CBSE Class 10 Maths Questions with Answers

Home

Author at PW

October 23, 2025

CBSE Class 10 Maths Questions with Answers provides students with a complete and practical guide to mastering important topics and solving exam-oriented problems confidently. This section covers a wide range of Class 10 Maths questions, including algebra, geometry, arithmetic, trigonometry, and statistics, ensuring students build conceptual clarity and accuracy. Learners can also refer to important questions for Class 10 Maths CBSE that frequently appear in board exams, helping them focus on key scoring areas.

Along with comprehensive CBSE Class 10th Maths solutions, students get access to CBSE Class 10th Maths previous year question papers with answers and CBSE sample papers for Class 10. These resources enable effective practice through step-by-step problem solving and real exam-type questions. For instance, students can try exercises such as “Prove that the circumference of a circle is 2πr” or “Find the mode of 10, 12, 11, 10, 15, 20, 19, 21, 11, 9, 10.” By consistently practising such questions, students can strengthen their problem-solving skills and perform confidently in board exams.

Check Out: CBSE Class 10 Books

CBSE Class 10 Maths Questions with Answers

Provided here are the CBSE Class 10 Maths Questions with Answers. Students can check below for the solution and complete a detailed answer for the same:

1. Prove that the circumference of a circle is 2πr

Question: Prove that the circumference of a circle is equal to 2πr.
Answer: C=2πrC = 2\pi rC=2πr

Explanation: The circumference of a circle is the distance around it. The ratio of the circumference to its diameter is always constant, denoted by π. This fundamental property of a circle gives the formula for the circumference.

Step-by-step solution:

Let the radius of the circle = r.
Then the diameter of the circle = 2r.
Circumference ÷ diameter = π → Circumference = π × diameter.
Substitute the diameter: Circumference = π × 2r = 2πr.

Note: The formula is derived from the property that all circles have the same ratio of circumference to diameter, which is π.

2. Find the mode of 10, 12, 11, 10, 15, 20, 19, 21, 11, 9, 10

Question: Find the mode of the following numbers: 10, 12, 11, 10, 15, 20, 19, 21, 11, 9, 10.
Answer: 10

Explanation: Mode is the value that appears most frequently in a dataset.

Step-by-step solution:

Count the frequency of each number:

10 → 3 times
11 → 2 times
12 → 1 time
15 → 1 time
19 → 1 time
20 → 1 time
21 → 1 time
9 → 1 time

Identify the number with the highest frequency → 10 appears 3 times.

Note: Mode is determined by checking the frequency of all numbers and selecting the number with the maximum occurrence.

3. Formula of the total surface area of a cone

Question: What is the formula for the total surface area of a cone?
Answer: TSA=πr(l+r)TSA = \pi r (l + r)TSA=πr(l+r)

Explanation: The Total surface area (TSA) of a cone is the sum of its curved surface area (CSA) and the base area.

Step-by-step solution:

Curved surface area (CSA) = πrl, where r = radius and l = slant height.
Base area = πr².
Total surface area = CSA + base area = πrl + πr² = πr(l + r).

Note: The formula combines the standard areas for the curved surface and the circular base.

4. Define class interval

Question: Define a class interval.
Answer: Class interval is the difference between the upper and lower boundaries of a class in a frequency distribution.

Step-by-step solution:

Consider the class 10–20.
Lower limit = 10, upper limit = 20.
Class interval = upper limit – lower limit = 20 – 10 = 10.

Note: The class interval represents the range of values that fall into each group in a frequency table.

5. Leap year has days: A) 365 B) 366 C) 367 D) 368

Question: How many days does a leap year have?
Answer: B) 366

Explanation: A leap year occurs every 4 years to account for the extra 0.25 days in Earth’s orbit. February has 29 days instead of 28.

Step-by-step solution:

Normal year = 365 days.
Extra day in leap year → February = 29 days.
Total days = 365 + 1 = 366.

Note: The extra day is added to align the calendar year with the astronomical year.

Check Out: PW 15 CBSE Sample Paper Class 10 Maths Standard for 2026 Exam

6. Every rational number is a: A) Natural number B) Integer C) Whole number D) None of these

Question: Every rational number is a: A) Natural number B) Integer C) Whole number D) None of these.
Answer: D) None of these

Explanation: A rational number can be expressed as p/q, where q ≠ 0. Rational numbers include fractions and integers, but not all are whole numbers or natural numbers.

Step-by-step solution:

Rational number = p/q, q ≠ 0.
Examples: 1/2, -3/4, 5, etc.
Check options: Not all rational numbers are natural, whole, or integer → None of these.

Note: Rational numbers are a broader set including fractions, integers, and negative numbers.

7. Split the middle term in the quadratic equation: x² + 5x + 6 = 0

Question: Solve the quadratic equation x² + 5x + 6 = 0 by splitting the middle term.
Answer: (x + 2)(x + 3) = 0 → x = -2, -3

Explanation: Split the middle term into two numbers whose sum = the middle coefficient and product = the constant term.

