Important Questions for CBSE Class 10 Maths – Chapter-Wise

CBSE Important Questions for Class 10 Maths chapter wise is provided on this page. Students preparing for the CBSE 10th exam 2026 are advised to solve and practice the Important Questions for CBSE Class 10 Maths. 

CBSE Important Questions for Class 10 Maths chapter wise: We have provided CBSE Class 10 Maths Important Questions on this page. Those who are appearing for the CBSE 10th board exam 2026 are advised to go through the CBSE important questions for Class 10 Maths PDF. They can also find the important questions for class 10 Maths with answers online. CBSE is expected to release the CBSE Class 10 Date Sheet 2026 in the second week of November 2026. CBSE 10th Maths exam 2026 will be held in February 2026 tentatively.
Students are advised to prepare for the exam, as per the CBSE 10th Syllabus 2026. Important Questions for Class 10 Maths CBSE Chapter wise PDF is available here.  The CBSE Important Questions for Class 10 Maths provided here will help you achieve good marks in the Maths exam. They can also check CBSE 10th preparation tips 2026.

CBSE Important Questions for Class 10 Maths Chapter wise

Students can find Most repeated questions in Maths Class 10 Standard on this page. The important questions are provided to give a better conceptual understanding to the students and help them to be familiar with what questions they can expect in CBSE 10th board exams. 

CBSE Important Questions for Class 10 Maths - Real Numbers

Check important questions of CBSE Class 10 Maths Real Numbers. 

1. Use Euclid’s division lemma to show that the square of any positive integer is either of form 3m or 3m + 1 for some integer m.
2. Express each number as a product of its prime factors:
(i) 140
(ii) 156
(iii) 3825
(iv) 5005
(v) 7429
3. Given that HCF (306, 657) = 9, find LCM (306, 657).

4. Find HCF and LCM of 404 and 96 and verify that HCF × LCM = Product of the two given numbers.
5. Using Euclid’s Algorithm, find the HCF of 2048 and 960.
6. The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form, p/q what can you say about the prime factors of q?
(i) 43.123456789
(ii) 0.120120012000120000. . .
7. Prove that 3 + 2√5 is irrational.
8. Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
(i) 13/3125 
(ii) 17/8
 (iii) 64/455 
(iv) 15/1600 

9. Check whether 6ⁿ can end with the digit 0 for any natural number n.

10. What is the HCF of the smallest prime number and the smallest composite number?

CBSE Important Questions for Class 10 Maths - QUADRATIC EQUATIONS

Check important questions of CBSE Class 10 Maths Quadratic equations.

1. Represent the following situations in the form of quadratic equations:

(i) The area of a rectangular plot is 528 m². The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

(ii) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. What is the speed of the train?

2. The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.
3. Find the roots of the following quadratic equations, if they exist, by the method of completing the square:

(i) 2x² – 7x +3 = 0

(ii) 2x² + x – 4 = 0
4. Find the discriminant of the equation 3x²– 2x +1/3= 0 and hence find the nature of its roots. Find them, if they are real.

5. Find the roots of quadratic equations by factorisation:
(i) √2 x² + 7x + 5√2=0
(ii) 100x² – 20x + 1 = 0

6. Solve the quadratic equation 2x² - 7x + 3 = 0 by using quadratic formula.

7. Is it possible to design a rectangular park of perimeter 80 and area 400 sq.m.? If so find its length and breadth.

8. Find two consecutive positive integers, the sum of whose squares is 365.

9. The sum of the areas of two squares is 468 m². If the difference of their perimeters is 24 m, find the sides of the two squares.

10. Find the values of k for each of the following quadratic equations, so that they have two equal roots.
(i) 2x² + kx + 3 = 0
(ii) kx (x – 2) + 6 = 0

CBSE Important Questions for Class 10 Maths - PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Check important questions of CBSE Class 10 Maths Pair of linear equations in two variables.

1. Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

2. The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs.160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs.300.
Represent the situation algebraically.
3. Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.

4. Formulate the following problems as a pair of equations, and hence find their solutions:
Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.

5. On comparing the ratios a1/a2, b1/b2, and c1/c2, find out whether the following pair of linear equations are consistent, or inconsistent.
(i) 3x + 2y = 5 ; 2x – 3y = 7
(ii) 2x – 3y = 8 ; 4x – 6y = 9

6. Solve the equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0 graphically.

7. Solve the following pair of linear equations by the substitution method.
(i) x + y = 14
x – y = 4
(ii) 3x – y = 3
9x – 3y = 9

8. Solve the following pair of linear equations by the substitution and cross-multiplication methods:
8x + 5y = 9
3x + 2y = 4

9. The coach of a cricket team buys 7 bats and 6 balls for Rs.3800. Later, she buys 3 bats and 5 balls for Rs.1750. Find the cost of each bat and each ball.

