Practice Paper Maths Class 10 (Standard), Assignments of Mathematics

Download Practice Paper Maths Class 10 (Standard) and more Assignments Mathematics in PDF only on Docsity! CBSE ADDITIONAL PRACTICE QUESTIONS MATHEMATICS STANDARD (041) Class X | 2023–24 Time allowed: 3 Hours Maximum marks: 80 General Instructions: 1. This Question paper contains - five sections A, B, C, D and E. 2. Section A has 18 MCQs and 02 Assertion-Reason based questions of 1 mark each. 3. Section B has 5 Very Short Answer (VSA)-type questions of 2 marks each. 4. Section C has 6 Short Answer (SA)-type questions of 3 marks each. 5. Section D has 4 Long Answer (LA)-type questions of 5 marks each. 6. Section E has 3 case based integrated units of assessment (4 marks each) with sub parts of the values of 1, 1 and 2 marks each respectively. 7. All questions are compulsory. However, an internal choice in 2 questions of 5 marks, 2 Qs of 3 marks and 2 questions of 2 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E. SECTION A (This section comprises of Multiple-choice questions (MCQ) of 1 mark each.) Serial No. Question Marks 1 Which of the following could be the graph of the polynomial? (x - 1)2(x + 2)? 1 =< zadi na Amrit Mahotsav C2e Ti (a) y eee Hee ear aeeecce (b)  What is the radius of the circle? (a) √0.4 units (b) 2 units (c) 4 units (d) √42.4 5 ΔPQR is shown below. ST is drawn such that ∠PRQ = ∠STQ. (Note: The figure is not to scale.) If ST divides QR in a ratio of 2:3, then what is the length of ST? (a) 10 3 cm (b) 8 cm (c) 12 cm (d) 40 3 cm 1 6 Two scalene triangles are given below. 1 (Note: The figures are not to scale.) Anas and Rishi observed them and said the following: Anas: ΔPQR is similar to ΔCBA Rishi: ΔPQR is congruent to ΔCBA Which of them is/are correct? (a) Only Anas (b) Only Rishi (c) Both Anas and Rishi (d) Neither of them, as two scalene triangles can never be similar or congruent. 7 Harsha made a wind chime using a frame and metal rods. She punched 8 holes in the frame, each 2 cm apart, and then hung 6 metal rods from the frame, as shown in the figure below. The ends of the metal rods are aligned over a line, shown by the dotted line in the figure. 1 (Note: The figure is not to scale.) If all of the rods are straight and not swaying, then what is the length of Rod P? (a) 69 7 cm (b) 53 5 cm (c) 76 5 cm (d) 111 7 cm 8 Two circles with centres O and N touch each other at point P as shown. O, P and N are collinear. The radius of the circle with centre O is twice that of the circle with centre N. OX is a tangent to the circle with centre N, and OX = 18 cm. (Note: The figure is not to scale.) What is the radius of the circle with centre N? (a) 18 √2 cm (b) 9 cm (c) 9 √2 cm (d) 18 √10 cm 1 9 Shown below is a circle with centre O having tangents at points P, T and S. 1 13 A circle with radius 6 cm is shown below. The area of the shaded region in the circle is of the area of the circle. (Note: The figure is not to scale.) What is the length of the circle's minor arc? (a) 16𝜋 3 cm (b) 20𝜋 3 cm (c) 16π cm (d) 20π cm 1 14 A regular pentagon is inscribed in a circle with centre O, of radius 5 cm, as shown below. What is the area of the shaded part of the circle? (a) 2π cm2 1 (b) 4π cm2 (c) 5π cm2 (d) 10π cm2 15 A cuboid of base area P sq units is filled with water upto a height of Q units. A sphere of volume R cu units is dropped into the cuboid such that it is completely submerged. A representation of the submerged sphere is shown below. Which of these represents the increase in the height of water? (a) 0 units (b) 𝑅 𝑃 units (c) R units (d) 𝑄 + 𝑅 𝑃 units 1 16 Sweety, Nitesh, and Ashraf visited a hospital for their annual body checkup, which included a blood pressure evaluation. The results of their systolic blood pressure readings are as follows: Sweety: 121 mmHg Nitesh: 147 mmHg Ashraf: 160 mmHg The table below depicts the systolic blood pressure ranges of all the patients who visited the hospital on the same day. Blood pressure (mmHg) Number of patients 115 - 125 10 125 - 135 9 135 - 145 12 145 - 155 19 155 - 165 10 Who among the three friends have a blood pressure reading that falls in the modal class? 