# CBSE Class 10 Maths Standard 2022 Question Paper

This question paper contains 14 questions. All questions are compulsory. This question paper is divided into three sections Sections A, B and C. Section A comprises of 6 questions (Q.no. 1 to 6) of 2 marks each.

Section B comprises of 4 questions (Q.no. 7 to 10) of 3 marks each. Section C comprises of 4 questions (Q.no. 11 to 14) of 4 marks each. It also contains two case study based questions.

### Section A

**1.** (a) Find the sum of first 30 terms of AP : -30, -24, -18, ..... .

OR

(b) In an AP if S_{n} = n (4n + 1), then find the AP.

**2.** A solid metallic sphere of radius 10.5 cm is melted and recast into a number of smaller cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so formed.

**3.** (a) Find the value of m for which the quadratic equation (m - 1)x^{2} + 2(m - 1)x + 1 = 0 has two real and equal roots.

OR

(b) Solve the following quadratic equation for x : √3x^{2} + 10x + 7√3 = 0

**4.** Find the mode of the following frequency distribution :

**5.** The product of Rehan's age (in years) 5 years ago and his age 7 years from now, is one more than twice his present age. Find his present age.

**6.** Two concentric circles are of radii 4 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

### Section B

**7. **For what value of x, is the median of the following frequency distribution 34.5 ?

**8.** Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Construct tangents to the circle from these two points P and Q.

**9.** (a) The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, then find the height of the building.

OR

(b) From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45° respectively. If the bridge is at a height of 3 m from the banks, then find the width of the river.

**10.** Following is the daily expenditure on lunch by 30 employees of a company :

Find the mean daily expenditure of the employees.

### Section C

**11. **(a) From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and same radius is hollowed out. Find the total surface area of the remaining solid.

OR

(b) Water in a canal, 8 m wide and 6 m deep, is flowing with a speed of 12 km/hour. How much area will it irrigate in one hour, if 0.05 m of standing water is required ?

**12.** In Figure 1, a triangle ABC with ∠B = 90° is shown. Taking AB as diameter, a circle has been drawn intersecting AC at point P. Prove that the tangent drawn at point P bisects BC.

**Case Study 1**

13. In Mathematics, relations can be expressed in various ways. The matchstick patterns are based on linear relations. Different strategies can be used to calculate the number of matchsticks used in different figures.

One such pattern is shown below. Observe the pattern and answer the following questions using Arithmetic Progression :

(a) Write the AP for the number of triangles used in the figures. Also, write the n^{th} term of this AP.

(b) Which figure has 61 matchsticks ?

**Case Study 2**

**14. **Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was built by the King of Jaisalmer and rebuilt by Gadsi Singh in 14^{th} century. The lake has many Chhatris. One of them is shown below :

Observe the picture. From a point A h m above from water level, the angle of elevation of top of Chhatri (point B) is 45° and angle of depression of its reflection in water (point C) is 60°. If the height of Chhatri above water level is (approximately) 10 m, then

(a) draw a well-labelled figure based on the above information;

(b) find the height (h) of the point A above water level. (Use √3 = 1.73)