Table of Contents

## Sample Paper Class 10 Maths 2023-24 with Solutions

The Central Board of Secondary Education has released the CBSE Class 10 Maths Sample Paper 2023-2024 on the official website of CBSE is **cbseacademic.nic.in.**The Central Board of Secondary Education has released a CBSE class 10 maths sample paper 2023 24 pdf for both basic and standard math.

Along with the sample paper, CBSE also releases the Marking Scheme of CBSE maths sample paper class 10 2024. So that students can get a clear idea of the board exam format, question kinds, answer options, and other features with the help of sample paper class 10 maths 2023-24 with solutions.

**Check: CBSE Class 10 Maths Previous Year Papers**

## CBSE Maths Sample Paper 2023-24: Exam Pattern

CBSE Maths sample paper class 10 2024 is created on the same question pattern as the actual 10th Maths Question paper. The Question paper pattern for both basic and standard math is similar. The maths sample paper class 10 2024 has a total of 80 Marks. Candidates have a maximum time of 3 hours to complete the Question paper.

**Must Check: CBSE Class 10 Math Syllabus 2023-24**

- CBSE Class 10 Maths Sample Paper 2024 has 5 Sections A, B, C, D and E.
- Section A contains 20 multiple-choice questions (MCQs) for one point each.
- Section B contains five questions for two points each.
- Section C contains six questions for three points each.
- Section D contains four 05-point questions.
- Section E comprises three case-based integrated units of assessment (04 marks each) with sub-parts of 1, 1, and 2 marks.
- All questions are required. However, an internal choice in two 5-point questions, two 3-point questions, and two 2-point questions has been supplied. In Section E’s two-mark questions, an internal choice has been supplied.
- Draw good figures wherever they are needed. If not specified, use =22/7 whenever it is needed.

**Also Read: CBSE Class 10 Maths Important Questions with Answers**

## Sample Paper Class 10 Maths with Solution 2024 PDF

Sample paper class 10 Maths with solution 2024 pdf for both basic and standard courses in given below. check here.

### Sample Paper Class 10 Maths with Solution 2023 PDF: Basic

Sample paper class 10 maths with solution 2023 pdf for class 10 basic mathematics is given below.

### Sample Paper Class 10 Maths with Solution 2024 PDF Standard

sample paper Class 10 maths standard with solution pdf is given below.

## Sample Paper Class 10 Maths with Solution 2023 24 PDF

Sample paper class 10 Maths with solution pdf is now available on cbseacademic.nic.in. Candidates can download them from the official website for future use. For the convenience of the students here, we will provide you with the both basic and standard sample paper class 10 Maths with solution 2023 pdf with the marking Scheme below

## Sample Paper Class 10 Maths with Solution 2024 PDF Based: **SECTION A**

sample paper class 10 maths 2023-24 with solutions is given below. check full sample paper class 10 maths 2023-24 with solutions here

**Section A consists of 20 questions of 1 mark each.**

1. If two positive integers a and b are written as a = x3y2 and b = xy3, where x, y are prime

numbers, then the result obtained by dividing the product of the positive integers by the LCM (a, b) is

(a) xy (b) xy² (c) x³y³ (d) x²y²

2.

The given linear polynomial y = f(x) has

(a) 2 zeros

(b) 1 zero and the zero is ‘3’

(c) 1 zero and the zero is ‘4’

(d) No zero

3. The given pair of linear equations is non-intersecting. Which of the following statements is true?

4. Write the nature of roots of the quadratic equation 9x² – 6x – 2 = 0.

(a) No real roots (b) 2 equal real roots

(c) 2 distinct real roots (d) More than 2 real roots

5. Two APs have the same common difference. The first term of one of these is –1 and that of

the other is – 8. Then the difference between their 4th terms is

(a) 1 (b) -7 (c) 7 (d) 9

6. Find the ratio in which the line segment joining (2,-3) and (5, 6) is divided by x-axis.

(a) 1:2 (b) 2:1 (c) 2:5 (d) 5:2

7. (x,y) is 5 unit from the origin. How many such points lie in the third quadrant?

(a) 0 (b) 1 (c) 2 (d) infinitely many

8. In ? ABC, DE ‖ AB. If AB = a, DE = x, BE = b and EC = c.

Express x in terms of a, b and c.

