Class 10 Mathematics Most Expected Questions 2025- Mathematics is one of the most important subjects in the Class 10 curriculum. Most students find it difficult but rewarding. As students approach their board examinations, they look for ways to focus on the right topics and practice effectively. This article provides a comprehensive list of important questions in Class 10 Mathematics, along with strategies to excel in the subject. Whether you are targeting high marks or an all-around understanding of the concepts, this guide will be your roadmap to success.
The Importance of Focusing on Key Questions
This broad scope of study encompasses algebra and geometry, through to statistics and trigonometry, in the study of mathematics in Class 10. You can narrow your preparation and get a boost of confidence by keeping a focus on important questions while dealing with a very vast syllabus. Questions on all types of answers that are to be given by students, short, and long answer questions, as well as those on higher-order thinking skills, or HOTS questions, have been included to assist you.
Class 10 Mathematics most expected questions 2025
1. Find the value of “x” in the polynomial 2a2 + 2xa + 5a + 10 if (a + x) is one of its factors.
2. Find the quadratic polynomial if its zeroes are 0, √5.
3. Find the value of “p” from the polynomial x2 + 3x + p, if one of the zeroes of the polynomial is 2.
4. Compute the zeroes of the polynomial 4×2 – 4x – 8. Also, establish a relationship between the zeroes and coefficients.
5. How many zeros does the polynomial (x – 3)2 – 4 have? Also, find its zeroes.
6. If the zeroes of the polynomial x3 – 3×2 + x + 1 are a – b, a, a + b, then find the value of a and b.
7. Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial f(x) = ax2 + bx + c, a ≠ 0, c ≠ 0.
8. 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.
9. Show that the square of any positive integer cannot be of the form (5q + 2) or (5q + 3) for any integer q.
10. If a is a positive rational number and n is a positive integer greater than 1, prove that an is a rational number.
11. Using Euclid’s Algorithm, find the HCF of 2048 and 960.
12. What is the HCF of the smallest prime number and the smallest composite number?
13. 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
14. 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. . .
15. 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.
16. 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.
17. On comparing the ratios a1/a2, b1/b2, and c1/c2, find out whether the following pair of linear equations are consistent, or inconsistent.
18. Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.
19. 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.
20. 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.
21. Formulate the following problem 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.
22. Find the roots of quadratic equations by factorisation: (i) √2 x2 + 7x + 5√2=0 (ii) 100×2 – 20x + 1 = 0
23. Find two consecutive positive integers, the sum of whose squares is 365.
24. 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.
25. Solve the quadratic equation 2×2 – 7x + 3 = 0 by using quadratic formula.
26. 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.
27. Is it possible to design a rectangular park of perimeter 80 and area 400 sq.m.? If so find its length and breadth.
28. In a flight of 600 km, an aircraft was slowed due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. Find the original duration of the flight.
29. Write the 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
30. Which term of the AP: 21, 18, 15, . . . is – 81? Also, is any term 0? Give a reason for your answer.
31. Check whether – 150 is a term of the AP: 11, 8, 5, 2 . . .
32. If the 3rd and the 9th terms of an AP are 4 and -8, respectively, then which term of this AP is zero.
33. How many multiples of 4 lie between 10 and 250?
34. 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.
35. 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.
36. 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
37. If ΔABC ~ ΔQRP, ar (ΔABC) / ar (ΔPQR) =9/4 , AB = 18 cm and BC = 15 cm, then find PR.
38. If the areas of two similar triangles are equal, prove that they are congruent.
39. O is any point inside a rectangle ABCD as shown in the figure. Prove that OB2 + OD2 = OA2 + OC2.
40. 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
41. 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.
42. Given ΔABC ~ ΔPQR, if AB/PQ = ⅓, then find (ar ΔABC)/(ar ΔPQR).
43. Find the distance of the point P (2, 3) from the x-axis.
44. Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5).
45. 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).
46. Find the ratio in which the line segment joining the points (– 3, 10) and (6, – 8) is divided by (– 1, 6).
47. 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.