10. A fraction becomes 9/11 if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 5/6. Find the fraction.

11. Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:

(i) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
(ii) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs.27 for a book kept for seven days, while Susy paid Rs.21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

CBSE Important Questions for Class 10 Maths - POLYNOMIALS

CBSE Class 10 Maths Polynomials important questions are given below. 

1. Does the polynomial a⁴ + 4a² + 5 have real zeroes?

2. Find the value of “p” from the polynomial x² + 3x + p, if one of the zeroes of the polynomial is 2.

3. Compute the zeroes of the polynomial 4x² – 4x – 8. Also, establish a relationship between the zeroes and coefficients.

4. Find the value of “x” in the polynomial 2a² + 2xa + 5a + 10 if (a + x) is one of its factors.

5. How many zeros does the polynomial (x – 3)2 – 4 have? Also, find its zeroes.

6. Find the quadratic polynomial if its zeroes are 0, √5.

7. If the zeroes of the polynomial x³ – 3x² + x + 1 are a – b, a, a + b, then find the value of a and b.

8. α and β are zeroes of the quadratic polynomial x² – 6x + y. Find the value of ‘y’ if 3α + 2β = 20.

9. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes, respectively.

10. Obtain all other zeroes of 3x⁴ + 6x³ – 2x² – 10x – 5, if two of its zeroes are √(5/3) and -√(5/3).

CBSE Important Questions for Class 10 Maths - ARITHMETIC PROGRESSIONS

1. Which term of the AP: 21, 18, 15, . . . is – 81? Also, is any term 0? Give reason for your answer.

2. Write first four terms of the AP when the first term a and the common difference d are given as follows:

(i) a = 10, d = 10
(ii) a = -2, d = 0
(iii) a = 4, d = – 3

3. Ramkali saved Rs 5 in the first week of a year and then increased her weekly saving by Rs 1.75. If in the nth week, her weekly savings become Rs 20.75, find n.

4. Which term of the AP 3, 15, 27, 39, … will be 132 more than its 54th term?

5. If the 3rd and the 9th terms of an AP are 4 and  -8, respectively, then which term of this AP is zero.

6. Check whether – 150 is a term of the AP: 11, 8, 5, 2 . . .

7. How many terms of the AP : 24, 21, 18, . . . must be taken so that their sum is 78?

8. The sum of 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.

9. How many multiples of 4 lie between 10 and 250?

10. If the sum of the first n terms of an AP is 4n − n², what is the first term (that is S1)? What is the sum of the first two terms? What is the second term? Similarly find the 3rd, the 10th and the nth terms.

11. The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

12. Find the sum of the first 22 terms of an AP in which d = 7 and 22nd term is 149.

CBSE Important Questions for Class 10 Maths - COORDINATE GEOMETRY

1: Find the value of k if the points A(2, 3), B(4, k) and C(6, –3) are collinear.

2: Find the distance of the point P (2, 3) from the x-axis. 

3: Find the ratio in which the line segment joining the points (– 3, 10) and (6, – 8) is divided by (– 1, 6).

4: Find the coordinates of the points of trisection (i.e., points dividing into three equal parts) of the line segment joining the points A(2, – 2) and B(– 7, 4).

5: Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5).

6: Name the type of triangle formed by the points A (–5, 6), B (–4, –2) and C (7, 5).

7: Find the area of triangle PQR formed by the points P(-5, 7), Q(-4, -5) and R(4, 5). 

8: Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, –1), (2, 1) and (0, 3). 
Find the ratio of this area to the area of the given triangle.

9: Find the ratio in which the line x – 3y = 0 divides the line segment joining the points (-2, -5) and (6, 3). Find the coordinates of the point of intersection.

10: If the point C(-1, 2) divides internally the line segment joining A(2, 5) and B(x, y) in the ratio 3 : 4, find the coordinates of B.

CBSE Important Questions for Class 10 Maths - TRIANGLES

1: A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

2: If ΔABC ~ ΔQRP, ar (ΔABC) / ar (ΔPQR) =9/4 , AB = 18 cm and BC = 15 cm, then find PR.

3: If the areas of two similar triangles are equal, prove that they are congruent.

4: Sides of triangles are given below. Determine which of them are right triangles.

In case of a right triangle, write the length of its hypotenuse.

(i) 7 cm, 24 cm, 25 cm

(ii) 3 cm, 8 cm, 6 cm

5: O is any point inside a rectangle ABCD as shown in the figure. Prove that OB² + OD² = OA² + OC².

6: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.

7: Sides of triangles are given below. Determine which of them are right triangles.
In case of a right triangle, write the length of its hypotenuse.

