SAMPLE QUESTION PAPER 2021-22
TERM II
CLASS X
MATHEMATICS (STANDARD) – 041
Time Allowed: 2 Hours Maximum Marks: 40
General Instructions:
1. The question paper consists of 14 questions divided into 3 sections A, B, C
2. All questions are compulsory
3. Section A comprises of 6 questions of 2 marks each. Internal choice as been provided in two questions.
4. Section B comprises of 4 questions of 3 marks each. Internal choice as been provided in one questions.
5. Section C comprises of 4 questions of 4 marks each. Internal choice as been provided in one questions.
It contains two case study based questions.
SECTION A
1. Solve for x: x2 – (2b – 1)x + (b2 – b + 20) = 0
2. The angles of a quadrilateral are in A.P. whose common difference is 100. Find the angles.
OR
The sum of the 2nd and the 7th term of an A.P. is 30. If its 15th term is 1 less than twice its 8th term, then find the A.P.
3. If ad ≠ bc, then prove that the equation (a2 + b2)x2 + 2(ac + bd)x + (c2 + d2) = 0 has no real roots.
4. If angle between two tangents drawn from a point P to a circle of radius ‘a’ and centre O is 900, then find the length of OP.
5. The length of a cold storage is double its breadth. Its height is 3 metres. The areas of its four walls (including doors) is 108 m2. Find its volume.
OR
The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recut into a solid right circular cylinder of height
Find the diameter of the base of the cylinder.
6. If the mode of the given data is 340, find the missing frequency x for the following data:
| Classes | 0 – 100 | 100 – 200 | 200 – 300 | 300 – 400 | 400 – 500 | 500 – 600 |
| Frequency | 8 | 12 | x | 20 | 14 | 7 |
SECTION B
7. The following table gives the literacy rate (in %) in 40 cities. Find the mean literacy rate.
| Literacy rate (in %) | 45 – 55 | 55 – 65 | 65 – 75 | 75 – 85 | 85 – 95 |
| Number of cities | 4 | 11 | 12 | 9 | 4 |
8. The angle of elevation of a cloud from a point 60 m above the surface of the water of a lake is 300 and the angle of depression of its shadow in water of lake is 600. Find the height of the cloud from the surface of water.
OR
From a point P on the ground, the angle of elevation of the top of a 10 m tall building is 300. A flagstaff is fixed at the top of the building and the angle of elevation of the top of the flagstaff from P is 450. Find the length of the flagstaff and the distance of the building from the point P. (Take √3 = 1.73)
9. In an apple orchard, the number of apples on 80 trees are as follows:
| Number of apples | 40 – 60 | 60 – 80 | 80 – 100 | 100 – 120 | 120 – 140 | 140 – 160 | 160 – 180 |
| Number of trees | 12 | 11 | 14 | 16 | 13 | 9 | 5 |
10. Construct a right triangle ABC with AB = 6 cm, BC = 8 cm and ∠B = 900. Draw BD, the perpendicular from B on AC. Draw the circle through B, C and D and construct the tangents from A to this circle.
SECTION C
11. A conical vessel of radius 12 cm and height 16 cm is completely filled with water. A sphere is lowered into the water and its size is such that, it touches the sides, it is just immersed. What fraction of the water overflows?
12. AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. The chords are on opposite sides of the centre and the distance between them is 17 cm. Find the radius of the circle.
OR
In the fig. RTP and STQ are common tangents to the two circles with centres A and B. The radii of the two circles are 3 cm and 5 cm respectively. If ST : TQ = 1 : 3 and RT = 4 cm, find the length of QT and AB
13. Amit is preparing for his upcoming semester exam. For this, he has to practice the chapter of Quadratic Equations. So he started with factorization method. Let two linear factors of ax2 + bx + c be (px + q) and (rx + s).
⸫ ax2 + bx + c = (px + q) and (rx + s) = prx2 + (ps + qr)x + qs
Now, factorize each of the following quadratic equations and find the roots.
(i) 6x2 + x – 2 = 0
(ii) x2 – 28x + 160 = 0
14. A boy is standing on the top of light house. He observed that boat P and boat Q are approaching to light house from opposite directions. He finds that angle of depression of boat P is 450 and angle of depression of boat Q is 300. He also knows that height of the light house is 100 m.
Based on the above information, answer the following questions
(i) Find the length of PD
(ii) Find the length of DQ