48. Write the coordinates of a point on the x-axis which is equidistant from points A(-2, 0) and B(6, 0).
49. If A(-5, 7), B(-4, -5), C(-1, -6) and D(4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.
50. If Sin A = 3/4, Calculate cos A and tan A.
51. If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠ A = ∠ B.
52. 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.
53. If tan (A + B) =√3 and tan (A – B) =1/√3, 0° < A + B ≤ 90°; A > B, find A and B.
54. If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A.
55. If sin θ + cos θ = √3, then prove that tan θ + cot θ = 1.
56. Prove that (sin A – 2 sin3A)/(2 cos3A – cos A) = tan A.
57. 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.
58. 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.
59. 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.
60. 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.
61. 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.
62. 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.
63. 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.
64. How many tangents can be drawn from the external point to a circle?
65. 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.
66. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
67. A quadrilateral ABCD is drawn to circumscribe a circle as shown in the figure. Prove that AB + CD = AD + BC
68. 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.
69. Prove that the lengths of tangents drawn from an external point to a circle are equal.
70. 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.
71. Draw a line segment of length 7 cm. Find a point P on it which divides it in the ratio 3:5.
72. Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding sides of the first triangle.
73. Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameters, each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.
74. Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.
75. Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on the outer circle, construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.
76. Construct an equilateral ΔABC with each side 5 cm. Then construct another triangle whose sides are 2/3 times the corresponding sides of ΔABC.
77. Construct a ΔABC in which AB = 6 cm, ∠A = 30° and ∠B = 60°. Construct another ΔAB’C’ similar to ΔABC with base AB’ = 8 cm.
78. If the radius of a circle is 4.2 cm, compute its area and circumference.
79. A chord subtends an angle of 90°at the centre of a circle whose radius is 20 cm. Compute the area of the corresponding major segment of the circle.
80. A square is inscribed in a circle. Calculate the ratio of the area of the circle and the square.
81. Find the area of the sector of a circle with a radius of 4cm and of angle 30°. Also, find the area of the corresponding major sector.
82. Calculate the perimeter of an equilateral triangle if it inscribes a circle whose area is 154 cm2
83. 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?
84. Find the area of the sector of a circle with a radius of 4 cm and of angle 30°. Also, find the area of the corresponding major sector (Use π = 3.14)
85. 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?
86. Two cones have their heights in the ratio 1 : 3 and radii in the ratio 3 : 1. What is the ratio of their volumes?
87. 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?
88. 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.
89. 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.
90. 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)
91. 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
92. Find the mean of the 32 numbers, such that if the mean of 10 of them is 15 and the mean of 20 of them is 11. The last two numbers are 10.
93. Find the value of y from the following observations if these are already arranged in ascending order. The Median is 63. : 20, 24, 42, y , y + 2, 73, 75, 80, 99
94. 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.
95. 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?
96. If the mean of first n natural numbers is 15, then find n.
97. In a continuous frequency distribution, the median of the data is 21. If each observation is increased by 5, then find the new median.
98. The average score of boys in the examination of a school is 71 and that of the girls is 73. The average score of the school in the examination is 71.8. Find the ratio of the number of boys to the number of girls who appeared in the examination.
99. 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?
100. 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.
101. A coin is tossed two times. Find the probability of getting at most one head.
102. If P(E) = 0.05, what is the probability of ‘not E’?
103. 12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen is taken out is a good one.
104. A die is thrown once. What is the probability of getting a number less than 3?
105. The probability of selecting a blue marble at random from a jar that contains only blue, black and green marbles is 1/5. The probability of selecting a black marble at random from the same jar is 1/4. If the jar contains 11 green marbles, find the total number of marbles in the jar.
