# CBSE Class 10 Maths Basic Sample Question Paper 2021 (with Answer Hints & Marking Scheme)

CBSE Sample Paper and Marking Scheme for Class 10 Basic Maths Board Exam 2021 are provided here to download in PDF format. This sample paper and marking scheme are very useful to know the pattern of examination and allotment of marks in the upcoming Board Exam 2021.

*CBSE Class 10 Basic Maths Sample Paper for Board Exam 2021*

CBSE Class 10 Maths Basic Sample Paper for Board Exam 2021 is released according to the reduced syllabus. Students should thoroughly check this sample paper to know the format based on which the question paper in Board Exam 2021 will be prepared. The marking scheme has also been released along with the sample paper which is again important to understand the step-wise marking scheme. It includes answer hints that give an idea about how to include important concepts/points in your answers to obtain maximum marks. CBSE Class 10 Maths Basic Sample Paper and its Marking Scheme can be downloaded from here in PDF format.

**Also Check: CBSE Class 10 Maths Examination Pattern 2021 with Question Paper Design & Marking Scheme**

**Class- X **

**Mathematics-Basic (241) **

**Sample Question Paper 2020-21**

**General Instructions: **

- This question paper contains two parts A and B.
- Both Part A and Part B have internal choices.

**Part – A:**

- It consists of two sections- I and II
- Section I has 16 questions. Internal choice is provided in 5 questions.
- Section II has four case study-based questions. Each case study has 5 case-based sub-parts. An examinee is to attempt any 4 out of 5 sub-parts.

**Part – B:**

- Question No 21 to 26 are Very Short Answer Type questions of 2 mark each.
- Question No 27 to 33 are Short Answer Type questions of 3 marks each.
- Question No 34 to 36 are Long Answer Type questions of 5 marks each.
- Internal choice is provided in 2 questions of 2 marks, 2 questions of 3 marks and 1 question of 5 marks.

**Part-A**

**Section-I**

1. Express 156 as the product of primes.

2. Write a quadratic polynomial, sum of whose zeroes is 2 and product is -8

3. Given that HCF (96,404) is 4, find the LCM ( 96,404).

**OR**

State the Fundamental Theorem of Arithmetic.

4. On comparing the ratios of the coefficients, find out whether the pair of equations x – 2y =0 and 3x + 4y -20 =0 is consistent or inconsistent.

5. If a and b are co-prime numbers, then find the HCF (a, b).

6. Find the area of a sector of a circle with radius 6cm if angle of the sector is 60°. (Take 𝜋 = 22/7)

**OR**

A horse tied to a pole with 28m long rope. Find the perimeter of the field where the horse can graze. (Take 𝜋 = 22/7)

7. In the given fig. DE || BC, ∟ADE =70° and ∠BAC=50°, then angle ∠BCA = ______

**OR**

In the given figure, AD = 2cm, BD = 3 cm, AE = 3.5 cm and AC = 7 cm. Is DE parallel to BC?

8. The cost of fencing a circular field at the rate of Rs.24 per metre is Rs. 5280. Find the radius of the field.

9. A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground where it makes an angle 30° . The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree from where it is broken.

10. If the perimeter and the area of a circle are numerically equal, then find the radius of the circle.

**Also Check:**

**CBSE Class 10 Maths Syllabus 2021 (Reduced)**

**CBSE Class 10 Maths Question Paper 2020**

11. Write the empirical relationship among mean, median and mode.

12. To divide a line segment BC internally in the ratio 3 : 5, we draw a ray BX such that ∠CBX is an acute angle. What will be the minimum number of points to be located at equal distances, on ray BX?

13. For what values of p does the pair of equations 4x + p y +8 =0 and 2x +2y +2 =0 has unique solution?

**OR**

What type of straight lines will be represented by the system of equations 2x + 3y =5 and 4x + 6y = 7?

14. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is red?

**OR**

A die is thrown once. What is the probability of getting a prime number?

15. A tower stands vertically on the ground. From a point on the ground, which is 15m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°.Find the height of the tower.

16. Probability of an event E + Probability of the event E̅ ( not E) is,_______

**Section-II **

**Case study-based questions are compulsory. Attempt any 4 sub parts from each question. Each question carries 1 mark**

17.

