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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 roots of the quadratic equation √2x^{2} + 7x + 5 √2 = 0

2. Which term of the A.P 3, 15, 27, 39, …… will be 120 more than its 21^{st} term ?

3. A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.

OR

In the given figure, a circle touches all the four sides of a quadrilateral ABCD. If AB = 6 cm, BC = 9 cm and CD = 8 cm, then find the length of AD.

4. Two cubes have their volumes in the ratio 1:27. Find the ratio of their surface areas.

OR

A cylindrical glass tube with radius 10 cm has water upto a height of 9 cm. A metal cube of 8 cm edge is immersed completely. By how much the water level will rise in the glass tube ?

5. The mean and median of 100 observations are 50 and 52 respectively. The value of the largest observation is 100. It was later found that itis 110 not 100, Find the true mean and median.

6. Consider the following distribution:

(i) What is the frequency of the class 30 – 40.

(ii) Find the class mark of class 10 -25.

**Section – B **

**[3 Marks Each]**

7. If 10^{th} term of an A.P is 52 and 17^{th} term is 20 more than the 13^{th} term, find the A.P

8. From the top of a 120 m high tower, a man observes two cars on the opposite sides of the tower and in straight line with the base of tower with angles of depression as 60° as 45°. Find the distance between two cars.

OR

The shadow of a tower at a time is three times as long as its shadow when the angle of elevation of the Sun is 60°. Find the angle of elevation of the Sun at the time of the longer shadow.

9. Sum of the area of two squares is 260 m^{2}. If the difference between of their perimeters is 24, then find the sides of the two squares.

10. Draw tangents to a circle of radius 3.5 cm from a point P at a distance of 7 cm away from the centre.

**Section – C **

**[4 Marks Each]**

11. Find the mode of the following frequency distribution.

OR

A survey regarding the heights in (cm) of 51 girls of class X of a school was conducted and the following data was obtained. Find the median height and the mean using their formulae.

12. In the given figure, AB is a chord of length 9.6 cm, of a circle with centre O and radius 6 cm. The tangents at A and B intersect at P. Find the length PA.

**Case Study – 1**

13. Art and craft teacher of Class X of a school have been allotted a colouring activity. He takes a lattu, which had no colour on it. He wanted to colour it with crayons. The top is shaped like a cone surmounted by a hemi-sphere. The entire top is 5 cm in height and the diameter of top is 3.5 cm.

(i) What is the slant height of conical part? [ 2 ]

(ii) How much cloth material will be required to cover the lattu? [ 2 ]

**Case Study – 2**

14. Amit is standing in the balcony of his house. He observes two cars on either side.

(i) At certain instant in the morning, Amit observed the ratio of the height of his house and the length of its shadow is √3 : 1, then find the angle of elevation of the Sun. [ 2 ]

(ii) At an instant, the angle of depression of the two cars were found to be 30° and 45° respectively. If the height at which he is standing 50 m. Find the distance between the cars. [ 2 ]