CBSE Class 10 Maths Sample Paper 2025

The graph of a quadratic polynomial p(x) passes through the points (-6,0), (0, -30), (4,-20) and (6,0). The zeroes of the polynomial are

• (A) - 6,0
• (B) 4, 6
• (C) - 30,-20
• (D) - 6,6 ✓

Answer (the board’s key): (D)

The value of k for which the system of equations 3x-ky= 7 and 6x+ 10y =3 is inconsistent, is

• (A) -10
• (B) -5 ✓
• (C) 5
• (D) 7

Answer (the board’s key): (B)

Which of the following statements is not true?

• (A) A number of secants can be drawn at any point on the circle.
• (B) Only one tangent can be drawn at any point on a circle.
• (C) A chord is a line segment joining two points on the circle
• (D) From a point inside a circle only two tangents can be drawn. ✓

Answer (the board’s key): (D)

If nth term of an A.P. is 7n-4 then the common difference of the A.P. is

• (A) 7 ✓
• (B) 7n
• (C) - 4
• (D) 4

Answer (the board’s key): (A)

The radius of the base of a right circular cone and the radius of a sphere are each 5 cm in length. If the volume of the cone is equal to the volume of the sphere then the height of the cone is

• (A) 5 cm
• (B) 20 cm ✓
• (C) 10 cm
• (D) 4 cm

Answer (the board’s key): (B)

If tan theta = 5/2 then (4 sin theta + cos theta) / (4 sin theta - cos theta) is equal to

• (A) 11/9 ✓
• (B) 3/2
• (C) 9/11
• (D) 4

Answer (the board’s key): (A)

In the given figure, a tangent has been drawn at a point P on the circle centred at O. If angle TPQ= 110 degree then angle POQ is equal to

• (A) 110 degree
• (B) 70 degree
• (C) 140 degree ✓
• (D) 55 degree

Answer (the board’s key): (C)

A quadratic polynomial having zeroes - sqrt(5/2) and sqrt(5/2) is

• (A) x^2 - 5/sqrt(2) x + 1
• (B) 8x^2 - 20 ✓
• (C) 15x^2 - 6
• (D) x^2 - 2sqrt(5) x - 1

Answer (the board’s key): (B)

Consider the frequency distribution of 45 observations. The upper limit of median class is

• (A) 20
• (B) 10
• (C) 30 ✓
• (D) 40

Answer (the board’s key): (C)

O is the point of intersection of two chords AB and CD of a circle. If angle BOC = 80 degree and OA = OD then triangle ODA and triangle OBC are

• (A) equilateral and similar
• (B) isosceles and similar ✓
• (C) isosceles but not similar
• (D) not similar

Answer (the board’s key): (B)

The roots of the quadratic equation x^2+x-1 = 0 are

• (A) Irrational and distinct ✓
• (B) not real
• (C) rational and distinct
• (D) real and equal

Answer (the board’s key): (A)

If theta = 30 degree then the value of 3tan theta is

• (A) 1
• (B) 1/sqrt(3)
• (C) 3/sqrt(3) ✓
• (D) not defined

Answer (the board’s key): (C)

The volume of a solid hemisphere is 396/7 cm^3. The total surface area of the solid hemisphere (in sq.cm) is

• (A) 396/7
• (B) 594/7 ✓
• (C) 549/7
• (D) 604/7

Answer (the board’s key): (B)

In a bag containing 24 balls, 4 are blue, 11 are green and the rest are white. One ball is drawn at random. The probability that drawn ball is white in colour is

• (A) 1/6
• (B) 3/8 ✓
• (C) 11/24
• (D) 5/8

Answer (the board’s key): (B)

The point on the x- axis nearest to the point (-4,-5) is

• (A) (0, 0)
• (B) (-4, 0) ✓
• (C) (-5, 0)
• (D) (sqrt(41), 0)

Answer (the board’s key): (B)

Which of the following gives the middle most observation of the data?

• (A) Median ✓
• (B) Mean
• (C) Range
• (D) Mode

Answer (the board’s key): (A)

A point on the x-axis divides the line segment joining the points A(2, -3) and B(5, 6) in the ratio 1:2. The point is

• (A) (4, 0)
• (B) (7/2, 3/2)
• (C) (3, 0) ✓
• (D) (0,3)

Answer (the board’s key): (C)

A card is drawn from a well shuffled deck of playing cards. The probability of getting red face card is

• (A) 3/13
• (B) 1/2
• (C) 3/52
• (D) 3/26 ✓

Answer (the board’s key): (D)

Assertion (A): HCF of any two consecutive even natural numbers is always 2. Reason (R): Even natural numbers are divisible by 2.

• (A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
• (B) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) ✓
• (C) Assertion (A) is true but reason (R) is false.
• (D) Assertion (A) is false but reason (R) is true.

Answer (the board’s key): (B)

Assertion (A): If the radius of sector of a circle is reduced to its half and angle is doubled then the perimeter of the sector remains the same. Reason (R): The length of the arc subtending angle theta at the centre of a circle of radius r = pi*r*theta/180.

• (A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
• (B) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)
• (C) Assertion (A) is true but reason (R) is false.
• (D) Assertion (A) is false but reason (R) is true. ✓

Answer (the board’s key): (D)

(A)Find the H.C.F and L.C.M of 480 and 720 using the Prime factorisation method. OR (A) The H.C.F of 85 and 238 is expressible in the form 85m -238. Find the value of m.

