marks each. 7. In Section E, Question numbers 36-38 are case study-based questions carrying 4 marks each with sub parts of the values of 1, 1 and 2 marks each respectively. 8. There is no overall choice. However, an internal choice in 2 questions of Section B, 2 questions of Section C and 2 questions of Section D has been provided. An internal choice has been provided in all the 2 marks questions of Section E. 9. Draw neat and clean figures wherever required. Take = 22/ 7 wherever required if not stated. 10. Use of calculators is not allowed. 1. 2. 3. 4. 5. SECTION A Section A consists of 20 questions of 1 mark each. The sum of two numbers is 1215 and their HCF is 81, then the possible number of pairs of such numbers are: (a) 1 (b) 2 (c) 3 (d) 4 1 1 If , are the zeros of the polynomial ( ) = 4 2 3 7, then + is 1 1 equal to 7 7 3 3 (a) (b) (c) (d) 3 3 7 7 If the system of equations 3 + = 1 and (2 1) + ( 1) = 2 + 1 1 is inconsistent, then = (a) 2 (b) 0 (c) 1 (d) 1 2 If the roots of ax + bx + c = 0 are equal in magnitude but opposite in sign, 1 then (a) a = 0 (b) b = 0 (c) c = 0 (d) none of these 1 1 1 The value of x for which , , , are the three consecutive terms of an 1 +2 +3 +5 AP a)1 (b) - 1 (c) 3 (d) 5 Page 1 of 7 6. 7. 8. 1 The ratio in which x-axis divides the join of (3, 6) and ( 12, 3) is (a) 2: 1 (b) 1:2 (c) 1:4 (d) 4:1 The fourth vertex D of a parallelogram ABCD whose three vertices are 1 A( 2,3), (6, 7), (8, 3) is (a) (0,1) (b) (0, 1) (c) ( 1, 0) (d) (1, 0) If in two triangles DEF and PQR, D= Q and R = E , then which of 1 the following is not true? (a) = (b) = (c) = (d) = 9. In the given figure, AB = BC = 10 cm. If AC = 7 cm, then the length of BP is : (a) 3.5 cm (b) 7 cm (c) 6.5 cm (d) 5 cm 1 10. In figure AT and AS are tangents to the circle with centre O such that OT = 4 cm and OAT = 30 . Then AS is equal to (a) 4 cm (b) 2 cm (c) 2 3 cm (d) 4 3 cm Which one of these is the value of tan ? 1 11. (a) 12. 13. cos (b) 1 2 sec 1 2 (c) sin 1 2 (d) 1 1 1 2 (Sin 30 +cos 60 ) (sin 60 + cos 30 ) is equal to: (a) 0 (b) 1 + 2 3 (c) 1 3 (d) 1 + 3 4 sin +3 cos If 2 tan = 3,then the value of is 1 1 4 sin 3 cos (a) 14. 15. 16. 7 13 (b) 1 13 (c)3 (d) does not exist If the area and circumference of a circle are numerically equal, then the diameter of the circle is : (a) 1 unit (b) 2 units (c) 3 units (d) 4 units The radius of a semicircular protractor is 7cm, then its perimeter is (a) 22cm (b) 36cm (c) 40cm (d) 41cm The distribution below gives the marks obtained by 80 students in a test: Marks Less Less Less Less Less Less than 10 than 20 than 30 than than than 40 50 60 No.of students 3 12 27 57 75 80 1 1 1 The modal class of this distribution is (a) 10 20 (b) 30 40 (c) 20 30 (d) 50 60 Page 2 of 7 17. 18. A card is drawn from a well shuffled deck of cards. What is the probability that the card drawn is neither a king nor a queen? 11 12 11 11 (a) (b) (c) (d) 13 13 26 52 The probability of guessing the correct answer to a certain test question is . 2 19. 20. 21. 22. 23. 24. 6 1 1 If the probability of not guessing the correct answer to this question is , 3 then the value of is : (a) 2 (b) 3 (c) 4 (d) 6 DIRECTION: In the question number 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option 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 and reason (R) is not the correct explanation of assertion (A) C)Assertion (A) is true but reason (R) is false. D)Assertion (A) is false but reason (R) is true Assertion (A): , , are in Arithmetic progression if and only if 2 = + 1 Reason (R): The sum of first odd natural numbers is 2 Assertion (A) : Two cubes of edge length 10 cm are joined together. The 1 3 total surface area of newly formed cuboid is 1200 cm Reason (R) : Area of each surface of a cube of side 10 cm is 100 cm2 Section B Section B consists of 5 questions of 2 marks each. Prove that 5 is an irrational number. The perimeters of two similar triangles ABC and PQR are 32 cm and 24 cm respectively. If PQ = 12 cm, find AB. In the given figure, OP is equal to diameter of the circle. Prove that ABP is an equilateral triangle. If tan = 1 7 , then show that 2 2 2 + 2 = 3 2 2 2 2 4 OR 1 If sin( ) = , cos( + ) = ; 0 < + 900 , > . Find and 2 2 A 3.5 m chord subtends an angle 600 at the centre of a circle. Find the length 2 of arc of minor sector? Draw rough figure and show your steps. OR 1 25. Page 3 of 7 The length of a minute hand of a clock is 21cm. Find the area swept by minute hand in 10 minutes. 26. 27. 