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**Maths Basic Term 2 Sample Paper 2022** **(Unsolved)**

**Class 10 Maths Basic Term 2 Sample Paper 2022**,** (Maths) exams are Students are taught thru NCERT books in some of the state board and CBSE Schools. As the chapter involves an end, there is an exercise provided to assist students to prepare for evaluation. Students need to clear up those exercises very well because the questions inside the very last asked from those.**

**Sometimes, students get stuck inside the exercises and are not able to clear up all of the questions. To assist students, solve all of the questions, and maintain their studies without a doubt, we have provided a step-by-step NCERT Sample Question Papers for the students for all classes. These answers will similarly help students in scoring better marks with the assist of properly illustrated Notes as a way to similarly assist the students and answer the questions right.**

**Class 10 Maths Basic Term 2 Sample Paper 2022**

**General Instructions: **

1. The question paper consists of 14 questions divided into 3 sections A, B, C.

2. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions.

3. Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one question.

4. Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one question. It contains two case study based questions.

**Section – A **

**[2 Marks each]**

1. Find the value of p, for which one root of the quadratic equation px^{2} – 14x + 8 = 0 is 6 times the other.

2. Find how many two digit natural numbers are divisible by 7?

OR

The angles of a triangle are in A.P. If the greatest angle equals the sum of the other two. Find the angles.

3. Draw a line segment of length 5 cm and divide it in the ratio 3 : 7.

4. Solve the quadratic equation abx^{2} + (b^{2} – ac)x – bc = 0 with factorisation method.

5. A solid metallic cuboid of dimensions 9 cm x 8 cm x 2 cm is melted and recast into solid cubes of edge 2 cm. Find the number of cubes so formed.

OR

Find the number of coins of 1.5 cm diameter and 0.2 cm thickness to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.

6. Answer the following questions:

(a) Write the empirical relation between mean, mode and median.

(b) If median and mode of some observations are given as 51.17 and 56. Find mean.

**Section – B**

**[3 Marks Each] **

7. On a straight line passing through the foot of a tower, two points Cand D are at distances of 4 m and 16 m from the foot respectively. If the angles of elevation from C and D of the top of the tower are complementary, then find the height of the tower.

OR

The angles of depression of the top and bottom of a 50 m high building from the top of a tower are 45° and 60° respectively. Find the height of the tower and the horizontal distance between the tower and the building. (Use √3 = 1.73) .

8. Find the median if the following observations.

9. PA and PB are tangents to the circle from one external point P. CD is another tangents touching the circle at Q and intersecting PA and PB at C and D respectively. If PA = 12 cm, QC = QD = 3 cm, then find PC + PD.

10. If the mean of the following distribution is 54. Find the value of p.

**Section – C **

**[4 Marks Each]**

11. Construct a tangent to a circle with centre O of radius 5 cm from a point on the concentric circle of radius 7 cm and measure the length.

12. The sides of a right triangle are x cm, x + 2 cm and x – 2 cm. Find the value of x and sides of the triangle.

OR

A train travels 300 km at a uniform speed. If the speed is 5 km/h more, it takes 2 hour less for the same journey. Find the usual speed of the train.

**Case Study – 1**

13. Aniket is standing near a statue placed above the pedestal. The angle of elevation of the foot and top of the statue from the point where he is standing are 45° & 60°.

Based on above situation answer the following questions:

(i) If the length of pedestal is 40 m. Find the distance between the point where Aniket is standing and the pedestal. [ 2 ]

(ii) Find the height of the statue. [ 2 ]

**Case Study – 2**

14. In a rain water harvesting system, the rain water collected on the roof of a building of dimensions 22 m x 20 m is drained into a cylindrical vessel having diameter 2 m and height 3.5 m.

(i) Find the volume of the cylindrical vessel. [ 2 ]

(ii) It the vessel is full upto the brim, find the height of the rain water on the roof. [ 2 ]