### CBSE Class 10 Maths Sample Paper 2023-24

Today you will get the information about cbse class 10 maths sample paper 2023-24 for students.

As you know CBSE class 10 mathematics knowledge improves your skills to move to the upper primary stage.

So, it is very important to acquire knowledge and understanding, particularly by way of motivation and visualization of basic concepts, terms, principles, and skills.

It is also very important to you to develop an interest in this subject by participating in related competitions.

Another objective for you is to develop an interest in studying number system questions for class 10 mathematics as a discipline because this subject is very useful in your daily life.

These questions have already been asked several times in examinations.

So, you need to take these questions seriously for the next level of learning.

These class 10th important questions may be asked again in the upcoming examinations too.

The best way to solve these questions smoothly, read the related chapter from your math textbook.

As well as memorize the formula.

Now write down the questions of the CBSE class 10 maths chapter wise question paper in your copy.

Start to solve them.

This question set is very good for you to practice and will be very helpful to you to make CBSE class 10 maths chapter wise notes in advance.

**Real numbers definition** - this is the union of both rational and irrational numbers.

That numbers can be positive or negative.

As well as they are denoted by the symbol "R".

You can say that all fractions, decimals, and natural numbers come in this category.

Now you will get the most important questions for the class 10 maths board exam 2024 in this post.

### CBSE Class 10 Maths Chapter Wise Important Questions

#### CBSE Class 10 Maths Real Numbers Important Questions

- What is the HCF of 52 and 130?
- The LCM and HCF of the two numbers are 240 and 12 respectively. If one of the numbers is 60, then find the other number.
- Find the [π»πΆπΉ × πΏπΆπ] for the numbers 100 and 190
- Prove that 3 + √2 is an irrational number
- Prove that √5 is an irrational number.
- Write whether the rational number 51/1500 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
- The HCF and LCM of the two numbers are 9 and 360 respectively. If one number is 45, write the other number.
- Use Euclid’s Division Lemma to show that the square of any positive integer is either of form 3π or (3π + 1) for some integer π.
- Show that the square of any positive odd integer is of form 8π + 1, for some integer π.
- Prove that 7 + 3√2 is not a rational number.
- Prove that 2 − 3√5 is an irrational number.
- Show that one and only one of n, n + 2 and n + 4 is divisible by 3.
- Using Euclid’s division algorithm, find the HCF of 56, 96 and 404.
- Find the HCF of 52 and 117 and express it in form 52x + 117y.
- Prove that x2 – x is divisible by 2 for all positive integers x.
- If HCF (6, a) = 2 and LCM (6, a) = 60, then find a.
- The floor of a room is to be fitted with square marble tiles of the largest possible size. The size of the room is 10 m × 7 m. What should be the size of tiles required that have to be cut and how many such tiles are required?
- If p and q are two coprime numbers, then find the HCF and LCM of p and q.
- Prime factorization of 120 is ...
- Find the LCM of the smallest prime and the smallest odd composite natural number

#### CBSE Class 10 Maths Polynomials Questions

- What will be the number of zeroes of a linear polynomial p(x) if its graph (i) passes through the origin. (ii) doesn’t intersect or touch the x-axis at any point?
- Find the quadratic polynomial whose zeroes are 5 + 2√3 and 5 – 2√3.
- Find the quadratic polynomial if its zeroes are 0, √5.
- Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes, respectively. (A) 1/4, -1 (B) 1, 1 (C) 4, 1

#### CBSE Class 10 Maths Pair Of Linear Equations In Two Variables Questions

- How many solutions does the pair of equations y = 0 and y = -5 have?
- Calculate the area bounded by the line x + y = 10 and both the co-ordinate axes
- Solve the following pair of linear equations: y -4x= 1, 6x- 5y= 9
- The sum of the denominator and numerator of a fraction is 3 less than twice the denominator. If each of the numerator and denominator is denominator is decreased by 1, the fraction becomes 1/2. Find the fraction.
- Solve the equations graphically. 2x+y=2 , 2y-x=4. Also, find the area of a triangle formed by the two lines and the line y=0.
- Draw the graphs of the pair of equations x + 2y = 5 and 2x-3y = – 4. Also, find the points where the lines meet the x-axis.

