CBSE Maths Class 10 Sample Paper 01 Page 1

Sample Paper 01
Class - 10th Exam - 2024 - 25
Mathematics - Standard
Time : 3 Hours Max. Marks : 80
General Instructions :
1. This question paper contains 38 questions.
2. This Question Paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are
Assertion - Reason based questions of 1 mark each.
4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each.
5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each.
6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each.
7. In Section E, Questions no. 36-38 are case study based questions carrying 4 marks each with sub parts
of the values of 1, 1 and 2 marks each respectively.
8. All Questions are compulsory. However, an internal choice in 2 Question of Section B, 2 Questions of
Section C and 2 Questions of Section D has been provided. An internal choice has been provided in all
the 2 marks questions of Section E.
9. Draw neat and clean figures wherever required.
10. Take π = 227 wherever required if not stated.
11. Use of calculators is not allowed.

Section - A
Section A consists of 20 questions of 1 mark each.

1. If x2 + y2 = 25 , xy = 12 , then x is

(a) (3, 4) (b) (3, - 3)

(c) (3, 4, - 3, - 4) (d) (3, - 3)

2. If the square of difference of the zeroes of the quadratic polynomial x2 + px + 45 is equal to 144, then the
value of p is
(a) ! 9 (b) ! 12
(c) ! 15 (d) ! 18

3. TABC and TBDE are two equilateral triangle such that D is the mid-point of BC . Ratio of the areas
of triangles ABC and BDE is ................. .
(a) 1 : 4 (b) 4 : 1
(c) 1 : 3 (d) 3 : 1

4. In the adjoining figure, TP and TQ are the two tangents to a circle with centre O . If +POQ = 110c,
then +PTQ is

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Page 2 Sample Paper 01 CBSE Maths Class 10

(a) 60c (b) 70c

(c) 80c (d) 90c

5. A set of numbers consists of three 4’s, five 5’s, six 6’s, eight 8’s and seven 10’s. The mode of this set of
numbers is
(a) 6 (b) 7
(c) 8 (d) 10

6. TABC is an equilateral triangle with each side of length 2p . If AD = BC then the value of AD is
(a) 3 (b) 3p
(c) 2p (d) 4p

7. The quadratic equation x2 − 4x − 3 2 = 0 has

(a) two distinct real roots (b) two equal real roots
(c) no real roots (d) more than 2 real roots

8. From an external point P , tangents PA and PB are drawn to a circle with centre O . If CD is the tangent
to the circle at a point E and PA = 14 cm . The perimeter of TPCD is
(a) 14 cm (b) 21 cm
(c) 28 cm (d) 35 cm

9. (cos 4 A - sin 4 A) is equal to

(a) 1 - 2 cos2 A (b) 2 sin2 A - 1
(c) sin2 A - cos2 A (d) 2 cos2 A - 1

10. An observer, 1.5 m tall is 20.5 away from a tower 22 m high, then the angle of elevation of the top of the
tower from the eye of observer is
(a) 30c (b) 45c
(c) 60c (d) 90c

11. Which of the following relationship is the correct?

(a) P (E ) + P (E ) = 1 (b) P (E ) − P (E ) = 1
(c) P (E ) = 1 + P (E ) (d) None of these

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CBSE Maths Class 10 Sample Paper 01 Page 3

12. The pair of equations x = a and y = b graphically represents lines which are
(a) parallel (b) intersecting at (b, a)
(c) coincident (d) intersecting at (a, b)

13. A tree casts a shadow 15 m long on the level of ground, when the angle of elevation of the sun is 45c. The
height of a tree is
(a) 10 m (b) 14 m
(c) 8 m (d) 15 m

14. From a solid circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the
same height and same base is removed, then the volume of remaining solid is
(a) 280 πcm3 (b) 330 πcm3
(c) 240 πcm3 (d) 440 π cm3

