CBSE Class 10 maths exam 2025: Chapter-wise most repeated questions for board exam 2025

CBSE Class 10 maths exam 2025: CBSE Class 10 Maths exam for 2025 is scheduled to take place on March 10, 2025, for both Mathematics Standard and Mathematics Basic. The exam will be held in the offline mode from 10:30 AM to 1:30 PM. Important chapters for this exam include Real Numbers, Polynomials, and Algebra.

These chapters are very important for board exams. Algebra is especially important because of its high weightage. Students can improve their preparation and do better in the exam if they practice from these chapters. The CBSE Class 10 exams started on February 15, 2025, and will end on March 18, 2025.

CBSE Class 10 Maths Question Paper Pattern 2025

Below is the CBSE Class 10th Maths Question Paper Pattern 2025:

CBSE Class 10 Maths Most Repeated Questions 2025

Here are the most important and frequently asked questions for the CBSE Class 10 Maths Board Exam 2025. Students should solve these questions to boost their confidence and improve their scores in the final exam.

• The King, Queen and Jack of clubs are removed from a pack of 52 cards and then the remaining cards are well shuffled. A card is selected from the remaining cards. Find the probability of getting a card (i) of spades (ii) of black king (iii) of clubs (iv) of jacks. (CBSE 2014-2017, 2020)
• In ¦¤ABC, altitude AD and CE intersect each other at the point P. Prove that (i) ¦¤¦¡¦±¦¥ ~ ¦¤CPD (ii) AP x PD = CP x PE (iii) ¦¤ADB ~ ¦¤§³§¦§£ (iv) AB ¡Á CE = BC X AD. (CBSE 2014, 2017, 2020)
• Solve the following pair of linear equations graphically: x + 3y = 6; 2x-3y = 12. Also, find the area of the triangle by the lines representing the given equation with the y-axis. (CBSE 2012-2020)

• A passenger, while boarding the plane, slipped from the stairs and got hurt. The pilot took the passenger to the emergency clinic at the airport for treatment. Due to this, the plane got delayed by half an hour. To reach the destination 1500 km away in time, so that the passengers could catch the connecting flight, the speed of the plane was increased by 250 km/hour than the usual speed. Find the usual speed of the plane. (CBSE 2011-2020)
• A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them being 3.5 cm and the total height of solid is 9.5 cm. Find the volume of the solid. [Use ¦Ð = 22/7] (CBSE 2011-2020)
• A thief runs with a uniform speed of 100 m/minute. After one minute a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/minute every succeeding minute. After how many minutes the policeman will catch the thief. (CBSE 2011, 2012, 2015-2020)

• The median of the following data is 525. Find the values of x and y, if total frequency is 100:

• There are 104 students in class X and 96 students in class IX in a school. In a house examination, the students are to be evenly seated in parallel rows such that no two adjacent rows are of the same class. (a) Find the maximum number of parallel rows of each class for the seating arrangement. (b) Also find the number of students of class IX and also of class X in a row. (CBSE 2011, 2013, 2015)
• As observed from the top of a 100 m high light house from the sea-level, the angles of depression of two ships are 30¡ã and 45¡ã. If one ship is exactly behind the other on the same side of the light house, find the distance between the two ships. [Use ¡Ì3 = 1.732] (CBSE 2011-2020)
• Prove that: (1 + cot A+ tan A) (sin A - cos A) = sec? A-cosec? A / sec? A. cosec? A (CBSE 2011-2020)
• Prove that (2+¡Ì3)/5 is an irrational number, given that ¡Ì3 is an irrational number. (CBSE 2011-2020)
• If sides AB, BC and median AD of ¦¤§¡§£§³ are proportional to the corresponding sides PQ, QR and median PM of PQR, show that ¦¤ABC ~ ¦¤PQR. (CBSE 2011-2020)
• Two people are 16 km apart on a straight road. They start walking at the same time. If they walk towards each other with different speeds, they will meet in 2 hours. Had they walked in the same direction with same speeds as before, they would have met in 8 hours. Find their walking speeds. (CBSE 2011-2020)
• If -4 is a root of the equation x?+2x+4p = 0. Find the value of k for which the quadratic equation x? + px(1+3k) +7(3 + 2k) = 0 has equal roots. (CBSE 2011-2020)
• The ratio of the 11th term to the 18th term of an A.P. is 2: 3. Find the ratio of the 5th term to the 21st term. Also, find the ratio of the sum of first 5 terms to the sum of first 21 terms. (CBSE 2020)
• A bird is sitting on the top of a 80 m high tree. From a point on the ground, the angle of elevation of the bird is 45¡ã. The bird flies away horizontally in such a way that it remained at a constant height from the ground. After 2 seconds, the angle of elevation of the bird from the same point is 30¡ã. Find the speed of the flying bird. (Use ¡Ì3 = 1.732) (CBSE 2011-2020)
• Find the sum of all the integers between 100 and 200 that are divisible by 9. (CBSE 2015)
• A bag contains 5 red balls, 8 blue balls, and 7 green balls. If 3 balls are drawn at random without replacement, find the probability that at least one ball is green. (CBSE 2017)
• In a triangle, the length of the hypotenuse is 10 cm and one of the legs is 6 cm. Find the length of the other leg. (CBSE 2018)
• Solve for x: 3x + 5 > 2x + 7 (CBSE 2019)
• Find the area of a triangle whose vertices are (1, 1), (3, 4), and (5, 2). (CBSE 2019)
• A line passes through (2, 3) and (4, 5). Find its equation. (CBSE 2018)
• If the sum of two numbers is 16 and their product is 48, find the numbers. (CBSE 2016)
• Prove that the sum of any two sides of a triangle is greater than the third side. (CBSE 2014)
• Find the equation of the line passing through (1, 2) with slope 3. (CBSE 2015)
• A box contains 5 red marbles, 8 blue marbles, and 4 green marbles. If three marbles are drawn at random without replacement, find the probability that none of them is green. (CBSE 2013)
• Solve the equation: x? - 4x - 21 = 0 (CBSE 2012)
• Find the volume of a cylinder with radius 4 cm and height 10 cm. [Use ¦Ð = 22/7] (CBSE 2011)
• In a right-angled triangle, the length of the hypotenuse is 5 cm and one of the legs is 3 cm. Find the length of the other leg. (CBSE 2016)
• Find the area of a circle with radius 7 cm. [Use ¦Ð = 22/7] (CBSE 2017)
• A line passes through (1, 2) and (3, 4). Find its slope. (CBSE 2018)
• Solve for x: x? + 5x + 6 = 0 (CBSE 2019)
• Find the equation of the line passing through (2, 3) with slope 2. (CBSE 2015)
• A bag contains 3 red balls, 5 blue balls, and 2 green balls. If 2 balls are drawn at random without replacement, find the probability that both are blue. (CBSE 2014)
• Prove that the diagonals of a rectangle bisect each other. (CBSE 2013)
• Find the area of a triangle whose base is 5 cm and height is 6 cm. (CBSE 2012)
• Solve the equation: x? - 7x + 12 = 0 (CBSE 2011)
• Find the volume of a cone with radius 3 cm and height 8 cm. [Use ¦Ð = 22/7] (CBSE 2016)
• In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the legs is 8 cm. Find the length of the other leg. (CBSE 2017)
• Find the equation of the line passing through (1, 1) with slope -2. (CBSE 2018)
• Solve for x: 2x + 5 > 11 (CBSE 2019)
• Find the area of a circle with radius 5 cm. [Use ¦Ð = 22/7] (CBSE 2015)
• A line passes through (2, 4) and (4, 6). Find its equation. (CBSE 2016)
• Solve the equation: x? + 2x - 15 = 0 (CBSE 2014)
• Find the volume of a sphere with radius 3 cm. [Use ¦Ð = 22/7] (CBSE 2013)
• In a triangle, the length of the hypotenuse is 13 cm and one of the legs is 5 cm. Find the length of the other leg. (CBSE 2012)
• Find the equation of the line passing through (3, 4) with slope 1. (CBSE 2017)
• Solve for x: x? - 9x + 20 = 0 (CBSE 2018)
• Find the area of a triangle whose vertices are (2, 3), (4, 5), and (6, 7). (CBSE 2019)
• A box contains 4 red marbles, 6 blue marbles, and 2 green marbles. If two marbles are drawn at random without replacement, find the probability that both are red. (CBSE 2016)