Step-by-step solution:

Constant term = 6, middle coefficient = 5 → numbers = 2 and 3.
Split middle term: x² + 2x + 3x + 6 = 0.
Factor by grouping: x(x + 2) + 3(x + 2) = 0 → (x + 2)(x + 3) = 0.
Solve each factor: x + 2 = 0 → x = -2, x + 3 = 0 → x = -3.

Note: Middle term splitting simplifies factoring of quadratic equations.

8. The predecessor of 99 is: A) 98 B) 100 C) 101 D) 97

Question: Find the predecessor of 99.
Answer: A) 98

Explanation: Predecessor of a number is the number immediately before it.

Step-by-step solution:

Number before 99 = 98.
Answer = 98.

Note: Predecessor = number – 1.

9. Leap years are there in the set of any co-prime numbers: True or False

Question: Leap years are in the set of any co-prime numbers: True or False.
Answer: False

Explanation: Leap years occur every 4 years, independent of whether numbers are co-prime.

Step-by-step solution:

Leap year rule: divisible by 4.
Co-prime numbers have no common factors except 1.
Leap year occurrence does not depend on co-prime numbers → False.

Note: The question tests understanding of the leap year concept versus number properties.

10. The diagonals of a rectangle are unequal in: A) Square B) Rhombus C) Parallelogram D) None of these

Question: In which of the following are the diagonals of a rectangle unequal?
Answer: D) None of these

Explanation: Diagonals of a rectangle are always equal.

Step-by-step solution:

Rectangle properties → diagonals are equal.
Unequal diagonals do not exist in a rectangle → Answer = None.

Note: Understanding rectangle properties helps identify the correct answer.

Check Out: PW 15 CBSE Class 10 Maths Basic Sample Paper for 2026 Board Exam

11. How many edges does a cube have?

Question: How many edges does a cube have?
Answer: 12

Explanation: A cube has 6 faces. Each face has 4 edges, and each edge is shared by 2 faces.

Step-by-step solution:

Number of edges per face = 4.
Total edges = (6 × 4)/2 = 12.

Note: Each edge is counted twice across faces, so divide by 2.

12. What is 24 as a percentage?

Question: Convert 24 into a percentage.
Answer: 2400%

Explanation: To convert a number to a percentage, multiply by 100.

Step-by-step solution:

24 × 100 = 2400%

Note: Percent = number × 100.

13. A boat goes 24 km upstream and 28 km downstream. Find speed in still water

Question: A boat goes 24 km upstream and 28 km downstream. Find the speed of the boat in still water.
Answer: Let the speed of the boat = b km/h, the speed of the stream = s km/h.

Explanation: Upstream speed = b–s, downstream speed = b + s. Use the distance ÷ time formula.

Step-by-step solution:

Upstream time = 24 / (b–s)
Downstream time = 28 / (b + s)
Total time = sum of upstream and downstream times.
Solve the equation for b (speed in still water).

Note: The Formula for speed, distance, and time helps find the boat’s speed in still water.

Sample Papers Class 10 CBSE

Students preparing for their board exams can now access PW Sample Papers Class 10 CBSE based on the latest syllabus pattern updated on 30th July 2025. These sample papers include 111 most probable questions and 50% competency-based questions, ensuring complete coverage of the CBSE Class 10 Maths syllabus. Learners can also refer to CBSE past year papers, marks breakdown tables, and chapter-wise mind maps to strengthen their understanding.

Each paper follows step-wise marking with answering templates aligned with the latest CBSE SQP. The important questions for Class 10 Maths CBSE are carefully curated to help students practice exam-level problems effectively. Additionally, CBSE 10th Maths previous year question papers with answers and CBSE Class 10th Maths solutions are provided for deeper concept clarity.

By solving CBSE sample papers for Class 10, students can enhance speed, accuracy, and confidence. These Class 10 Math questions serve as a complete revision tool for board exam success, blending concept practice with exam-oriented preparation.

CBSE Class 10 Maths Questions With Answers FAQs

Q1: Where can I find CBSE Class 10 Maths questions with answers?
A: You can access them through CBSE sample papers, NCERT solutions, and past year question papers with step-by-step solutions. These resources also include important questions for Class 10 Maths CBSE and Class 10 Math questions frequently asked in exams.

Q2: What are “important questions for Class 10 Maths CBSE”?
A: These are selected problems that appear often in CBSE exams or reflect key concepts. They help you focus your practice on topics with higher probability, such as quadratic equations, circles, statistics, etc.

Q3: How do I use CBSE 10th Maths previous year question papers with answers effectively?
A: Solve the paper in exam-like conditions first, then check CBSE Class 10th Maths solutions, analyse mistakes, and refer to CBSE sample papers for Class 10 to compare question types and patterns.

Q4. What is the formula for the circumference of a circle?
A: The circumference of a circle is C=2πrC = 2\pi rC=2πr, where r is the radius.

Q5. How do you find the mode of a set of numbers?
A: The mode is the number that appears most frequently in the dataset.

Recommended for you

See All