CBSE Class 10 Maths Sample Paper 2023-24 PDF Download
CBSE has officially released the Sample Paper for Class 10 Maths with Solution for the year 2024 in PDF format. You can download the CBSE Class 10 Maths Sample Paper 2023-24 PDF, covering both basic and standard maths, from here.
Ananya Gupta19 Jan, 2024
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CBSE Class 10 Maths Sample Paper 2023-24 : The Central Board of Secondary Education (CBSE) has officially released the CBSE Class 10 Maths Sample Paper 2023-24. Students can access the sample paper on the official CBSE website at cbseacademic.nic.in. The CBSE Class 10 Maths Sample Paper for the academic year 2023-24 is available in PDF format, for both basic and standard math levels. This resource is designed to assist students in their preparation for the upcoming examinations.
CBSE Class 10 Previous Year Question Papers
CBSE Class 10 Maths Sample Paper 2023-24
In addition to the CBSE Maths Sample Paper for Class 10, 2024, the Central Board of Secondary Education (CBSE) has also released the Marking Scheme for the sample paper. This Marking Scheme serves as a valuable resource for students, offering insights into the board exam format, types of questions, answer options, and other crucial features. The CBSE Maths Sample Paper for Class 10, 2024, along with its Marking Scheme, provides students with a comprehensive understanding of the examination pattern, aiding them in better preparation for their upcoming board exams.CBSE Class 10 Maths Additional Practice Paper Questions 2023-24
Maths Sample Paper Class 10 2024: Exam Pattern
CBSE Sample Paper Class 10 Maths with Solution 2024 PDF
The Sample Paper for Class 10 Maths with Solution for the year 2024 is now available for download on the official website cbseacademic.nic.in. Candidates can access and download these sample papers for future reference. For the convenience of students, we are providing both the Basic and Standard Sample Paper for Class 10 Maths with Solution for the year 2024 in PDF format along with the Marking Scheme.CBSE Class 10 Maths Sample Paper 2023-24 with Solution PDF Based: SECTION A
For your convenience, the full Sample Paper for Class 10 Maths for the academic year 2023-24, along with solutions, is provided below. You can check the complete sample paper 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 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 2024 PDF Based: 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.
Sample Paper Class 10 Maths with Solution 2024 PDF Based: 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.
Sample Paper Class 10 Maths with Solution 2024 PDF Based: Section E
Section D consists of 4 questions of 5 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?
Benefits of CBSE Class 10 Maths Sample Paper 2023-24
Using CBSE Class 10 Maths Sample Papers for the academic year 2023-24 can have several benefits to students:Familiarity with Exam Pattern: Sample papers provide students with an understanding of the exam pattern, question distribution, and marking scheme. This familiarity helps reduce anxiety during the actual exam.
Practice with Variety of Questions: Sample papers usually include a diverse set of questions covering different topics. This allows students to practice a wide range of problems and enhances their problem-solving skills.
Time Management Skills: Solving sample papers within the stipulated time helps students practice time management. This is crucial for answering all questions during the actual exam.
Self-Assessment: After solving sample papers, students can evaluate their performance using the provided solutions or answer keys. This self-assessment helps identify weak areas that need improvement.
Boosts Confidence: Regular practice with sample papers helps build confidence as students become more comfortable with the exam format and types of questions.
ISC 12th Admit Card 2024 FAQs
Where can I find the CBSE Class 10 Maths Sample Paper 2023-24?
The CBSE Class 10 Maths Sample Paper for the academic year 2023-24 can be found on the official CBSE website at cbseacademic.nic.in.
Is the CBSE Class 10 Maths Sample Paper 2023-24 available in both Basic and Standard versions?
Yes, the CBSE Class 10 Maths Sample Paper 2023-24 is available in both Basic and Standard versions to cater to the different needs of students.
Can I download the CBSE Class 10 Maths Sample Paper 2023-24 in PDF format?
Yes, the CBSE Class 10 Maths Sample Paper 2023-24 is available for download in PDF format for the convenience of students.
Where can I find the solutions for the CBSE Class 10 Maths Sample Paper 2023-24?
The solutions for the CBSE Class 10 Maths Sample Paper 2023-24 are provided along with the sample paper on the official CBSE website.
Are there different sections in the CBSE Class 10 Maths Sample Paper 2023-24?
Yes, the CBSE Class 10 Maths Sample Paper 2023-24 usually consists of different sections with various types of questions, such as multiple-choice, short answer, and long answer questions.
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