15. If median is 137 and mean is 137.05, then the value of mode is
(a) 156.90 (b) 136.90
(c) 186.90 (d) 206.90

16. If the circumference of a circle increases from 4 π to 8 π , then its area is

(a) halved (b) doubled
(c) tripled (d) quadrupled

17. A chord of a circle of radius 10 cm, subtends a right angle at its centre. The length of the chord (in cm) is
(a) 5 (b) 5 2
2
(c) 10 2 (d) 10 3

18. If a number x is chosen at random from the numbers - 2, - 1, 0, 1, 2 . Then, the probability that x2 1 2
is
(a) 2 (b) 4
5 5

(c) 1 (d) 3
5 5

19. Assertion : The value of sin θ = 43 is not possible.

Reason : Hypotenuse is the largest side in any right angled triangle.
(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 but 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.

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Page 4 Sample Paper 01 CBSE Maths Class 10

20. Assertion : an - an - 1 is not independent of n then the given sequence is an AP.

Reason : Common difference d = an − an − 1 is constant or independent of n .
(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 but 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.

Section - B
Section B consists of 5 questions of 2 marks each.

21. Find the ratio in which the point ^- 3, k h divides the line segment joining the points ^- 5, - 4h and ^- 2, 3h .
Also find the value of k .

22. From an external point P , tangents PA and PB are drawn to a circle with centre O. If +PAB = 50º,
then find +AOB.

23. Write a rational number between 2 and 3.

24. Find the 7th term from the end of AP 7, 10, 13, .... 184.


O
The fourth term of an AP is 11. The sum of the fifth and seventh terms of the AP is 34. Find the common
difference.

25. How many two digits numbers are divisible by 3?

Section - C
Section C consists of 6 questions of 3 marks each.

26. Two dice are tossed simultaneously. Find the probability of getting
(i) an even number on both dice.
(ii) the sum of two numbers more than 9.

27. An electric pole is 10 m high. A steel wire tied to top of the pole is affixed at a point on the ground to
keep the pole up right. If the wire makes an angle of 45º with the horizontal through the foot of the pole,
find the length of the wire. [Use 2 = 1.414 ]

28. Solve for x : 1 − 1 = 11 x ! - 4, - 7 .

x+4 x+7 30

29. Prove that the rectangle circumscribing a circle is a square.

O
If O is centre of a circle, PQ is a chord and the tangent PR at P makes an angle of 50c with PQ , find
+POQ .

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CBSE Maths Class 10 Sample Paper 01 Page 5

30. From a solid right circular cylinder of height 14 cm and base radius 6 cm, a right circular cone of same
height and same base removed. Find the volume of the remaining solid.


O
A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weights, a conical hole is drilled in the
cylinder. The conical hole has a radius of 32 cm and its depth 89 cm. Calculate the ratio of the volume of
metal left in the cylinder to the volume of metal taken out in conical shape.

31. A fraction becomes 13 when 2 is subtracted from the numerator and it becomes 1
2 when 1 is subtracted
from the denominator- Find the fraction.

Section - D
Section D consists of 4 questions of 5 marks each.

32. In Figure, a square OABC is inscribed in a quadrant OPBQ . If OA = 15 cm , find the area of the shaded
region. (Use π = 3.14 ).

33. Find the zeroes of the quadratic polynomial 7y2 - 113 y - 23 and verify the relationship between the zeroes
and the coefficients.

O
2
If α and β are the zeroes the polynomial 2x − 4x + 5, find the values of
(i) α2 + β2 (ii) 1 + 1
α β

(iii) ^α − βh2 (iv) 12 + 12

α β
(v) α2 + β2

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Page 6 Sample Paper 01 CBSE Maths Class 10

34. In TABC, AD is a median and O is any point on AD. BO and CO on producing meet AC and AB at
E and F respectively. Now AD is produced to X such that OD = DX as shown in figure.
Prove that :
(1) EF || BC
(2) AO : AX = AF : AB

35. If sin A = 3 calculate sec A.

4

O

Evaluate : 4 ^sin 4 30º + cos 4 60ºh − 3 ^cos2 45 − sin2 90ºh

Section - E
Section E consists of 3 case study based questions of 4 marks each.

