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

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

**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 has been provided in two questions

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

5. 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. If the ratio of the sum of the first n terms of two A.Ps is ( 7n + 1 ) : ( 4n + 27 ) , then find the ratio of their 9th terms .

OR

Find the sum of all odd numbers between 0 and 50 .

2. Find the roots of the quadratic equation .

3x – 8/x = 2

3. A tangent AB is drawn parallel to a chord CD of a circle , as shown in figure . Prove that ACD is an isosceles triangle .

4. A sphere of maximum volume is cut out from a solid hemisphere of radius 12 cm . Find the volume of the cut out sphere .

5. Find the unknown entries in the following distribution of heights of students in a class :

How many total students are there in the class ?

6. Find the value of k for the following quadratic equation , so that the roots are equal .

X^{2} – 3 ( k + 1 ) x + 12k = 0

OR

The diagonal of a rectangular field is 16 metre more than the shorter side . If the longer side is 14 metre more than the shorter side , then find the length of the sides of the field .

**Section – B **

**[ 3 Marks Each ]**

7. Find the mode of the following data :

8. Draw a circle of radius 4 cm , from a point P , 8 cm away from the centre draw two tangents to the circle . Write steps of constructions .

9. Find the mean of the following distribution .

10. A player is sitting on the top of a tower at height of 15 m . He observes the angle of depression of a ball lying on the ground as 30 ° . Find the distance between the foot of the tower and the ball .

OR

Two poles of equaI heights are standing opposite to each other on either side of a road , which is 100 m wide . From a point between them on the road , angles of elevation of their top are 30° and 60°. Find the height of the poles and distance of point from poles . [ √3 = 1.731 ]

**Section – C **

**[ 4 Marks Each ]**

11. A metallic sphere of radius 2.1 cm is melted and recast into the shape of a cylinder of radius 3 cm . Find the height of the cylinder .

12. In the given figure , a circle is inscribed in a △ABC , such that it touches the sides AB , BC , CA at points D , E , F respectively . If the lengths of the sides AB , BC , CD are 15 cm , 11 cm and 12 cm respectively , find the lengths of AD , BE and CF.

OR

A tangent PA is drawn form an external point P to a circle of radius 3 cm such that the distance of the point P from O is 6 cm as shown in the figure . Find the value of length of AP .

**Case Study – 1**

13. Form a point P on the ground , the angle of elevation of the top of a 10 m tall building is 30 °. A flag is hoisted at the top of the building and angle of elevation of the top of the flagstaff from P is 45° .

( i ) Find the length of flagstaff . [ 2 ]

( ii ) Find the distance of the building from the point P. [ 2 ]

**Case Study – 2**

14. Saving is the best option for human life . Mr. Bhargav , child put ₹ 1 on day one , ₹ 2 on day 2 , ₹ 3 on day 3 and continued doing so till the end of the month .

( i ) Find the total money saved in month of January . [ 2 ]

( ii ) If he spent ₹ 305 of his pocket money and found that at the end of the month he still had ₹ 200 with him , then how much was his pocket money for the month ? [ 2 ]