CBSE Class 10 Mathematics Basic Term 2 Sample Paper (Set-1)

CBSE Class 10 Mathematics Basic Term 2 Sample Paper

Class – X Exam 2021-22

Mathematics Basic (241)

Time Allowed: 120 minutes (Maximum Marks: 40)

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General Instructions:

1. The question paper consists of 14 questions divided into 3 sections A, B,
2. All questions are
3. Section A comprises of 6 questions of 2 marks Internal choice has been provided in two questions.
4. Section B comprises of 4 questions of 3 marks Internal choice has been provided in one question.
5. Section C comprises of 4 questions of 4 marks An internal choice has been provided in one question. It contains two case study based questions. (01)

Section A

1. If 3/5, a, 4 are three consecutive terms of an A.P., then find the value of a.

2. A vertical pole is 100 metres high. Find the angle subtended by the pole at a point on the ground 100 3 meters from the base of the pole.

3. PQ is a tangent to a circle with centre O at point P. If TOPQ is an isosceles triangle, then find +OQP.

4. If the radius of the sphere is increased by 100%, then how much volume of the corresponding sphere is increased ?

5. The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm. What is the length of the wire?

6. If the mean of the observation x x,,, +++ 357 x x and x + 10 is 9, the find the mean of the last three observation

OR

Find the class-marks of the classes 10-25 and 35-66.

Section B

7. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

8. Water is being pumped out through a circular pipe whose internal diameter is 8 cm. If the rate of flow of water is 80 cm/s, then how many litres of water is being pumped out through this pipe in one hour?

9. Compute the mode for the following frequency distribution:

Size of items (in cm)	0-4	4-8	8-12	12-16	16-20	20-24	24-28
Frequency	5	7	9	17	12	10	6

10. The mean of the following frequency distribution is 18. The frequency f in the class interval 19-21 is missing. Determine f .

Class interval	11-13	13-15	15-17	17-19	19-21	21-23	23-25
Frequency	3	6	9	13	f	5	4

OR

Compute the mode for the following frequency distribution:

Size of items (in cm)	0- 4	4- 8	8- 12	12-16	16-20	20-24	24-28
Frequency	5	7	9	17	12	10	6

11. If S_n denotes the sum of first n terms of an AP, prove that, S₃₀ = 3^S₂₀ − S₁₀h

12. Draw two tangents to a circle of radius 4 cm, which are inclined to each other at an angle of 60c.

OR

Draw two concentric circle of radii 3 cm and 5 cm. Taking a point on the outer circle, construct the pair of tangents to the inner circle.

13. Model Rocketry : A model rocket is a small rocket designed to reach low altitudes and be recovered by a variety of means. Flying model rockets is a relatively safe and inexpensive way for person to learn the basics of forces and the response of a vehicle to external forces. Like an airplane, a model rocket is subjected to the forces of weight, thrust, and aerodynamics during its flight.

Shalvi is a member of first rocket club of India named STAR Club. She launches her latest rocket from a large field. At the moment its fuel is exhausted, the rocket has a velocity of 240 ft/sec and an altitude of 544 ft. After t sec, its height h (t) above the ground is given by the function h (t) =− 16t2 + 240t + 544 .

• What is the maximum height attained by the rocket?
• How many seconds was the rocket airborne after its fuel was exhausted?

14. Well Embankment : Well embankment is a raised wall that is built around the These are often constructed using soils obtained from a digging well. It provide protection to person from felling into the well.

A well of diameter 6 m is dug 14 m deep 1/15 of the earth taken out is spread evenly all around the well to form

• Find the volume of the earth taken out.
• If the height of embankment is 2 m, what is the width of the embankment ?