Chapter-Wise Most Repeated Questions in Class 10 CBSE Maths Board 2025

Below are the Chapter-Wise Most Repeated Questions in Class 10 CBSE Maths Board 2025:

Chapter 1: Number Systems

• Prove that root 2 is an irrational number.
• Find the HCF and LCM of 12 and 15.
• Express 0.6£þ in the form p/q, where pp and qq are integers and q¡Ù.
• If a=0.9999£þ, then find the value of 10000a?1/9.
• Prove that 33 is an irrational number.
• Find the value of xx in the equation x+1/x=3.
• Express 0.3£þin the form p/q, where p and q are integers and q¡Ù0.

Chapter 2: Polynomials

• Find the value of k if x+1 is a factor of x3+kx2+2x+3.
• Divide x3?3x2+5x?7 by x?1.
• If f(x)=x3?2x2?7x+1, find f(0) and f(1).
• Find the remainder when x3+3x2+5x+9 is divided by x+2.
• Divide x4+2x3?3x2+x+1 by x2+1.
• If f(x)=x2?3x+2, find f(?1) and f(2).
• Find the value of aa if x?2x?2 is a factor of x3+ax2+5x+10.

Chapter 3: Pair of Linear Equations in Two Variables

• Solve the system of equations: x+y=4 and 2x?2y=?2.
• Find the value of k if the system of equations x+2y=3x+2y=3 and 5x+ky=75x+ky=7 has a unique solution.
• Solve for x and y in the equations x+y=5 and x?y=1.
• Graphically represent the equations x+y=2 and x?y=0.
• Solve the system of equations: 2x+3y=7 and x?2y=?3.
• Find the value of k if the system of equations x+y=2 and kx+2y=5 has infinitely many solutions.
• Solve the system of equations: 3x+4y=10 and 2x?2y=?2.

Chapter 4: Quadratic Equations

• Solve the quadratic equation x?+5x+6=0.
• Find the roots of the equation x??7x+12=0.
• Solve the equation x?+2x?6=0. by factorisation.
• Find the value of kk if the roots of x?+kx+3=0 are real and distinct.
• Solve the equation x??4x?3=0. using the quadratic formula.
• Find the roots of the equation x??9x+20=0.
• Solve the equation x?+6x+8=0 by factorisation.

Chapter 5: Arithmetic Progressions

• Find the sum of the first 20 terms of an A.P. whose first term is 3 and common difference is 2.
• Determine the nth term of an A.P. whose first term is 5 and common difference is 3.
• Find the sum of the first 15 terms of an A.P. with first term 7 and common difference 3.
• Find the value of n if the sum of n terms of an A.P. is 150, the first term is 1, and the common difference is 2.
• Find the sum of the first 10 terms of an A.P. whose first term is 2 and common difference is 3.
• Determine the common difference of an A.P. whose first term is 5 and the sum of the first 10 terms is 235.
• Find the sum of the first 12 terms of an A.P. with first term 4 and common difference 5.

Chapter 6: Triangles

• In a triangle, prove that the sum of any two sides is greater than the third side.
• Prove that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
• In a triangle ABC, if AB=AC, prove that ¡ÏB=¡ÏC.
• Prove that the sum of all interior angles of a triangle is 180¡ã.
• If in a triangle ABC, ¡ÏA=90¡ã and AB=AC, find ¡ÏB and ¡ÏC.
• Prove that the diagonals of a parallelogram bisect each other.
• In a triangle ABC, if AB=5 cm, BC=6 cm, and AC=7 cm, find the area using Heron's formula.

Chapter 7: Coordinate Geometry

• Find the equation of the line passing through the points (2,3) and (4,5).
• Determine the distance between the points (1,1) and (4,5).
• Find the equation of the line passing through (2,3) with slope 22.
• Find the coordinates of the point which is equidistant from (2,3) and (4,5).
• Find the equation of the line passing through (1,2) and perpendicular to the line 2x+3y=5.
• Find the distance between the points (0,0) and (3,4).

Chapter 8: Introduction to Trigonometry

• Find the value of sin?30¡ã.
• Prove that sin?2¦È+cos?2¦È=1.
• Find the value of tan?45¡ã.
• If sin?¦È=35, find cos?¦È.
• Find the value of cos?60¡ã.
• Prove that tan?¦È=sin?¦Ècos?¦È.
• Find the value of sin?90¡ã.