(A) Two dice are rolled together bearing numbers 4, 6, 7, 9, 11, 12. Find the probability that the product of numbers obtained is an odd number OR (B) How many positive three digit integers have the hundredths digit 8 and unit's digit 5? Find the probability of selecting one such number out of all three digit numbers.

Evaluate: (2sin^2 60 degree - tan^2 30 degree) / (sec^2 45 degree)

Find the point(s) on the x-axis which is at a distance of sqrt(41) units from the point (8, -5).

Show that the points A(-5,6), B(3, 0) and C( 9, 8) are the vertices of an isosceles triangle.

(A) In triangle ABC, D, E and F are midpoints of BC,CA and AB respectively. Prove that triangle FBD ~ triangle DEF and triangle DEF ~ triangle ABC OR (B) In triangle ABC, P and Q are points on AB and AC respectively such that PQ is parallel to BC. Prove that the median AD drawn from A on BC bisects PQ.

The sum of two numbers is 18 and the sum of their reciprocals is 9/40. Find the numbers.

If alpha and beta are zeroes of a polynomial 6x^2 -5x+1 then form a quadratic polynomial whose zeroes are alpha^2 and beta^2.

If cos theta + sin theta = 1 , then prove that cos theta - sin theta = +/- 1

(A) The minute hand of a wall clock is 18 cm long. Find the area of the face of the clock described by the minute hand in 35 minutes. OR (B) AB is a chord of a circle centred at O such that angle AOB=60^o. If OA = 14 cm then find the area of the minor segment. (take sqrt(3) =1.73)

Prove that sqrt(3) is an irrational number.

(A) Solve the following system of linear equations graphically: x+2y = 3, 2x-3y+8 = 0 OR (B) Places A and B are 180 km apart on a highway. One car starts from A and another from B at the same time. If the car travels in the same direction at different speeds, they meet in 9 hours. If they travel towards each other with the same speeds as before, they meet in an hour. What are the speeds of the two cars?

Prove that the lengths of tangents drawn from an external point to a circle are equal. Using above result, find the length BC of triangle ABC. Given that, a circle is inscribed in triangle ABC touching the sides AB, BC and CA at R, P and Q respectively and AB= 10 cm, AQ= 7cm ,CQ= 5cm.

A boy whose eye level is 1.35 m from the ground, spots a balloon moving with the wind in a horizontal line at some height from the ground. The angle of elevation of the balloon from the eyes of the boy at an instant is 60^o. After 12 seconds, the angle of elevation reduces to 30^o. If the speed of the wind is 3m/s then find the height of the balloon from the ground. (Use sqrt(3)= 1.73)

Find the mean and median of the following data: Class 85-90, 90-95, 95-100, 100-105, 105-110, 110-115; frequency 15, 22, 20, 18, 20, 25. OR The monthly expenditure on milk in 200 families of a Housing Society is given below: Monthly Expenditure (in Rs.) 1000-1500, 1500-2000, 2000-2500, 2500-3000, 3000-3500, 3500-4000, 4000-4500, 4500-5000; Number of families 24, 40, 33, x, 30, 22, 16, 7. Find the value of x and also find the mean expenditure

Ms. Sheela visited a store near her house and found that the glass jars are arranged one above the other in a specific pattern. On the top layer there are 3 jars. In the next layer there are 6 jars. In the 3rd layer from the top there are 9 jars and so on till the 8th layer. On the basis of the above situation answer the following questions. (i) Write an A.P whose terms represent the number of jars in different layers starting from top . Also, find the common difference. (ii) Is it possible to arrange 34 jars in a layer if this pattern is continued? Justify your answer. (iii) (A) If there are 'n' number of rows in a layer then find the expression for finding the total number of jars in terms of n. Hence find S8 . OR (iii) (B) The shopkeeper added 3 jars in each layer. How many jars are there in the 5th layer from the top?

Triangle is a very popular shape used in interior designing. The picture given above shows a cabinet designed by a famous interior designer. Here the largest triangle is represented by triangle ABC and smallest one with shelf is represented by triangle DEF. PQ is parallel to EF. (i) Show that triangle DPQ ~ triangle DEF. (ii) If DP= 50 cm and PE = 70 cm then find PQ/EF. (iii) (A) If 2AB = 5DE and triangle ABC ~ triangle DEF then show that perimeter of triangle ABC / perimeter of triangle DEF is constant. OR (iii) (B) If AM and DN are medians of triangles ABC and DEF respectively then prove that triangle ABM ~ triangle DEN.

Metallic silos are used by farmers for storing grains. Farmer Girdhar has decided to build a new metallic silo to store his harvested grains. It is in the shape of a cylinder mounted by a cone. Dimensions of the conical part of a silo is as follows: Radius of base = 1.5 m Height = 2 m Dimensions of the cylindrical part of a silo is as follows: Radius = 1.5 m Height = 7 m On the basis of the above information answer the following questions. (i) Calculate the slant height of the conical part of one silo. (ii) Find the curved surface area of the conical part of one silo. (iii)(A) Find the cost of metal sheet used to make the curved cylindrical part of 1 silo at the rate of ₹2000 per m^2. OR (iii) (B) Find the total capacity of one silo to store grains.