**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 9 times of 9^{th} term is equal to 15 times of 15^{th} term in AP . Find the 24^{th} term .

OR

How many terms of the A.P 34 , 32 , 30 , …….. will give the sum of 286 ?

2. In a class test , the sum of the marks obtained by Amit in Mathematics and Science is 28. She got 3 marks more in mathematics and 4 marks less in science . The product of marks obtained in two subjects is 180. Find the marks obtained in the two subjects separately .

3. PB is a tangent to the circle with centre O to B. AB is a chord of length 24 cm at a distance of 5 cm from the centre . If the tangent is of length 20 cm , find the length of PO .

4. A cone of height 24 cm and radius of base 6 cm is made up of modelling clay . A child reshapes it in the form of a sphere . Find the radius of the sphere .

5. Find the median of the following data .

6. If roots of the quadratic equation x^{2 }+ 2px + mn = 0 are real and equal , show that the roots of the quadratic equation x^{2} – 2 ( m + n ) x + ( m² + n² + 2p² ) = 0 are also equal .

OR

Find the nature of the roots of the quadratic equation 2x² -2√6x + 3 = 0 . If the real roots exist , then find the roots .

**Section – B **

**[ 3 Marks Each ]**

7. The mean of the following data is 50. Find the missing frequencies x and y .

8. Draw a line segment of length 8 cm and divide it internally in the ratio 4 : 5 .

9. Find the mean and mode of the following data .

10. At a point A , 20 metre above the level of water in a lake , the angle of elevation of a cloud is 30 ° . The angle of depression of the reflection of the cloud in the lake , at A is 60 ° . Find the distance of the cloud from A ?

OR

A kite is flying at a height of 75 m from the level ground , attached to a string inclined at 60 ° to the horizontal . Find the length of the string to the nearest metre .

**Section – C **

**[ 4 Marks Each ]**

11. A solid is in the form of a cone standing on a hemisphere with both their radii being equal to 2 cm and the height of the cone is equal to its radius . Find the volume of the solid in terms of π .

12. In the given figure , O is the centre of the circle , MN is a tangent to the circle at A. If ∠MAB = 60 ° . Find ∠ABN and ∠ANB .

OR

Prove that tangent drawn at any point of a circle is perpendicular to the radius through the point of contact .

**Case Study – 1**

13. A straight highway leads to the foot of tower . A man standing at the top of the tower observes a car at an angle of depression of 30 ° , which approaching the foot of the tower with a uniform speed . Six seconds later , the angle of depression of the car is found to be 60 ° .

( i ) Find the time taken by the car to reach the foot of the tower from point D to B. [ 2 ]

( ii ) Write the value of sec 30 ° . [ 2 ]

**Case Study – 2**

14. In a potato race , a bucket is placed at the starting point , which is 5 m from the first potato and the other potatoes are placed 3 m apart in a straight line . There are ten potatoes in the line ( see figures ) .

A competitor starts from the bucket , picks up the nearest potato , runs back with it , drops it in the bucket , runs back to pick up the next potato , runs to the bucket to drop it in , and she continues in the same way until all the potatoes are dropped in the bucket .

( i ) What is the distance run to pick up the 4^{th} potato ? [ 2 ]

( ii ) What is the total distance run by the competitor ? [ 2 ]