HBSE Class 10 Math Stadndard + Basic Important Question Answer 2026

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Most of students search over Google for Haryana Board (HBSE) Important Questions 2026. Here is the Main reason because HBSE Board Says that in HBSE Exam 2026 (last 3 Years of Questions will Repeat) so that here are the selected List of Questions of Haryana Board For Class 10.

HBSE Class 10 Math Standard + Basic Important Question Answer 2026

Chapter 1 – Real Number

Q1. Find HCF of 510 and 92. Most Most Important

Q2. Prove that \displaystyle \sqrt{5} is an irrational number.  Most Important

Q3. Prove that \displaystyle \sqrt{3} is an irrational number. Most Important

Q4. Prove that \displaystyle \sqrt{2} is an irrational number. Most Important

Q5. Prove that \displaystyle 3\sqrt{2} is an irrational number. Most Important

Q6. Express 3825 as a product of prime factors: Most Important

Chapter 2 – Polynomials

Q1. Find a quadratic polynomial, the sum and product of whose zeroes are -3 and 2 respectively. Most important

Q2. Find the product of zeroes of quadratic polynomial x2 + 7x + 10. Most important

Q3. Find a quadratic polynomial with the given number as the sum and product of its zeroes respectively are 5 and 3. Most Important

Q4. Find a quadratic polynomial whose zeros are -3 and 5. Most Important

Q5. Find the sum of zeroes of quadratic polynomial x2 – 2x – 8. Most important

Chapter 3 – Pair of Linear Equations in Two Variables

Q1. If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes \displaystyle \frac{1}{2} if we only add 1 to denominator. Find the fraction. Most Important

Q2. 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 ?.

Chapter 4 – Quadratic Equations

Q1. Find the root of the quadratic equation by factorization method \displaystyle \sqrt{2}{{x}^{2}}+7x+5\sqrt{2}=0

Q2. For what value of k the roots of the quadratic equation 2x2 + kx + 3 = 0 are equal?

Q3. Sum of the roots of the quadratic polynomial 7x2 – 3x + 1 is __________.

Q4. Semi perimeter of a rectangular garden, whose length is 4m more: than its width is 36m. Find the dimensions of the garden.

Q5. Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Chapter 5 – Arithmetic Progression

Q1. If the sum of first 7 terms of A. P. is 49 and sum of first 17 terms is 289, then find the sum of n terms of A. P. Most Important

 

Q2. Find 11th term of A.P. 7, 13, 19 …………. Most Important

Q3. Find the common difference of the A.P. : 3, 1, −1, -3, ……………. Most Important

Chapter 6 – Triangles

Q1. All squares are ___________. (similar, congruent) Most Important

Q2. All  __________ triangles are similar. (isosceles, equilateral) Most Important

Q3. In figure DE || BC. Find the value of EC: Most Most Important

Chapter 7 – Coordinate Geometry

Q1. Find the distance between the points (-5, 7) and (-1, 3). Most Important

Q2. Find the ratio in which the line joining (3, 4) and (-4, 7) is divided by y- axis. Also find the coordinates of the point of intersection. Most Important

Q3. Find the coordinates of the point which divide the line segment joining the points (4, -3) and (8, 5) in a ratio 3 : 1 internally. Most Important

Chapter 8 – Introduction to Trigonometry  

Q1. Prove that :   \displaystyle \frac{{\tan \theta }}{{1-\cot \theta }}+\frac{{\cot \theta }}{{1-\tan \theta }} = 1 + secθ cosecθ

Most Important

Q2. Prove that:   \displaystyle \frac{{\sin \theta +\cos \theta -1}}{{\sin \theta -\cos \theta +1}}=\frac{1}{{\sec \theta +\tan \theta }}     

Most Important

Q3. Find the value of sin 45° + cos 45°.    Most Important

Q4. If tan (A + B) = \displaystyle \sqrt{3} and tan(A – B) = \displaystyle \frac{1}{{\sqrt{3}}}, 0° < A + B ≤ 90°, A > B, then find the value of A and B.

Most Important

Chapter 9 – Some Application of Trigonometry

Q1. The shadow of a tower standing on a level ground is found to be 40 m longer when the altitude (the angle of elevation) of sun changes from 60° to 30°. Find the height of tower.

Q2. An observer 1.6m tall is 20m away from a tower. The angle of elevation of the top of the tower from his eyes is 60°. Find the height of the tower? Most Important

Q3. A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 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. Most Important

Q4. A 1.2m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval. Most Important

Chapter 10 – Circles

Q1. A circle can have _______ parallel tangents at the most. Most Important

Q2. All circles are _________. (Similar/Congruent) Most Important

Q3. A line intersecting a circle in two points is called ___________. Most Important

Q4. A tangent to a circle intersects it in _________ point(s). Most Important

Q5. The common point of a tangent to a circle and the circle is called __________. Most Important

Q6. Prove that the length of tangents drawn from an external point to a circle are equal. Most Most Important

Chapter 11 – Areas Related to Circles

Q1. Find the area of the sector of a circle with radius 7 cm and the angle at the centre is 30°.  Most Most Important

Chapter 12 – Surface Areas and Volumes

Q1. Two cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid. Most Important

Chapter 13 – Statistics

Q1. 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:

Number of letters 1-4 4-7 7-10 10-13 13-16 16-19
Number of surnames  66 30 40 16 4 4

Find the median numbers of letters in the surnames.

Q2. The median of the following data is 28.5. Find the values of x and y, if the total frequency is 60.

Class interval 0-10 10-20 20-30 30-40 40-50 50-60
Frequency 5 x 20 15 y 5

 

Q3. The following distribution shows the daily pocket allowance of children of a locality: The mean pocket allowance is Rs. 18. Find the missing frequency f.

Daily pocket (in Rs.) 11-12 13-15 15-17 17-19 19-21 21-23 23-25
Number of chapter 7 6 9 13 f 5 4

Q4. The following data gives the information on the life-time (in hours) of 75 electrical instruments:

Life-time (in hours) 0-20 20-40 40-60 60-80 80-100 100-120
Frequency 10 15 12 21 8 9

 

Q5. The table below shows daily expenditure on food of 25 households in a locality :

Daily Expenditure (in Rs.) 100-150 150-200 200-250 250-300 300-350
No. of households. 4 5 12 2 2

Find the mean daily expenditure on food by suitable method.

Q6. The following distribution shows the daily pocket money of children of a school:

Daily Pocket Money (Rs.) 11-13  13-15  15-17 17-19  19-21 21-23 23-25
Number of Children 7 6 9 13 20 5 4

Find the average daily pocket money of children.

Chapter 14 – Probability

Q1. A die is thrown once. Find the probability of getting (i) a prime number (ii) a number lying between 2 and 6 (iii) an odd number. Most Important

Q2. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (i) a king of red colour (ii) a face card. Most Most Important

Q3. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (i) red (ii) not red? Most Most Important

Q4. Two dice are thrown at the same time. Find the probability of getting the sum on the dice is 13. Most Important

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