#### CBSE Class 10 Maths Quadratic Equations Important Questions

- 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?
- Find the roots of quadratic equations by factorisation:- (A) √2 x2 + 7x + 5√2=0 (B) 100x2 – 20x + 1 = 0
- Find the value of π, for which one root of the quadratic equation ππ₯2 − 14π₯ + 8 = 0 is six times the other.
- If the quadratic equation ππ₯2 − 2√5 ππ₯ + 15 = 0 has two equal roots, then find the value of π.
- Find the value of π, for which one root of the quadratic equation ππ₯2 − 14π₯ + 8 = 0 is 6 times the other.
- If the sum of two natural numbers is 8 and their product is 15, find the numbers.
- For what value of π, are the roots of the quadratic equation ππ₯(π₯ − 2)+ 6 = 0 equal?
- A pole has to be erected at a point on the boundary of a circular park of diameter 17 π in such a way that the differences of its distances from two diametrically opposite fixed gates π΄ and π΅ on the boundary are 7 metres. Find the distances from the two gates where the pole is to be erected.
- Three-eighths of the students of a class opted for visiting an old age home. Sixteen students opted for having a nature walk. The square root of the total number of students in the class opted for tree plantation in the school. The number of students who visited an old age home is the same as the number of students who went for a nature walk and did a tree plantation. Find the total number of students. What values are inculcated in students through such activities?
- A train, travelling at a uniform speed for 360 ππ would have taken 48 minutes less to travel the same distance if its speed were 5 ππ/β more. Find the original speed of the train.

#### CBSE Class 10 Maths Arithmetic Progression Important Questions

- Find the tenth term of the sequence √2, √8, √18, ............
- Find the 9th term from the end (towards the first term) of the A.P. 5,9,13, … …,185.
- For what value of π will π + 9, 2π − 1 and 2π + 7 be the consecutive terms of an A.P.?
- How many two-digit numbers are divisible by 7?
- The ninth term of an A.P. is equal to seven times the second term and the twelfth term exceeds five times the third term by 2. Find the first term and the common difference.
- A contract on a construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs. 200 for Ist day,, Rs. 250 for the second day, Rs. 300 for the third day and so on. If the contractor pays Rs. 27750 as a penalty, find the number of days for which the construction work is delayed.
- The minimum age for children to be eligible to participate in a painting competition is 8 years. It is observed that the age of the youngest boy was 8 years and the ages of the rest of the participants had a common difference of 4 months. If the sum of the ages of all the participants is 168 years, find the age of the eldest participant in the painting competition.

#### CBSE Class 10 Maths Triangles Important Questions

- πΈ is a point on the side π΄π· produced of a parallelogram π΄π΅πΆπ· and π΅πΈ intersects πΆπ· at πΉ. Show that Ξπ΄π΅πΈ~ΞπΆπΉπ΅.
- Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. The area of the equilateral triangle described on the side of a square is half the area of the equilateral triangle described on its diagonal.
- In ∆πΏππ, ∠πΏ = 50° and ∠π = 60°. If ∆πΏππ~∆πππ , then find ∠π.