28. Section -C Section C consists of 6 questions of 3 marks each. 4 Bells toll together at 9.00 am. They toll after 7, 8, 11 and 12 seconds 3 respectively. How many times will they toll together again in the next 3 hours? Find the value of p such that the sum of the zeroes of the polynomial 3 3 + 2 + (2 + 3 ) + 8 is 10 more than the sum of product of zeroes taken two at a time. The students of a class are made to stand in rows. If 3 students are extra in a 3 row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class. OR 29. Solve for x and y: = 0 and + = 2 + 2 Two tangents TP and TQ are drawn to a circle with centre O from an external 3 point T. Prove that = 2 OR A circle touches the side BC of a at a point P and touches AB and AC when produced at Q and R respectively. 1 Show that AQ = (Perimeter of ). 2 1 30. If 1 + = 3 , then prove that tan = 1 or tan = 31. The mean of the following frequency distribution is 50. Find x, y and z if 3 y:z =4:3 and sum of the frequencies is 120. Class 0-20 20-40 40-60 60-80 80-100 Frequency 17 x y z 19 Section -D Section D consists of 4 questions of 5 marks each Two water taps together can fill a tank in 6 hours. The tap of larger diameter 5 takes 9 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank. OR A motorboat whose speed is 24km/hr in still water takes 1 hour more to go 32km upstream than to return downstream to the same spot. Find the speed of the stream. In the given fig, PA, QB and RC are all perpendiculars to AC. Prove that 5 1 1 1 + = . 32. 33. 2 2 3 Page 4 of 7 34. 35. 36. A tent is in the shape of a right circular cylinder up to a height of 3 m and then a right circular cone, with a maximum height of 13.5 m above the ground. Calculate the cost of painting the inner side of the tent at the rate of 2 per square metre, if the radius of the base is 14 m. OR A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere of same radius. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy. Also, find the total surface area of the toy. Find the median of the following data . Marks More More More More More More More than than than than than than than 80 90 100 110 120 130 140 No of 150 141 124 105 60 27 12 Students Section-E Section E consists of 3 case study based questions of 4 marks each. Mohan is an auto driver. His autorickshaw was too old and he had to spend a lot of money on repair and maintenance every now and then. One day he got to know about the EV scheme of the Government of India where he can not only get a good exchange bonus but also avail heavy discounts on the purchase of an electric vehicle. So, he took a loan of 1,18,000 rupees from a reputed bank and purchased a new autorickshaw. Mohan repays his total loan of 118000 rupees by paying every month starting with the first instalment of 1000 rupees. (i) If he increases the instalment by 100 rupees every month, then what amount will be paid by him in the 30th instalment? (ii) If he increases the instalment by 100 rupees every month, then what amount will be paid by him in the 100th instalment (iii) If he increases the instalment by 100 rupees every month, then what amount of loan does he still have to pay after 30th instalment? OR (iii)If he increases the instalment by 200 rupees every month, then what amount would he pay in 40th instalment? 5 5 1 1 2 or 2 Page 5 of 7 37. 38. A group of class X students goes to picnic during winter holidays. Aman, Kirti and Chahat are three friends. The position of three friends Aman, Kirti and Chahat are shown by the points P, Q and R. Based on the above information answer the following questions (i) Find the distance between P and R. (ii) Is Q, the midpoint of PR? Justify by finding midpoint of PR. (iii) Find the point on x-axis which is equidistant from P and Q. OR (iii) Let S be a point which divides the line joining PQ in ratio 2:3. Find the coordinates of S. Trigonometry in the form of triangulation forms the basis of navigation, whether it is land, sea or air. GPS a radio navigation system helps to locate our position on earth with help of satellites. A guard, stationed at the top of a 240 m tower, observed an unidentified boat coming towards it. A clinometer or inclinometer an instrument used for measuring angles of slopes (tilt). The guard used the clinometer to measure the angle of depression of the boat coming towards the lighthouse and found it to be30 . (i) Draw a labelled figure on the basis of the given information. (ii) Calculate the distance of the boat from the foot of the observation tower. (iii)As the boat covered 240( 3 -1) m towards the tower in10 minutes, the alarm started. What was the new angle of depression of the boat from the top of the observation tower? OR (iii) As the boat covered 240( 3 -1) m towards the tower in10 minutes, the alarm started. Another guard observed the boat from the window just below the window at the top at the angle of depression 30 . What is the distance between two windows? 1 1 2 or 2 1 1 2 or 2 Page 6 of 7 Page 7 of 7

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