(a) ??/b

(b) ??/ ?+?

(c) ??/?

(d)??/?+c

9. If O is the center of a circle and Chord PQ makes an angle of 50° with the tangent PR at the point of contact P, find the angle made by the chord at the center.

(a) 130° (b) 100°

(c) 50° (d) 30°

10. A Quadrilateral PQRS is drawn to circumscribe a circle.

If PQ = 12 cm, QR = 15 cm, and RS = 14 cm, find the length of SP.

(a) 15 cm (b) 14 cm (c) 12 cm (d) 11 cm

11.Given that sin θ = ?/?’ , find cos θ .

12. (sec A + tan A) (1 – sin A) =

(a) sec A (b) sin A (c) cosec A (d) cos A

13. A pole 6 m high casts a shadow 2 √3m long on the ground, then the Sun’s elevation is

(a) 60° (b) 45° (c) 30° (d) 90°

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

is

(a) 2 units (b) π units (c) 4 units (d) 7 units

15. It is proposed to build a single circular park equal in area to the sum of areas of two circular

parks of diameters 16 m and 12 m in a locality. The radius of the new park is

(a) 10m (b) 15m (c) 20m (d) 24m

16. There is a green square board of side ‘2a’ unit circumscribing a red circle. Jayadev is asked

to keep a dot on the abovesaid board. Find the probability that he keeps the dot on the green

region.

(a) ?/4

(b) 4−?/4

(c) ?−4/4

(d)4/?

17. 2 cards of hearts and 4 cards of spades are missing from a pack of 52 cards. What is the probability of getting a black card from the remaining pack?

(a) 22/ 52

(b) 22/ 46

(c)24 /52

(d) 24 /46

18. Find the upper limit of the modal class from the given distribution.

(a) 165 (b) 160 (c) 155 (d) 150

**19. DIRECTION: In question number 19 and 20, a statement of assertion (A) is followed by ****a statement of Reason (R). Choose the correct option**

Statement A (Assertion): Total Surface area of the top is the sum of the curved surface area of the hemisphere and the curved surface area of the cone.

Statement R( Reason): Top is obtained by fixing the plane surfaces of the hemisphere and cone together.

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

(c) Assertion (A) is true but reason (R) is false.

(d) Assertion (A) is false but reason (R) is true.

20. Statement A (Assertion): -5,−5/2, 0,5/ 2 , …. is in Arithmetic Progression.

Statement R (Reason) : The terms of an Arithmetic Progression cannot have both positive

and negative rational numbers.

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

(c) Assertion (A) is true but reason (R) is false.

(d) Assertion (A) is false but reason (R) is true.

**Sample Paper Class 10 Maths with Solution 2024 PDF Based: SECTION B**

**SECTION B**

**Section B consists of 5 questions of 2 marks each.**

21. Prove that √2 is an irrational number.

22. ABCD is a parallelogram. Point P divides AB in the ratio 2:3 and point Q divides DC in the ratio 4:1. Prove that OC is half of OA.

23. From an external point P, two tangents, PA and PB are drawn to a circle with centre O.

At a point E on the circle, a tangent is drawn to intersect PA and PB at C and D,respectively. If PA = 10 cm, find the perimeter of ∆PCD.

24. If tan (A + B) = √3 and tan (A – B) = 1/√3; 0° < A + B < 90°; A > B, find A and B.

[or]

Find the value of x

2 cosec²30 + x sin²60 – 3/4 tan²30 = 10

25. With vertices A, B and C of ΔABC as centres, arcs are drawn with radii 14 cm and the three

portions of the triangle so obtained are removed. Find the total area removed from the

triangle.

[or]

Find the area of the unshaded region shown in the given figure.

## Sample Paper Class 10 Maths with Solution 2023 PDF Based: Section C

**SECTION C**

**Section C consists of 6 questions of 3 marks each**

26. National Art convention got registrations from students from all parts of the country, of

which 60 are interested in music, 84 are interested in dance and 108 students are interested

in handicrafts. For optimum cultural exchange, organisers wish to keep them in minimum

number of groups such that each group consists of students interested in the same artform

and the number of students in each group is the same. Find the number of students in each

group. Find the number of groups in each art form. How many rooms are required if each

group will be allotted a room?