#### CBSE Class 10 Maths Coordinate Geometry Important Questions

- If the distance between the points (4, π) and (1,0) is 5, then what can be the possible values of π?
- Find the area of a triangle whose vertices are (3, 0), (7, 0).and (8, 4).
- Find the value of π so that the point (3, π) lies on the line represented by 2π₯ − 3π¦ = 5
- Let π and π be the points of trisection of the line segment joining the points π΄(2, −2) and π΅(−7,4) such that π is nearer to π΄. Find the coordinates of π and π.
- For what value of π are the points (8, 1), (3, −2π) and (π, −5) collinear?
- The points π΄(1, −2), π΅(2,3), πΆ(π, −2) and π·(−4, −3) are the vertices of a parallelogram. Find the value of π and the altitude of the parallelogram corresponding to the base π΄π΅.
- Prove that the area of a triangle with vertices (π‘, π‘ − 2), (π‘ + 2, π‘ + 2) and (π‘ + 3, π‘) is independent of t.
- The base π΅πΆ of an equilateral triangle π΄π΅πΆ lies on π¦–axis. The coordinates of point πΆ are (0, −3). The origin is the midpoint of the base. Find the coordinates of the points π΄ and π΅. Also, find the coordinates of another point π· such that π΅π΄πΆπ· is a rhombus.

#### CBSE Class 10 Maths Trigonometry Important Questions

- Find the value of cosec 30°, geometrically.
- Find the value of sec 45° geometrically.
- Find the value of tan 60°, geometrically.
- If sec 2π΄ = cosec(π΄ − 42°), where 2π΄ is an acute angle, find the value of π΄.
- What is the maximum value of 1/sec π?
- If sec π΄ = 15/7 and π΄ + π΅ = 90°, find the value of cosec π΅.
- Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°

#### CBSE Class 10 Maths Circles Important Questions

- If the angle between two tangents drawn from an external point π to a circle of radius π and centre π, is 60°, then find the length of ππ.
- ππ is a tangent drawn from an external point π to a circle with centre π, πππ is the diameter of the circle. If ∠ πππ = 120°, what is the measure of ∠ πππ?
- The length of the tangent from a point π΄ at a distance of 5 ππ from the centre of the circle is 4 ππ. What will be the radius of the circle?
- Prove that the tangents drawn at the endpoints of a chord of a circle make equal angles with the chord.
- A circle touches all four sides of a quadrilateral π΄π΅πΆπ·. Prove that π΄π΅ + πΆπ· = π΅πΆ + π·π΄.
- From a point π outside a circle of centre π, tangents ππ and ππ are drawn to the circle. Prove that ππ is the right bisector of line segment ππ.
- Two concentric circles of radii π and π (π > π) are given. Find the length of the chord of the larger circle which touches the smaller circle.
- The radii of two concentric circles are 13 ππ and 8 ππ. π΄π΅ is the diameter of the bigger circle and π΅π· is tangent to the smaller circle touching it at π· and intersecting the larger circle at π, on producing. Find the length of π΄π.

#### CBSE Class 10 Maths Constructions Important Questions

- Draw a line segment of length 6 ππ. Using compasses and ruler, find a point π on it which divides it in the ratio 3∶4.
- Draw a line segment π΄π΅ of length 8 ππ. Taking A as the centre, draw a circle of radius 4 ππ and taking π΅ as the centre, draw another circle of radius 3 ππ. Construct each circle from the centre of the other circle.
- Draw a pair of tangents to a circle of radius 3 ππ, which are inclined to each other at an angle of 60°.
- Draw a line segment π΄π΅ of length 7 ππ. Taking π΄ as the centre, draw a circle of radius 3 ππ and taking π΅ as the centre, draw another circle of radius 2 ππ. Construct tangents to each circle from the centre of the other circle.
- Draw a circle of radius 3 ππ. From a point π, 6 ππ away from its centre, construct a pair of tangents to the circle. Measure the lengths of the tangents.
- Draw a pair of tangents inclined to each other at an angle of 60° to a circle of radius 3 ππ.

#### CBSE Class 10 Maths Areas Related To Circles Important Questions

- What is the area of a circle whose circumference is 44 cm?
- Calculate the area of a sector of angle 60°. Given, the circle has a radius of 6 cm.
- If the diameter of a semi-circular protractor is 14 ππ, then find its perimeter.
- What is the ratio of the areas of a circle and an equilateral triangle whose diameter and side are respectively equal?
- The length of the minute hand of a clock is 14 ππ. Find the area swept by the minute hand in 10 minutes.
- A chord of a circle of radius 10 ππ subtends a right angle at the centre. Find the area of the corresponding minor segment and hence find the area of the major segment. [Use π = 3.14]
- A chord ππ of a circle of radius 10 ππ subtends an angle of 60° at the centre of the circle. Find the area of major and minor segments of the circle.

