CBSE Class 10 Mathematics Basic Term 2 Sample Paper
Class – X Exam 2021-22
Mathematics Basic (241)
Time Allowed: 120 minutes (Maximum Marks: 40)
General Instructions:
- The question paper consists of 14 questions divided into 3 sections A, B,
- All questions are
- Section A comprises of 6 questions of 2 marks Internal choice has been provided in two questions.
- Section B comprises of 4 questions of 3 marks Internal choice has been provided in one question.
- 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. (02)
Section A
1. If 4 times the 4th term of an AP is equal to 18 times the 18th term, then find the 22nd term.
OR
In an A.P., if the common difference d =− 3 and the eleventh term a11 = 15, then find the first term.
2. From a point on the ground, 20 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is 60°. Find the height of the tower.
3. In figure, O is the centre of PQ is a chord and PT is tangent at P which makes an angle of 50c with PQ.
Find the angle <POQ .
4. A solid piece of iron in the form of a cuboid of dimensions 49 cm # # 33 cm 24 cm, is moulded to form a solid sphere. What is the radius of the sphere ?
5. A solid metallic cuboid 24 cm # 11 cm # 7 cm is melted and recast into solid cones of base radius 3.5 cm and height 6 cm. Find the number of cones so formed.
6. Find the mode of the following grouped frequency distribution.
| Class | Frequency |
| 3-6 | 2 |
| Class | Frequency |
| 6-9 | 5 |
| 9-12 | 10 |
| 12-15 | 23 |
| 15-18 | 21 |
| 18-21 | 12 |
| 21-24 | 03 |
OR
If the mean of the first n natural number is 15, then find n .
Section B
7. In the given figure, BOA is a diameter of a circle and the tangent at a point P meets BA when produced at T. If +PBO = 30º , what is the measure of +PTA?
8. A cone of height 36 cm and radius of base 9 cm is made up of moulding A child reshapes it in the form of a sphere. Find the diameter of the sphere.
9. Find the mode of the following frequency distribution:
| Class | 15-20 | 20-25 | 25-30 | 30-35 | 35-40 | 40-45 |
| Frequency | 3 | 8 | 9 | 10 | 3 | 2 |
10. The weekly expenditure of 500 families is tabulated below :
| Weekly Expenditure(Rs.) | Number of families |
| 0-1000 | 150 |
| 1000-2000 | 200 |
| 2000-3000 | 75 |
| 3000-4000 | 60 |
| 4000-5000 | 15 |
Find the median expenditure.
Section C
11. If the sum of first four terms of an AP is 40 and that of first 14 terms is Find the sum of its first n terms.
12. Draw two concentric circles of radii 2 cm and 5 cm. Take a point P on the outer circle and construct a pair of tangents PA and PB to the smaller Measure PA.
OR
Draw a circle of radius 3 cm. From a point P , 7 cm away from centre draw two tangents to the circle. Measure the length of each tangent.
13. Maximum Profit : A kitchen utensils manufacturer can produce up to 200 utensils per The profit made from the sale of these utensils can be modelled by the function P (x) =− 0.5x + 175x − 330 , where P (x) is the profit in Rupees, and x is the number of utensils made and sold. Based on this model,
-
- Find the x -intercepts and explain what they mean in this context.
- How many utensils should be sold to maximize profit?
14. Irrigation Canals : Irrigation canals are the main waterways that bring irrigation water from a water source to the areas to be irrigated. The water is taken either from the river, tank or reservoirs. The canals can be constructed either by means of concrete, stone, brick or any sort of flexible membrane which solves the durability issues like seepage and erosion.
One such canal shown above is of width 5.4 m wide and depth 1.8 m deep through which water is flowing with a speed of 25 km/hour.
- How much water is flowing through the canal in 1 hour.
- At some distance from canal, a framer is having a large cylindrical tank the radius of whose base is 2 m. Suppose the farmer connects this tank to canal by a circular pipe of internal diameter of 4 cm for irrigation his If water is flowing at 7 m/s through a circular pipe, find the increase in water level in 30 minutes.