27. If ?, β are zeroes of quadratic polynomial 5x

2 + 5x + 1, find the value of

1. ?² + ?²

2. ?−1 + ?−1

28. The sum of a two-digit number and the number obtained by reversing the digits is 66. If the

digits of the number differ by 2, find the number. How many such numbers are there?

[or]

29. PA and PB are tangents drawn to a circle of centre O from an external point P. Chord AB

makes an angle of 30° with the radius at the point of contact.

If length of the chord is 6 cm, find the length of the tangent PA and the length of the radius OA.

[or]

Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove

that ∠ PTQ = 2 ∠ OPQ.

30. If 1 + sin2θ = 3sinθ cosθ , then prove that tanθ = 1 or 1/ 2

31. The length of 40 leaves of a plant are measured correct to nearest millimetre, and the data

obtained is represented in the following table.

## Class 10 Maths Sample Paper 2023 24: Section D

**SECTION D**

**Section D consists of 4 questions of 5 marks each**

32. A motor boat whose speed is 18 km/h in still water takes 1 hr. more to go 24 km upstream

than to return downstream to the same spot. Find the speed of stream.

[or]

Two water taps together can fill a tank in 9(3/8) hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

33. (a) State and prove Basic Proportionality theorem.

(b) In the given figure ∠CEF = ∠CFE. F is the midpoint of DC.

Prove that ??/?? =??/ ??

34. Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by

21 cm? What should be the speed of water if the rise in water level is to be attained in 1 hour?

[or]

A tent is in the shape of a cylinder surmounted by a conical top. If the height and radius of the cylindrical part are 3 m and 14 m respectively, and the total height of the tent is 13.5 m, find the area of the canvas required for making the tent, keeping a provision of 26 m2 of canvas for stitching and wastage. Also, find the cost of the canvas to be purchased at the rate of ₹ 500 per m².

35. The median of the following data is 50. Find the values of ‘p’ and ‘q’, if the sum of all frequencies is 90. Also find the mode.

## CBSE Maths Sample Paper 2023-24: Section E

**SECTION E**

**Section E consists of 3 questions of 4 marks each.**

36. Manpreet Kaur is the national record holder for women in the shot-put discipline. Her throw of 18.86m at the Asian Grand Prix in 2017 is the biggest distance for an Indian female athlete.

Keeping her as a role model, Sanjitha is determined to earn gold in Olympics one day. Initially her throw reached 7.56m only. Being an athlete in school, she regularly practiced both in the

mornings and in the evenings and was able to improve the distance by 9cm every week.

During the special camp for 15 days, she started with 40 throws and every day kept increasing the number of throws by 12 to achieve this remarkable progress.

(i) How many throws Sanjitha practiced on 11th day of the camp? 1

(ii) What would be Sanjitha’s throw distance at the end of 6 months?

(or)

When will she be able to achieve a throw of 11.16 m? 2

(iii) How many throws did she do during the entire camp of 15 days ? 1

37. Tharunya was thrilled to know that the football tournament is fixed with a monthly timeframe from 20th July to 20th August 2023 and for the first time in the FIFA Women’s World Cup’s history, two nations host in 10 venues. Her father felt that the game can be better understood if the position of players is represented as points on a coordinate plane.

(i) At an instance, the midfielders and forward formed a parallelogram. Find the position of the central midfielder (D) if the position of other players who formed the parallelogram are :- A(1,2), B(4,3) and C(6,6). 1

(ii) Check if the Goal keeper G(-3,5), Sweeper H(3,1) and Wing-back K(0,3) fall on a same straight line.

[or]

Check if the Full-back J(5,-3) and centre-back I(-4,6) are equidistant from forward C(0,1) and if C is the mid-point of IJ. 2

(iii) If Defensive midfielder A(1,4), Attacking midfielder B(2,-3) and Striker E(a,b) lie on the same straight line and B is equidistant from A and E, find the position of E. 1

38.One evening, Kaushik was in a park. Children were playing cricket. Birds were singing on a nearby tree of height 80m. He observed a bird on the tree at an angle of elevation of 45°.

When a sixer was hit, a ball flew through the tree frightening the bird to fly away. In 2 seconds, he observed the bird flying at the same height at an angle of elevation of 30° and the ball flying towards him at the same height at an angle of elevation of 60°.