#### CBSE Class 10 Maths Surface Area And Volume Important Questions

- The volume and surface area of a solid hemisphere are numerically equal. What is the diameter of the hemisphere?
- A solid metallic cuboid of dimensions 9 π × 8 π × 2 π is melted and recast into solid cubes of edge 2 π. Find the number of cubes so formed.
- A solid is in the shape of a cone mounted on a hemisphere of the same base radius. If the curved surface areas of the hemispherical part and the conical part are equal, then find the ratio of the radius and the height of the conical part.
- A cone of height 20 ππ and radius of base 5 ππ is made up of modelling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere
- The dimensions of a metallic cuboid are 100 ππ × 80 ππ × 64 ππ. It is melted and recast into a cube. Find the surface area of the cube.
- The slant height of a frustum of a cone is 4 ππ and the perimeters of its circular ends are 18 ππ and 6 ππ. Find the curved surface area of the frustum.
- The perimeters of the ends of the frustum of a cone are 207.24 ππ and 169.56 ππ. If the height of the frustum is 8 ππ, find the whole surface area of the frustum. (Use π = 3.14)
- A cubical block of side 10 ππ is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of ₹ 5 πππ 100 π π. ππ. [Use π = 3.14]

#### CBSE Class 10 Maths Statistics Important Questions

- If the difference between the mode and median of the data is 24, then find the difference between the median and mean.
- Find the mean of the first n odd natural numbers.
- Find the median of the first 9 prime numbers.
- Write the empirical relation between mean, mode and median.
- Find the median of 10, 16,12, 20, 14, and 18.
- If the median of 12, 13, 16, x + 2, x + 4, 28, 30, 32 is 23, when x + 2, x + 4 lies between 16 and 30, then find the value of x.
- If the mode of 12, 16, 19, 16, x, 12, 16, 19, 12 is 16, then find the value of x.
- The abscissa of the point of intersection of the less than type and of the more than type ogives gives which Central tendency?

#### CBSE Class 10 Maths Probability Important Questions

- If the card is replaced after the third draw, what is the probability of drawing a card bearing a number greater than 17 by the fourth boy?
- A die is thrown once. Find the probability of getting a number less than 3.
- A die is thrown once. Find the probability of getting a number greater than 5.
- Find the probability that a number selected at random from numbers 3, 4, 5, ...., 25 is prime.
- Find the probability that a number selected from the numbers 1 to 25 is not a prime number when each of the given numbers is equally likely to be selected.
- A card is drawn from a pack of 52 cards. Find the probability that the card drawn is not a face card.
- If the card is replaced after the fourth draw, what is the probability of drawing a card bearing a multiple of 3 or 7 by the fifth boy?
- 20 tickets, on which numbers 1 to 20 are written, are mixed thoroughly and then a ticket is drawn at random out of them. What is the probability that the number on the drawn ticket is a multiple of 3 or 7?

**Class 10 Maths Textbook 2024**

- Mathematics for Class 10th - R.D. Sharma
- Secondary School Mathematics (10th Class) - R.S. Aggarwal & V Aggarwal
- Mathematics for Class 10th - Written by National Council of Educational Research and Training
- All in one mathematics - Arihant
- Mathematics for Class 10th - VK Global Publications Pvt. Ltd.
- Understanding ICSE Mathematics Class 10th - M.L. Aggarwal
- ICSE Mathematics Class 10th - Mr. O.P.Malhotra
- Class 10th TextBook Mathematics - K.C.Sinha
- Mathematics for Class 10th - RS Aggarwal

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