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 consists of 14 questions All questions are compulsory.
- This question paper is divided into 3 Sections - Sections A, B, and C.
- Section A comprises 6 questions (Q Nos. 1 to 6) of 2 marks each. Internal choice has been provided i1t two questions.
- Section B comprises 4 questions (Q Nos. 7 to 10) of 3 marks each. Internal choice has been provided in one question.
- Section C comprises 4 questions (Q Nos. 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.
Find the value of 'k' so that the quadratic equation 3x2 – 5x – 2k = 0 has real and equal roots.
Chapter: [0.023] Quadratic Equations
Determine the 36th term of the A.P. whose first two terms are –3 and 4 respectively.
Chapter: [0.024] Arithmetic Progressions
Write the next two terms of the A.P.: `sqrt(27), sqrt(48), sqrt(75)`......
Chapter: [0.024] Arithmetic Progressions
Find the modal and median classes of the following distribution.
| Class | 0 – 20 | 20 – 40 | 40 – 60 | 60 – 80 | 80 – 100 |
| Frequency | 11 | 22 | 19 | 18 | 7 |
Chapter: [0.071] Statistics
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.
Chapter: [0.062] Surface Areas and Volumes
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Find the volume of a solid hemisphere whose total surface area is 462 sq.m.
Chapter: [0.062] Surface Areas and Volumes
The distance between two tangents parallel to each other of a circle is 13 cm. Find the radius of the circle.
Chapter: [0.042] Circles
Find the value(s) of 'a' for which the quadratic equation x2 – ax + 1 = 0 has real and equal roots.
Chapter: [0.023] Quadratic Equations
Draw a line segment AB of length 6 cm and mark a point X on it such that AX = `4/5` AB. [Use a scale and compass]
Chapter: [0.033] Constructions
In an A.P., the first term is 12 and the common difference is 6. If the last term of the A.P. is 252, then find its middle term.
Chapter: [0.024] Arithmetic Progressions
Find the sum of first 16 terms of the A.P. whose nth term is given by an = 5n – 3.
Chapter: [0.024] Arithmetic Progressions
Two poles of heights 25 m and 35 m stand vertically on the ground. The tops of two poles are connected by a wire, which is inclined to the horizontal at an angle of 30°. Find the length of the wire and the distance between the poles.
Chapter: [0.053] Some Applications of Trigonometry
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Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
Chapter: [0.042] Circles
If a circle is touching the side BC of ΔABC at P and is touching AB and AC produced at Q and R respectively (see the figure). Prove that AQ = `1/2` (perimeter of ΔABC).
Chapter: [0.042] Circles
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
Chapter: [0.042] Circles
If a circle is touching the side BC of ΔABC at P and is touching AB and AC produced at Q and R respectively (see the figure). Prove that AQ = `1/2` (perimeter of ΔABC).
Chapter: [0.042] Circles
Read the following passage and answer the questions given below.
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Electric buses are becoming popular nowadays. These buses have the electricity stored in a battery. Electric buses have a range of approximately 280 km with just charge. These buses are superior to diesel buses as they reduce brake wear and also reduce pollution. 'transport department of a city wants to buy some electric buses for the city. So, the department wants to know the distance travelled by existing public transport buses in a day. The following data shows the distance travelled by 50 existing public transport buses in a day.
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| Daily distance travelled (in km) | 100 – 120 | 120 – 140 | 140 – 160 | 160 – 180 | 180 – 200 |
| Number of buses | 12 | 14 | 8 | 6 | 10 |
- Find the 'median' distance travelled by a bus.
- Find the 'mean (average)' distance travelled by a bus.
Chapter: [0.071] Statistics
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A company deals in casting and moulding of metal on orders received from its clients. In one such order, company is supposed to make 50 toys in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of hemisphere. If the radius of the base of the cone is 21 cm and height is 28 cm.
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- find the volume of 50 toys:
- fine the ratio of the volume of hemisphere to the volume of cone.
Chapter: [0.062] Surface Areas and Volumes
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