English Medium
Academic Year: 2021-2022
Date: April 2022
Duration: 2h
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General Instructions:
- The question paper consists of 14 questions divided into 3 sections A, B, and C.
- All questions are compulsory.
- Section A comprises 6 questions of 2 marks each. Internal choice has been provided in two questions.
- Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one question.
- Section C comprises 4 questions of 4 marks each. An internal choice has been provided in one question. It contains two case study based questions.
Find the value of a25 – a15 for the AP: 6, 9, 12, 15, ………..
Chapter: [0.024] Arithmetic Progressions
If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the value of its 12th term.
Chapter: [0.024] Arithmetic Progressions
Find the value of đť‘š so that the quadratic equation đť‘šđť‘Ą(5đť‘Ą − 6) = 0 has two equal roots.
Chapter: [0.023] Quadratic Equations
From a point P, two tangents PA and PB are drawn to a circle C(0, r). If OP = 2r, then find ∠APB. What type of triangle is APB?
Chapter: [0.042] Circles
The curved surface area of a right circular cone is 12320 cm2. If the radius of its base is 56 cm, then find its height.
Chapter: [0.062] Surface Areas and Volumes
Mrs. Garg recorded the marks obtained by her students in the following table. She calculated the modal marks of the students of the class as 45. While printing the data, a blank was left. Find the missing frequency in the table given below.
| Marks Obtained |
0 − 20 | 20 − 40 | 40 − 60 | 60 − 80 | 80 − 100 |
| Number of Students |
5 | 10 | − | 6 | 3 |
Chapter: [0.071] Statistics
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If Ritu were younger by 5 years than what she really is, then the square of her age would have been 11 more than five times her present age. What is her present age?
Chapter: [0.023] Quadratic Equations
Solve for x: 9x2 – 6px + (p2 – q2) = 0
Chapter: [0.023] Quadratic Equations
Following is the distribution of the long jump competition in which 250 students participated. Find the median distance jumped by the students. Interpret the median
| Distance (in m) |
0 – 1 | 1 – 2 | 2 – 3 | 3 – 4 | 4 – 5 |
| Number of Students |
40 | 80 | 62 | 38 | 30 |
Chapter: [0.071] Statistics
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
The distribution given below shows the runs scored by batsmen in one-day cricket matches. Find the mean number of runs.
| Runs scored |
0 – 40 | 40 – 80 | 80 – 120 | 120 – 160 | 160 – 200 |
| Number of batsmen |
12 | 20 | 35 | 30 | 23 |
Chapter: [0.071] Statistics
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Two vertical poles of different heights are standing 20m away from each other on the level ground. The angle of elevation of the top of the first pole from the foot of the second pole is 60° and angle of elevation of the top of the second pole from the foot of the first pole is 30°. Find the difference between the heights of two poles. (Take `sqrt(3)` = 1.73)
Chapter: [0.053] Some Applications of Trigonometry
A boy 1.7 m tall is standing on a horizontal ground, 50 m away from a building. The angle of elevation of the top of the building from his eye is 60°. Calculate the height of the building. (Take `sqrt(3)` = 1.73)
Chapter: [0.053] Some Applications of Trigonometry
The internal and external radii of a spherical shell are 3cm and 5cm respectively. It is melted and recast into a solid cylinder of diameter 14 cm, find the height of the cylinder. Also find the total surface area of the cylinder. (Take `pi = 22/7`)
Chapter: [0.062] Surface Areas and Volumes
Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segments joining the points of contact to the centre.
Chapter: [0.042] Circles
Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2∠OPQ.
Chapter: [0.042] Circles
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Case Study Trigonometry in the form of triangulation forms the basis of navigation, whether it is by land, sea or air. GPS a radio navigation system helps to locate our position on earth with the help of satellites. |
- Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower.
- After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(`sqrt(3)` - 1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower?
Chapter: [0.031] Lines (In Two-dimensions)
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Case Study Push-ups are a fast and effective exercise for building strength. These are helpful in almost all sports including athletics. While the push-up primarily targets the muscles of the chest, arms, and shoulders, support required from other muscles helps in toning up the whole body.
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- Form an A.P representing the number of push-ups per day and hence find the minimum number of days he needs to practice before the day his goal is accomplished?
- Find the total number of push-ups performed by Nitesh up to the day his goal is achieved.
Chapter: [0.024] Arithmetic Progressions
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