English Medium
Academic Year: 2021-2022
Date & Time: 5th May 2022, 10:30 am
Duration: 2h
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General Instructions :
- This question paper contains of 14 questions. All questions are compulsory.
- This question paper is divided into four sections -A, B, C, and D.
- Section A contains 6 questions (Q No.1 to 6) of 2 marks each. Internal choice has been provided in two questions.
- Section B contains 4 questions (Q No. 7 to 10) of 3 marks each. Internal choice has been provided in one question.
- Section C contains 4 questions (Q No. 11 to 14) of 4 marks each. An internal choice has been provided in one question. It also contains two case study board questions.
- Use of calculator is not permitted.
The mode of a grouped frequency distribution is 75 and the modal class is 65-80. The frequency of the class preceding the modal class is 6 and the frequency of the class succeeding the modal class is 8. Find the frequency of the modal class.
Chapter: [0.071] Statistics
How many natural numbers are there between 1 and 1000 which are divisible by 5 but not by 2?
Chapter: [0.024] Arithmetic Progressions
If the sum of the roots of the quadratic equation ky2 – 11y + (k – 23) = 0 is `13/21` more than the product of the roots, then find the value of k.
Chapter: [0.023] Quadratic Equations
If x = –2 is the common solution of quadratic equations ax2 + x – 3a = 0 and x2 + bx + b = 0, then find the value of a2b.
Chapter: [0.023] Quadratic Equations
Find the mean of the following frequency distribution:
| Class | 1 – 5 | 5 – 9 | 9 – 13 | 13 – 17 |
| Frequency | 4 | 8 | 7 | 6 |
Chapter: [0.071] Statistics
In the given figure, there are two concentric circles with centre O. If ARC and AQB are tangents to the smaller circle from the point A lying on the larger circle, find the length of AC, if AQ = 5 cm.
Chapter: [0.042] Circles
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The curved surface area of a right circular cylinder is 176 sq cm and its volume is 1232 cu cm. What is the height of the cylinder?
Chapter: [0.062] Surface Areas and Volumes
The largest sphere is carved out of a solid cube of side 21 cm. Find the volume of the sphere.
Chapter: [0.062] Surface Areas and Volumes
Construct a pair of tangents to a circle of radius 4 cm, which are inclined to each other at an angle of 60°.
Chapter: [0.042] Circles
Find the value of 'p' for which the quadratic equation p(x – 4)(x – 2) + (x –1)2 = 0 has real and equal roots.
Chapter: [0.023] Quadratic Equations
Had Aarush scored 8 more marks in a Mathematics test, out of 35 marks, 7 times these marks would have been 4 less than square of his actual marks. How many marks did he get in the test?
Chapter: [0.023] Quadratic Equations
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An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 30° and 60° respectively. Find the distance between the two planes at that instant.
Chapter: [0.053] Some Applications of Trigonometry
If the last term of an A.P. of 30 terms is 119 and the 8th term from the end (towards the first term) is 91, then find the common difference of the A.P. Hence, find the sum of all the terms of the A.P.
Chapter: [0.024] Arithmetic Progressions
In the given figure, if a circle touches the side QR of ΔPQR at S and extended sides PQ and PR at M and N, respectively, then prove that PM = `1/2` (PQ + QR + PR)
Chapter: [0.042] Circles
In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 6 cm and 8 cm respectively. If the area of ΔABC is 84 cm2, find the lengths of sides AB and AC.
Chapter: [0.042] Circles
From the top of an 8 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower. (Take `sqrt(3)` = 1.732).
Chapter: [0.053] Some Applications of Trigonometry
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Yoga is an ancient practice which is a form of meditation and exercise. By practising yoga, we not even make our body healthy but also achieve inner peace and calmness. The International Yoga Day is celebrated on the 21st of June every year since 2015.
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| Age Group | 15 – 25 | 25 – 35 | 35 – 45 | 45 –55 | 55 –65 | 65 –75 | 75 – 85 |
| Number of People |
8 | 10 | 15 | 25 | 40 | 24 | 18 |
Based on the above, find the following:
- Find the median age of people enrolled for the camp.
- If x more people of the age group 65 – 75 had enrolled for the camp, the mean age would have been 58. Find the value of x.
Chapter: [0.071] Statistics
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Khurja is a city in the Indian state of Uttar Pradesh famous for the pottery. Khurja pottery is traditional Indian pottery work which has attracted Indians as well as foreigners with a variety of tea sets, crockery and ceramic tile works. A huge portion of the ceramics used in the country is supplied by Khurja and is also referred as "The Ceramic Town". One of the private schools of Bulandshahr organised an Educational Tour for class 10 students to Khurja. Students were very excited about the trip. Following are the few pottery objects of Khurja.
Students found the shapes of the objects very interesting and they could easily relate them with mathematical shapes viz sphere, hemisphere, cylinder etc. |
Maths teacher who was accompanying the students asked the following questions:
- The internal radius of hemispherical bowl (filled completely with water) in I is 9 cm and the radius and height of the cylindrical jar in II are 1.5 cm and 4 cm respectively. If the hemispherical bowl is to be emptied in cylindrical jars, then how many cylindrical jars are required?
- If in the cylindrical jar full of water, a conical funnel of the same height and same diameter is immersed, then how much water will flow out of the jar?
Chapter: [0.062] Surface Areas and Volumes
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