Class 10th Math Objective Question With Solution
- The prime factorisation of natural number 288 is: (a) 24X33 (b) 24X32 (c) 25X32 (d) 25X31 1
- If two positive integers p and q can be expressed as p = 18a2 X b 4 and q = 20a3 X b2 where a and b are prime numbers, then LCM (p, q) : (a) 2a2b2 (b) 180a2b2 (c)12a2b2 (d)180a3b4
- If the sum of zeroes of polynomial p(x)= 2x2-k√2x+1 is √2 then the value of k is: (a)√2 (b)2 (C)2√2 (d)1/2
- The zeroes of the polynomial X2+px+q are twice the zeroes of the polynomial 4×2-5x-6. The value of p is: (a) -5/2 (b)5/2 (c)-5 (d)0
- The sum and the product of zeroes of the polynomial p(x)= X2+5x+6 are: (a)5,-6 (b)-5,6 (c)2,3 (d)-2,-3
- The least positive value of k, for which the quadratic equation 2x2+kx-4=0 has rational roots, is: (a) 2√2 (b)2 (c)-2 (d)√2
- The discriminant of the quadratic equation 2x2-5x-3=0 is: (a)1 (b)49 (c)7 (d)19
- In an A.P., if the first term a=7, n term an=84 and the sum of the first n terms sn= 2093/2, then n is equal to: (a)22 (b)24 (c)23 (d)26
- If p-1, p+1 and 2p+3 are in A.P., then the value of p is:(a)-2 (b)4 (c)0 (d)2
- The seventh term of an A.P. whose first term is 28 and common difference -4 is: (a)0 (b)4 (c)52 (d)56
- The sides of two similar triangles are in ratio 4:7. the ratio of their perimeter is:(a)4:7 (b)12:21 (c)16:49 (d)7:4
- The distance between the points (2,-3) and (-2,3) is:(a)2√13 (b)5 units (c)13√2 units (d)10 units
- If the distance between points (3,-5) and (x,-5) is 15 units, then the values of x are:(a) 12, -18 (b)-12, 18 (c)18, 5 (d)-9,-12
- In what ratio, does x-axis divide the line segment joining the points A(3,6) and B(-12,-3)?: (a)1:2 (b)1:4 (c)4:1 (d)2:1
- If sinθ= 1/3, then secθ is equal to: (a)2√2/3 (b)3/2√2 (c)3 (d)1/√3
- If secθ-tanθ= m, then value of secθ+tanθ is: (a)1-1/m (b)m2-1 (c)1/m (d)-m
- A solid sphere is cut into two hemispheres. The ratio of the surface areas of the sphere to that of two hemispheres taken together is: (a)1:1 (b)1:4 (c)2:3 (d)3:2
- The radius of a sphere is 7/2 cm. The volume of the sphere is: (a)231/3 cu cm (b)539/12 cu cm (c)539/3 cu cm (d)154 cu cm
- The mean and median of statistical data are 21 and 23 respectively. The mode of the data is: (a)27 (b)22 (c)17 (d)23
- The probability of happening of an event is denoted by p and the probability of the non-happening of the event is denoted by q. Relation between p and q is: (a)p+q=1 (b)p=1, q=1 (c)p=q-1 (d)p+q+1=0
Benefits of Solving Most Expected Questions Class 10 Mathematics
Mastering Class 10 Mathematics is a significant step for students. It lays down the foundation for future academic success. One of the most effective ways to achieve success in this subject is to solve important questions. Most of these questions are prepared based on essential concepts, frequently asked exam topics, and real-life applications. This is why time spent solving such questions can transform your preparation and boost your confidence.
- Conceptual Strength
Solving important questions will help you strengthen your conceptual understanding of the core mathematical concepts. You are exposed to many scenarios where theories are applied, and it becomes easier to understand and remember information.
2. Improves Problem-Solving Skills
Every question will challenge your problem-solving skills, encouraging analytical thinking. This practice will improve your efficiency in approaching and solving complex problems, which is invaluable during exams.
3. Improves Time Management
Solving important questions regularly under time constraints helps you practice. This not only improves your time management skills during the exams but also increases your confidence in handling long papers.
4. Identifies Weak Areas
Working through these questions will identify areas where you need improvement. Identifying weaknesses early on will help you to focus on them, thereby making sure that you are fully prepared.
5. Align Preparation with Exam Patterns
Important questions are often designed to mirror the latest exam trends and patterns. Solving them ensures your preparation aligns with the syllabus and gives you an edge over others.
By including the practice of solving important questions in your study routine, you can significantly enhance your mathematical proficiency and exam readiness. Prioritize these questions, and watch your performance soar!