(i) 7 cm, 24 cm, 25 cm

(ii) 3 cm, 8 cm, 6 cm

8: Given ΔABC ~ ΔPQR, if AB/PQ = 1/3, then find (ar ΔABC)/(ar ΔPQR).

9: In the figure, DE || BC. Find the length of side AD, given that AE = 1.8 cm, BD = 7.2 cm and CE = 5.4 cm.

10: The sides of two similar triangles are in the ratio 7 : 10.  Find the ratio of areas of these triangles.

11: In an equilateral ΔABC, D is a point on side BC such that BD = (1/3) BC. Prove that 9(AD)² = 7(AB)².

12: Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

13: Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.

CBSE Important Questions for Class 10 Maths - CIRCLES

1: Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

2: From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. Find the radius of the circle.

3: Let s denote the semi-perimeter of a triangle ABC in which BC = a, CA = b, AB = c. If a circle touches the sides BC, CA, AB at D, E, F, respectively, prove that BD = s – b.

4: Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

5: A quadrilateral ABCD is drawn to circumscribe a circle as shown in the figure. Prove that AB + CD = AD + BC.

6: Prove that the lengths of tangents drawn from an external point to a circle are equal.

7: In the figure, two tangents TP and TQ are drawn to a circle with centre O from an external point T, prove that ∠PTQ = 2OPQ.

8: In the figure, from an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If OP = 2r, show that ∠OTS = ∠OST = 30⁰.

9: What should be the angle between the two tangents which are drawn at the end of two radii and are inclined at an angle of 45 degrees?

10: Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the endpoints of the arc.

CBSE Important Questions for Class 10 Maths - INTRODUCTION TO TRIGONOMETRY

1: If Sin A = 3/4, Calculate cos A and tan A. 

2 : In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine:
(i) sin A, cos A
(ii) sin C, cos C

3: If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠ A = ∠ B.

4: Prove that sec² x + cosec² x can never be less than 2.

5. If 3 cot A = 4, check whether (1 – tan²A)/(1 + tan²A) = cos² A – sin² A or not.

6. Evaluate 2 tan2 45° + cos2 30° – sin2 60°.

7. In triangle PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.

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

9. Show that :

(i) tan 48° tan 23° tan 42° tan 67° = 1

(ii) cos 38° cos 52° – sin 38° sin 52° = 0

10. If A, B and C are interior angles of a triangle ABC, then show that sin [(B + C)/2] = cos A/2.

CBSE Important Questions for Class 10 Maths - SOME APPLICATIONS OF TRIGONOMETRY

1: The shadow of a tower standing on level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it is 60°. Find the height of the tower.

2: Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.

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

4: The angle of elevation of the top of a tower from two points distant s and t from its foot are complementary. Prove that the height of the tower is √st.

5: An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high. Determine the angle of elevation of the top of the tower from the eye of the observer.

6: A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°. 

7: The angle of elevation of the top of a tower from a certain point is 30°. If the observer moves 20 metres towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower.

8: A bridge across the river makes an angle of 45° with the river bank. If the length of the bridge across the river is 150 m, what is the width of the river? 

9: A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7m. From a point on the plane, the angle of elevation of the bottom of the flagstaff is 30° and that of the top of the flagstaff is 45°. Find the height of the tower. 

10: From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.

CBSE Important Questions for Class 10 Maths - AREAS RELATED TO CIRCLES

1. The radii of two circles are  9 cm and  19 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.

2. The cost of fencing a circular field at the rate of Rs. 24 per metre is Rs. 5280. The field is to be ploughed at the rate of Rs. 0.50 per m². Find the cost of ploughing the field (Take π = 22/7).

3. The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?

4. The circumference of a circular field is 528 cm. Then its radius is

5.  The circumference of a circle exceeds its diameter by 180  cm. Then its radius is

6. Find the area of the segment AYB shown in the figure, if the radius of the circle is 21 cm and ∠ AOB = 120°. (Use π = 22/7).

7. A round table cover has six equal designs as shown in the figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs. 0.35 per cm2. (Use 3 = 1.7) 

8. The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?

9. Find the area of the minor segment of a circle of radius 14 cm, when the angle of the corresponding sector is 60°.

10. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

CBSE Important Questions for Class 10 Maths - SURFACE AREAS AND VOLUMES

1. Two cones have their heights in the ratio 1 : 3 and radii in the ratio 3 : 1. What is the ratio of their volumes?

2. Three cubes of a metal whose edges are in the ratio 3:4:5 are melted and converted into a single cube whose diagonal is 12√3 cm. Find the edges of the three cubes.