Chapter 9: Some Applications of Trigonometry

• A tower stands vertically upright. From a point on the ground, its angle of elevation of the top is 60¡ã. If this point is 15 meters away from the foot of the tower, find the height of the tower.
• From the top of a building 20 meters high, the angle of depression of a car is 30¡ã. How far is the car from the building?
• A kite is flying at a height of 30 meters from the ground. The string makes an angle of 60¡ã with the ground. Find the length of the string.
• The angle of elevation of the top of a tower from a point on the ground is 45¡ã. If the point is 1010 meters away from the foot of the tower, find the height of the tower.
• A man is standing on the top of a cliff and observes the angle of depression of a ship to be 30¡ã. If the height of the cliff is 5050 meters, how far is the ship from the cliff?
• The angle of elevation of the top of a building from a point on the ground is 60¡ã. If the point is 2020 meters away from the foot of the building, find the height of the building.
• From a point on the ground, the angle of elevation of the top of a tower is 45¡ã. If the point is 1515 meters away from the foot of the tower, find the height of the tower.

Chapter 10: Circles

• Prove that the line joining the centre and the point of contact is perpendicular to the tangent.
• Find the equation of a circle with centre (2,3) and radius 44.
• Prove that the tangents drawn from an external point to a circle are equal in length.
• Find the equation of a circle with centre (?1,2) and radius 3.
• Prove that the radius is perpendicular to the tangent at the point of contact.
• Find the equation of a circle with centre (0,0)and radius 5.
• Prove that the angle in a semicircle is a right angle.

Chapter 11: Conic Sections

• Find the equation of a circle with centre (1,1) and radius 2.
• Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
• Find the equation of a circle with centre (?2,?3) and radius 1.
• Prove that the angle subtended by an arc at the centre is double the angle it subtends at any point on the remaining part of the circle.
• Find the equation of a circle with centre (0,0) and radius 1.
• Prove that the line joining the centre to the point of contact is perpendicular to the tangent.
• Find the equation of a circle with centre (3,4) and radius 2.

Chapter 12: Surface Areas and Volumes

• Find the volume of a cube with an edge length 5 cm.
• Find the surface area of a cuboid with length 6 cm, breadth 4 cm, and height 2 cm.
• Find the volume of a cuboid with length 10 cm, breadth 5 cm, and height 3 cm.
• Find the surface area of a sphere with radius 3 cm.
• Find the volume of a sphere with radius 4 cm.
• Find the surface area of a cylinder with radius 2 cm and height 10 cm.
• Find the volume of a cylinder with radius 3 cm and height 5 cm.

Chapter 13: Statistics

• Find the mean of the numbers 2, 4, 6, 8, and 10.
• Find the median of the numbers 1, 3, 5, 7, and 9.
• Find the mode of the numbers 2, 4, 6, 8, 8, 10.
• Find the range of the numbers 10, 20, 30, 40, and 50.
• Find the mean deviation of the numbers 1, 2, 3, 4, and 5 from their mean.
• Find the variance of the numbers 2, 4, 6, 8, and 10.
• Find the standard deviation of the numbers 1, 3, 5, 7, and 9.

Chapter 14: Probability

• A coin is tossed. What is the probability of getting a head?
• A die is rolled. What is the probability of getting a 6?
• A card is drawn from a pack of 52 cards. What is the probability of getting a king?
• Two coins are tossed. What is the probability of getting at least one head?
• A bag contains 5 red balls and 3 blue balls. What is the probability of drawing a red ball?
• A dice is rolled twice. What is the probability of getting a sum of 7?
• A card is drawn from a pack of 52 cards. What is the probability of getting a spade?

Students to prepare well for the CBSE Class 10 Maths exam in 2025, first understand the question pattern and syllabus properly. Make a study plan and follow it. Give more time to important chapters like Geometry, Algebra, and Mensuration, as they have more marks.

Now, start by solving all the exercises in the NCERT book, then practice extra questions from books like R.D. Sharma. Solve previous years¡¯ question papers and sample papers to understand the types of questions asked. Regular revision and timed practice will help you complete the exam on time. Keep a separate notebook to write down formulas and important points for quick revision.

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