(i) At what distance from the foot of the tree was he observing the bird sitting on the tree? 1

(ii) How far did the bird fly in the mentioned time?

(or)

After hitting the tree, how far did the ball travel in the sky when Kaushik saw the ball? 2

(iii) What is the speed of the bird in m/min if it had flown 20(√3 + 1) m?

Read: CBSE Class 10 Maths MCQ Questions with Answers

## CBSE Class 10 Maths Additional Practice Paper 2024

CBSE Maths Additional Practice Paper Class 10 2023-24 has been released e at the official website i.e. cbseacademic.nic.in. Students studying for the Secondary School Examination (Class 10) can download and practice the CBSE Class 10 Maths Additional Questions 2023-2024 to become familiar with the actual exam-level question paper. Along with the CBSE Class 10 Maths Additional Practice Question Paper 2024, the CBSE also provides the Marking Scheme so that students may understand how marks are distributed across various sections.

## CBSE Maths Practice Paper Class 10 2023-2024

**SECTION A**

**(This section comprises of Multiple-choice questions (MCQ) of 1 mark each.)**

1 Which of the following could be the graph of the polynomial?

(x – 1)²(x + 2)?

2 The lines k1, k2 and k3 represent three different equations as shown in the graph below. The solution of the equations represented by the lines k1 and k3 is x = 3 and y = 0 while the solution of the equations represented by the lines k2 and k3 is x = 4 and y = 1.

Which of these is the equation of the line k3?

(a) x – y = 3

(b) x – y = -3

(c) x + y = 3

(d) x + y = 1

3. What is/are the roots of 3x² = 6x?

(a) only 2

(b) only 3

(c) 0 and 6

(d) 0 and 2

4. The coordinates of the centre of the circle, O, and a point on the circle, N, are shown in the figure below.

What is the radius of the circle?

(a) √0.4 units

(b) 2 units

(c) 4 units

(d) √42.4

5 ΔPQR is shown below. ST is drawn such that ∠PRQ = ∠STQ

If ST divides QR in a ratio of 2:3, then what is the length of ST?

(a) 10/3 cm

(b) 8 cm

(c) 12 cm

(d) 40/3 cm

6. Two scalene triangles are given below.

(Note: The figures are not to scale.)

Anas and Rishi observed them and said the following:

Anas: ΔPQR is similar to ΔCBA

Rishi: ΔPQR is congruent to ΔCBA

Which of them is/are correct?

(a) Only Anas

(b) Only Rishi

(c) Both Anas and Rishi

(d) Neither of them, as two scalene triangles can never be similar or congruent.

7. Harsha made a wind chime using a frame and metal rods. She punched 8 holes in the frame, each 2 cm apart, and then hung 6 metal rods from the frame, as shown in the figure below. The ends of the metal rods are aligned over a line, shown by the dotted line in the figure.

(Note: The figure is not to scale.)

If all of the rods are straight and not swaying, then what is the length of Rod P?

(a) 69/7 cm

(b) 53/5 cm

(c) 76/ 5cm

(d) 111/ 7 cm

8. Two circles with centers O and N touch each other at point P as shown. O, P, and N are collinear. The radius of the circle with center O is twice that of the circle with center N. OX is tangent to the circle with center N, and OX = 18 cm.

What is the radius of the circle with center N?

(a) 18/√2 cm

(b) 9 cm

(c) 9/√2 cm

(d) 18/√10 cm

9 Shown below is a circle with center O having tangents at points P, T, and S.

If QR = 12 cm and the radius of the circle is 7 cm, what is the perimeter of the polygon PQTRSO?

(a) 26 cm

(b) 31 cm

(c) 38 cm

(d) (cannot say with the given information.)

10. Shown below is a table with values of cosecant and secant of different angles.

θ | 35° | 65° |

cosec θ | P | 1.1 |

sec (90° – θ) | 1.7 | Q |

What are the values of P and Q respectively?

(a) 1/1.7 and 1/1.1

(b) 1.1 and 1.7

(c) 1.7 and 1.1

(d) (cannot be found with the given information)

11. In the figure below, PQRS is a square.

(Note: The figure is not to scale.)

What is the value of sin ∠SPT?

(a) 8/ 17

(b) 8/ 15

(c) 15/ 17

(d) (cannot be found with the given information)

12 Shown below is a solved trigonometric problem

In which step is there an error in solving?