3. A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 3.5 cm and the height of the cone is 4 cm. The solid is placed in a cylindrical tub, full of water, in such a way that the whole solid is submerged in water. If the radius of the cylindrical tub is 5 cm and its height is 10.5 cm, find the volume of water left in the cylindrical tub. (Use π = 22/7)

4. A canal is 300 cm wide and 120 cm deep. The water in the canal is flowing at a speed of 20 km/h. How much area will it irrigate in 20 minutes if 8 cm of standing water is desired?

5. A cubical ice-cream brick of edge 22 cm is to be distributed among some children by filling ice-cream cones of radius 2 cm and height 7 cm up to its brim. How many children will get the ice cream cones? 

6. Find the number of solid spheres each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm.

7. Rasheed got a playing top (lattu) as his birthday present, which surprisingly had no colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere. The entire top is 5 cm in height, and the diameter of the top is 3.5 cm. Find the area he has to colour. (Take π = 22/7)

8. Mayank made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end, as shown in the figure. The height of the cylinder is 1.45 m, and its radius is 30 cm. Find the total surface area of the bird-bath. (Take π = 22/7)

9. 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.

10. A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs. 500 per m². (Note that the base of the tent will not be covered with canvas.)

11. A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm, and the diameter of the base is 4 cm. Determine the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference between the volumes of the cylinder and the toy. (Take π = 3.14)

CBSE Important Questions for Class 10 Maths - STATISTICS

1. If the mean of first n natural numbers is 15, then find n.

2. If the mean of 4 numbers, 2,6,7 and a is 15 and also the mean of other 5 numbers, 6, 18, 1, a, b is 50. What is the value of b?

3. Consider the following distribution of daily wages of 50 workers of a factory.

Daily wages (in Rs.)	100-120	120-140	140-160	160-180	180-200
Number of workers	12	14	8	6	10

Find the mean daily wages of the workers of the factory by using an appropriate method.

4. Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute was recorded and summarised as follows. Find the mean heartbeats per minute for these women, choosing a suitable method.

Number of heart beats per minute	65-68	68-71	71-74	74-77	77-80	80-83	83-86
Number of women	2	4	3	8	7	4	2

5. The following data gives the distribution of the total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure :

Expenditure	Number of families
1000-1500	24
1500-2000	40
2000-2500	33
2500-3000	28
3000-3500	30
3500-4000	22
4000-4500	16
4500-5000	7

6. Construct the cumulative frequency distribution of the following distribution : 

Class	12.5 – 17.5	17.5 – 22.5	22.5 – 27.5	27.5 – 32.5	32.5 – 37.5
Frequency	2	22	19	14	13

7. An aircraft has 120 passenger seats. The number of seats occupied during 100 flights are given in the following table :

Number of seats	100-104	104-108	108-112	112-116	116-200
Frequency	15	20	32	18	15

Determine the mean number of seats occupied over the flights.

8. If the mean of 4 numbers, 2,6,7 and a is 15 and also the mean of other 5 numbers, 6, 18, 1, a, b is 50. What is the value of b?

9. A student scored the following marks in 6 subjects:

30, 19, 25, 30, 27, 30

Find his modal score.

10. While checking the value of 20 observations, it was noted that 125 was wrongly noted as 25 while calculating the mean and then the mean was 60. Find the correct mean.

CBSE Important Questions for Class 10 Maths - PROBABILITY

1: A bag contains a red ball, a blue ball and a yellow ball, all the balls being of the same size. Kritika takes out a ball from the bag without looking into it. What is the probability that she takes out the

(i) yellow ball?

(ii) red ball?

(iii) blue ball?

2: Two dice are numbered 1, 2, 3, 4, 5, 6 and 1, 1, 2, 2, 3, 3, respectively. They are thrown, and the sum of the numbers on them is noted. Find the probability of getting each sum from 2 to 9 separately.

3: Two dice are thrown at the same time. Find the probability of getting

(i) the same number on both dice.

(ii) different numbers on both dice.

4: One card is drawn from a well-shuffled deck of 52 cards. Calculate the probability that the card will

(i) be an ace,

(ii) not be an ace.

5: An integer is chosen at random from the first two hundreds digit. What is the probability that the integer chosen is divisible by 6 or 8.

6: A bag contains 8 red balls and x blue balls, the odd against drawing a blue ball are 2: 5. What is the value of x.

7: A card is drawn from a well shuffled deck of cards.

i) What are the odds in favour of getting spade?

ii) What are the odds against getting a spade?

iii) What are the odds in favour of getting a face card?

iv) What are the odds in favour of getting a red king

8: A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball. determine the number of blue balls in the bag. 

9: Two dice are numbered 1, 2, 3, 4, 5, 6 and 1, 1, 2, 2, 3, 3, respectively. They are thrown, and the sum of the numbers on them is noted. Find the probability of getting each sum from 2 to 9 separately.

10: A coin is tossed two times. Find the probability of getting at most one head.