Mathematics teacher of a school took her 10th standard students to show Red fort. It was a part of their Educational trip. The teacher had interest in history as well. She narrated the facts of Red fort to students. Then the teacher said in this monument one can find combination of solid figures. There are 2 pillars which are cylindrical in shape. Also 2 domes at the corners which are hemispherical.7 smaller domes at the centre. Flag hoisting ceremony on Independence Day takes place near these domes.

i) How much cloth material will be required to cover 2 big domes each of radius 2.5 metres? (Take 𝜋 = 22/7)

a) 75m^{2 }

b) 78.57m^{2}

c) 87.47m^{2}

d) 25.8m^{2}

ii) Write the formula to find the volume of a cylindrical pillar.

a) Πr^{2}h

b) Πrl

c) Πr(l + r)

d) 2Πr

iii) Find the lateral surface area of two pillars if height of the pillar is 7m and radius of the base is 1.4m.

a) 112.3cm^{2}

b) 123.2m^{2}

c) 90m^{2}

d) 345.2cm^{2}

iv) How much is the volume of a hemisphere if the radius of the base is 3.5m?

a) 85.9 m^{3}

b) 80 m^{3}

c) 98 m^{3}

d) 89.83 m^{3}

v) What is the ratio of sum of volumes of two hemispheres of radius 1cm each to the volume of a sphere of radius 2 cm?

a) 1:1

b) 1:8

c) 8 :1

d) 1:16

18. Class X students of a secondary school in Krishnagar have been allotted a rectangular plot of a land for gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1m from each other. There is a triangular grassy lawn in the plot as shown in the fig. The students are to sow seeds of flowering plants on the remaining area of the plot.

Considering A as origin, answer question (i) to (v)

i) Considering A as the origin, what are the coordinates of A?

a) (0,1)

b) (1,0)

c) (0,0)

d)(-1,-1)

ii) What are the coordinates of P?

a) (4,6)

b)( 6,4)

c) (4,5)

d) (5,4)

iii) What are the coordinates of R?

a) (6,5)

b) (5,6)

c) ( 6,0)

d) (7,4)

iv) What are the coordinates of D?

a) (16,0)

b) (0,0)

c) (0,16)

d) (16,1)

v) What are the coordinate of P if D is taken as the origin?

a) ( 12,2)

b) (-12,6)

c) (12,3)

d) (6,10)

19.

Rahul is studying in X Standard. He is making a kite to fly it on a Sunday. Few questions came to his mind while making the kite. Give answers to his questions by looking at the figure.

i) Rahul tied the sticks at what angles to each other?

a) 30°

b) 60°

c) 90°

d) 60°

ii) Which is the correct similarity criteria applicable for smaller triangles at the upper part of this kite?

a) RHS

b) SAS

c) SSA

d) AAS

iii) Sides of two similar triangles are in the ratio 4:9. Corresponding medians of these triangles are in the ratio,

a) 2:3

b) 4:9

c) 81:16

d) 16:81

iv) In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. This theorem is called as,

a) Pythagoras theorem

b) Thales theorem

c) Converse of Thales theorem

d) Converse of Pythagoras theorem

v) What is the area of the kite, formed by two perpendicular sticks of length 6 cm and 8 cm?

a) 48 cm^{2}

b) 14 cm^{2}

c) 24 cm^{2}

d) 96 cm^{2}

20. Due to heavy storm an electric wire got bent as shown in the figure. It followed a mathematical shape. Answer the following questions below.

i) Name the shape in which the wire is bent

a) Spiral

b) ellipse

c) linear

d) Parabola

ii) How many zeroes are there for the polynomial (shape of the wire)

a) 2

b) 3

c) 1

d) 0

iii) The zeroes of the polynomial are

a) -1, 5

b) -1, 3

c) 3, 5

d) -4, 2

iv) What will be the expression of the polynomial?

a) x^{2}+2x -3

b) x^{2} -2x +3

c) x^{2 }- 2x -3

d) x^{2} +2x+3

v) What is the value of the polynomial if x = -1?

a) 6

b) -18

c) 18

d) 0

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**The complete sample paper and its marking scheme can be accessed from the links mentioned below:**

**Also Check:**

**CBSE Class 10 Sample Papers and Marking Scheme 2021 - All Subjects **

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