(a) Step 1

(b) Step 2

(c) Step 3

(d) There is no error

13 A circle with radius 6 cm is shown below. The area of the shaded region in the circle is of the area of the circle.

What is the length of the circle’s minor arc?

(a) 16𝜋/ 3 cm

(b) 20𝜋/ 3 cm

(c) 16π cm

(d) 20π cm

14. A regular pentagon is inscribed in a circle with centre O, of radius 5 cm, as shown below.

What is the area of the shaded part of the circle?

(a) 2π cm²

(b) 4π cm²

(c) 5π cm²

(d) 10π cm²

15 A cuboid of base area P sq units is filled with water upto a height of Q units. A sphere of volume R cu units is dropped into the cuboid such that it is completely submerged. A representation of the submerged sphere is shown below.

Which of these represents the increase in the height of water?

(a) 0 units

(b) 𝑅/𝑃 units

(c) R units

(d) 𝑄 + 𝑅/ 𝑃 units

16. Sweety, Nitesh, and Ashraf visited a hospital for their annual body checkup, which included a blood pressure evaluation. The results of their systolic blood pressure readings are as follows:

Sweety: 121 mmHg

Nitesh: 147 mmHg

Ashraf: 160 mmHg

The table below depicts the systolic blood pressure ranges of all the patients who visited the hospital on the same day.

Blood pressure (mmHg) | Number of patients |

115 – 125 | 10 |

125 – 135 | 9 |

135 – 145 | 12 |

145 – 155 | 19 |

155 – 165 | 10 |

Who among the three friends have a blood pressure reading that falls in the modal class?

(a) Sweety

(b) Nitesh

(c) Ashraf

(d) Both Sweety and Ashraf

17.The table below depicts the weight of the students of class 6 of Red Bricks Public School. There are 18 students in the class that weigh above the median weight.

Weight in Kg |
Number of students |

25-28 | 6 |

28-32 | 8 |

31-34 | 7 |

34-37 | 10 |

37=40 | ? |

If there are no students with the same weight as median weight, how many students weigh between the range of 37 – 40 kgs?

(a) 5

(b) 7

(c) 18

(d) 31

18 Ginny flipped a fair coin three times and tails came up each time. Ginny wants to flip the coin again.

What is the probability of getting heads in the next coin flip?

(a) 0

(b) 0.25

(c) 0.5

(d) 1

19 A number q is prime factorised as 32 × 72 × b, where b is a prime number other than 3 and 7.

Based on the above information, two statements are given below – one labelled Assertion (A) and the other labelled Reason (R). Read the statements carefully and choose the option that correctly describes statements (A) and (R).

*Assertion (A)*: q is definitely an odd number.

*Reason (R):* 32 × 72 is an odd number.

(a) Both (A) and (R) are true and (R) is the correct explanation for (A).

(b) Both (A) and (R) are true but (R) is not the correct explanation for (A).

(c) (A) is true but (R) is false.

(d) (A) is false but (R) is true.

20 P (-2, 5) and Q (2, -1) are two points on the coordinate plane.

Two statements are given below – one labelled Assertion (A) and the other labelled Reason (R). Read the statements carefully and choose the option that correctly describes statements (A) and (R).

*Assertion (A):* The midpoint (0, 2) is the only point equidistant from P and Q.

*Reason (R):* There are many points (x, y) where (x + 2)² + (y – 5)² = (x – 2)² + (y + 1)² are equidistant from P and Q.

(a) Both (A) and (R) are true and (R) is the correct explanation for (A).

(b) Both (A) and (R) are true and (R) is not the correct explanation for (A).

(c) (A) is true but (R) is false.

(d) (A) is false but (R) is true.

## Maths Model Question Paper 2024 Class 10 PDF

CBSE Maths model question paper 2024 class 10 along with the marking scheme is now available to download on the official website of CBSE. Candidates may download the CBSE maths model question paper 2024 class 10 provided here in PDF format. and enhance their preparation for the upcoming CBSE Class 10 Board Exams.

Class 10 Maths Model Paper 2024 PDF |

CBSE Class 10 Maths Model Question Paper 2024 PDF Download |

Maths Model Paper 2024 Class 10 Solutions and Marking Scheme |