1 (a) Sweety (b) Nitesh (c) Ashraf (d) Both Sweety and Ashraf 17 The table below depicts the weight of the students of class 6 of Red Bricks Public School. There are 18 students in the class that weigh above the median weight. If there are no students with the same weight as median weight, how many students weigh between the range of 37 - 40 kgs? (a) 5 (b) 7 (c) 18 (d) 31 1 18 Ginny flipped a fair coin three times and tails came up each time. Ginny wants to flip the coin again. What is the probability of getting heads in the next coin flip? (a) 0 (b) 0.25 (c) 0.5 (d) 1 1 19 A number q is prime factorised as 32 × 72 × b, where b is a prime number other than 3 and 7. Based on the above information, two statements are given below - one labelled Assertion (A) and the other labelled Reason (R). Read the statements carefully and choose the option that correctly describes statements (A) and (R). 1 (Note: The figure is not to scale.) Find the angle which the slant height makes with the base radius. Show your work. (Note: Take π as 3, √2 as 1.4 and √3 as 1.7.) OR Shown below are two right triangles. (Note: The figure is not to scale.) Find the length of the unknown side marked '?'. Show your work. 2 25 ABCD is a rhombus with side 3 cm. Two arcs are drawn from points A and C respectively such that the radius equals the side of the rhombus. The figure is shown below. 2 (Note: The figure is not to scale.) If BD is a line of symmetry for the figure, then find the area of the shaded part of the figure in terms of 𝜋. Show your work. OR Wasim made a model of Pac-Man, after playing the famous video game of the same name. The area of the model is 120π cm2. Pac-Man's mouth forms an angle of 60° at the centre of the circle. A picture of the model is shown below. (Note: The figure is not to scale.) Wasim wants to decorate the model by attaching a coloured ribbon to the entire boundary of the shape. What is the minimum length of the ribbon required in terms of ? Show your work. 2 SECTION C (This section comprises of short answer type questions (SA) of 3 marks each) Serial No. Question Marks 26 Prime factorisation of three numbers A, B and C is given below: A = (2r × 3p × 5q) B = (2p × 3r × 5p) C = (2q × 3q × 5p) such that, p < q < r and p, q, & r are natural numbers.. ♦ The largest number that divides A, B and C without leaving a remainder is 30. ♦ The smallest number that leaves a remainder of 2 when divided by each of A, B and C is 5402. Find A, B and C. Show your work. 3 27 Riddhi throws a stone in the air such that it follows a parabolic path before it lands at P on the ground as depicted by the graph below. (Note: The figure is not to scale.) 3 31 Naima is playing a game and has two identical 6-sided dice. The faces of the dice have 3 even numbers and 3 odd numbers. She has to roll the two dice simultaneously and has two options to choose from before rolling the dice. She wins a prize if: Option 1: the sum of the two numbers appearing on the top of the two dice is odd. Option 2: the product of the two numbers appearing on top of the two dice is odd. Which option should Naima choose so that her chances of winning a prize is higher? Show your work. 3 SECTION D (This section comprises of long answer-type questions (LA) of 5 marks each) Serial No. Question Marks 32 Manu and Aiza are competing in a 60 km cycling race. Aiza's average speed is 10 km/hr greater than Manu's average speed and she finished the race in hours less than Manu. Find the time taken by Manu to finish the race. Show your work. OR 5 Shown below is a cuboid with water in two different orientations. The length, breadth and height of the cuboid are distinct. The cuboid has 480 cm3 of water. (Note: The figures are not to scale.) 