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 nature of the roots of the quadratic equation:
4x2 – 5x – 1 = 0
Chapter: [0.023] Quadratic Equations
Which term of the A.P. 3, 8, 13, 18, ..., is 78?
Chapter: [0.024] Arithmetic Progressions
Find the common difference of an A.P. whose nth term is given by an = 6n – 5.
Chapter: [0.024] Arithmetic Progressions
3 cubes each of 8 cm edge are joined end to end. Find the total surface area of the cuboid.
Chapter: [0.062] Surface Areas and Volumes
In the given figure, perimeter of ΔPQR is 20 cm. Find the length of tangent PA.
Chapter: [0.042] Circles
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In the given figure, BC is tangent to the circle at point B of circle centred at O. BD is a chord of the circle so that ∠BAD = 55°. Find m∠DBC.
Chapter: [0.042] Circles
Find the mode of the following frequency distribution:
| Class: | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 | 60 – 70 |
| Frequency: | 25 | 30 | 45 | 42 | 35 |
Chapter: [0.071] Statistics
Find the sum of first 15 multiples of 8.
Chapter: [0.024] Arithmetic Progressions
Draw a circle of radius 2.5 cm. Construct a pair of tangents from a point Pat a distance of 6 cm from the centre of the circle.
Chapter: [0.033] Constructions
As observed from the top of a light house 100 m above sea level, the angle of depression of a ship, sailing directly towards it, changes from 30° to 45°. Determine the distance travelled by the ship during this time. [Use `sqrt(3)` = 1.732]
Chapter: [0.053] Some Applications of Trigonometry
At a point on level ground, the angle of elevation of a vertical tower is, found to be α such that tan α = `1/3`. After walking 100 m towards the tower, the angle of elevation β becomes such that tan β = `3/4`. Find the height of the tower.
Chapter: [0.053] Some Applications of Trigonometry
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Find the mean of the following frequency distribution:
| Class: | 10 – 15 | 15 – 20 | 20 – 25 | 25 – 30 | 30 – 35 |
| Frequency: | 4 | 10 | 5 | 6 | 5 |
Chapter: [0.071] Statistics
The median of the following frequency distribution is 25. Find the value of x.
| Class: | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |
| Frequency: | 6 | 9 | 10 | 8 | x |
Chapter: [0.071] Statistics
Prove that a parallelogram circumscribing a circle is a rhombus.
Chapter: [0.042] Circles
Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.
Chapter: [0.042] Circles
‘The sum of the ages of a boy and his sister (in years) is 25 and product of their ages is 150. Find their present ages.
Chapter: [0.023] Quadratic Equations
Read the following passage and answer the questions given below.
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Qutub Minar, located in South Delhi, India was built in the year 1193. It is 72 m high tower. Working on a school project, Charu and Daljeet visited the monument. They used trigonometry to find their distance from the tower. Observe the picture given below. Points C and D represent their positions on the ground in line with the base of tower, the angles of elevation of top of the tower (Point A) are 60° and 45° from points C and D respectively.
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- Based on the above information, draw a well-labelled diagram.
- Find the distances CD, BC and BD. [use `sqrt(3)` = 1.73]
Chapter: [0.053] Some Applications of Trigonometry
Read the following passage and answer the questions given below.
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A solid cuboidal toy is made of wood. It has five cone-shaped cavities to hold toy carrots. The dimensions of the toy cuboid are – 10 cm × 10 cm × 8 cm. Each cone carved out – Radius = 2.1 cm and Height = 6 cm
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- Find the volume of wood carved out to make five conical cavities.
- Find the volume of the wood in the final product.
Chapter: [0.062] Surface Areas and Volumes
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