5 If the height of water in orientation II is half of that in orientation I, then find the heights of water in both orientations. Show your work. 33 In the following figure, ΔABC is a right-angled triangle, such that: ♦ AC = 25 cm ♦ PT || AB and SR || BC (Note: The figure is not to scale.) Find the area of ΔPQR. Show your work. 5 34 Two rectangular sheets of dimensions 45 cm × 155 cm are folded to make hollow right circular cylindrical pipes, such that there is exactly 1 cm of overlap when sticking the ends of the sheet. Sheet 1 is folded along its length, while Sheet 2 is folded along its width. That is, the top edge of the sheet is joined with its bottom edge in both the sheets, as depicted by the arrow in the figure below. Both pipes are closed on both ends to form cylinders. (Note: The figures are not to scale.) 5 i) Find the difference in the curved surface areas of the two cylinders. ii) Find the ratio of the volumes of the two cylinders formed. Show your work. (Note: Use π as 22 7 . Assume that the sheets have negligible thickness.) OR Shown below is a cylindrical can placed in a cubical container. i) How many of these cans can be packed in the container such that no more cans are fitted? ii) If the capacity of one can is 539 ml, find the internal volume of the cubical container. Show your work. (Note: Take π as 22 7 .) 5 35 A car assembly unit assembles a limited number of cars daily, depending on the prevailing demand. The following table presents an analysis of the number of cars assembled by the unit over three consecutive months: 5 (i) After shooting two arrows, Rohan scored 25 points. Write one set of coordinates for each arrow that landed on the target. 1 (ii) If one player's arrow lands on (2, 2.5), how many points will be awarded to the player? Show your work. 1 (iii) One of Rohan’s arrow landed on (1.2, 1.6). He wants his second arrow to land on the line joining the origin and first arrow such that he gets 10 points for it. Find one possible pair of coordinates of the second arrow's landing mark. Show your work. OR 2 (iii) An arrow landed on the boundary and is worth 20 points. The coordinates of the landing mark were of the form (m, -m). Find all such coordinates. Show your steps. 2 38 Answer the questions based on the given information. A drone, is an aircraft without any human pilot and is controlled by a remote- control device. Its various applications include policing, surveillance, photography, precision agriculture, forest fire monitoring, river monitoring and so on. David used an advanced drone with high resolution camera during an expedition in a forest region which could fly upto 100 m height above the ground level. David rode on an open jeep to go deeper into the forest. The initial position of drone with respect to the open jeep on which David was riding is shown below. David’s jeep started moving to enter the forest at an average speed of 10 m/s. He Simultaneously started flying the drone in the same direction as that of the jeep. (i) David reached near one of the tallest trees in the forest. He stopped the drone at a horizontal distance of 5√3 m from the top of the tree and at a vertical distance of 65 m below its maximum vertical range. (Note: The figure is not to scale.) If the angle of elevation of the drone from the top of the tree was 30°, find the height of the tree. Show your work. 1 (ii) The drone was flying at a height of 30√3 metres at a constant speed in the horizontal direction when it spotted a zebra near a pond, right below the drone. The drone travelled for 30 metres from there and it could see the zebra, at the same place, at an angle of depression of θ from it. Draw a diagram to represent this situation and find θ. Show you work. 1 (iii) After 2 minutes of starting the expedition both the drone and the jeep stopped at the same moment so that the drone can capture some images. The position of the drone and the jeep when they stopped is as shown below. 2 (Note: The figure is not to scale.) Find the average speed of the drone in m/s rounded off upto 2 decimal places. Show your work. OR (iii) At some point during the expedition, David kept the drone stationary for some time to capture the images of a tiger. The angle of depression from the drone to the tiger changed from 30° to 45° in 3 seconds as shown below. (Note: The figure is not to scale.) What was the average speed of the tiger during that time? Show your work. (Note: Take √3 as 1.73.) 2