36. Heart Rate : The heart rate is one of the ‘vital signs,’ or the important indicators of health in the human
body. It measures the number of times per minute that the heart contracts or beats. The speed of the
heartbeat varies as a result of physical activity, threats to safety, and emotional responses. The resting
heart rate refers to the heart rate when a person is relaxed. While a normal heart rate does not guarantee
that a person is free of health problems, it is a useful benchmark for identifying a range of health issues.
After the age of 10 years, the heart rate of a person should be between 60 and 100 beats per minute while
they are resting.

Thirty women were examined by doctors of AIIMS and the number of heart beats per minute were
recorded and summarised as follows.

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CBSE Maths Class 10 Sample Paper 01 Page 7

Number of heart beats per minute Number of women ^ f ih

65-68 2

68-71 4

71-74 3

74-77 8

77-80 7

80-83 4

83-86 2
Based on the above information, answer the following questions.
(i) What is the mean heart beats per minute for these women ?
(ii) What is the upper limit of median value of heart beats per minute for these women ?
(iii) What is the lower limit of mode value of heart beats per minute for these women ?


O
How many women are having heart beat in range 68-77?

37. Volume of a Bird Cage. A company makes rectangular shaped bird cages with height b inches and square
bottoms. The volume of these cages is given by the function V = b 3 − 6b2 + 9b .
(i) Find an expression for the length of each side of the square bottom.
(ii) Use the function to find the volume of a cage with a height of 18 inches.
(iii) Use the remainder theorem to find the volume of a cage with a height of 15 inches.

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Page 8 Sample Paper 01 CBSE Maths Class 10

38. Morning assembly is an integral part of the school’s schedule. Almost all the schools conduct morning
assemblies which include prayers, information of latest happenings, inspiring thoughts, speech, national
anthem, etc. A good school is always particular about their morning assembly schedule. Morning assembly
is important for a child’s development. It is essential to understand that morning assembly is not just
about standing in long queues and singing prayers or national anthem, but it’s something beyond just
prayers. All the activities carried out in morning assembly by the school staff and students have a great
influence in every point of life. The positive effects of attending school assemblies can be felt throughout
life.

Have you noticed that in school assembly you always stand in row and column and this make a coordinate
system. Suppose a school have 100 students and they all assemble in prayer in 10 rows as given below.

Here A, B, C and D are four friend Amar, Bharat, Colin and Dravid.
(i) What is the distance between A and B ?
(ii) What is the distance between C and D ?
(iii) What is the distance between A and C ?


O
What is the distance between D and B ?

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CBSE Maths Class 10 Sample Paper 02 Page 1

Sample Paper 02
Class - 10th Exam - 2024 - 25
Mathematics - Standard
Time : 3 Hours Max. Marks : 80
General Instructions :
1. This question paper contains 38 questions.
2. This Question Paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are
Assertion - Reason based questions of 1 mark each.
4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each.
5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each.
6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each.
7. In Section E, Questions no. 36-38 are case study based questions carrying 4 marks each with sub parts
of the values of 1, 1 and 2 marks each respectively.
8. All Questions are compulsory. However, an internal choice in 2 Question of Section B, 2 Questions of
Section C and 2 Questions of Section D has been provided. An internal choice has been provided in all
the 2 marks questions of Section E.
9. Draw neat and clean figures wherever required.
10. Take π = 227 wherever required if not stated.
11. Use of calculators is not allowed.

Section - A
Section A consists of 20 questions of 1 mark each.

1. If α and β are the roots of ax2 − bx + c = 0 (a ! 0), then value of α + β is

(a) b (b) a
a b

(c) 2a (d) a
b 2b

2. What are the values of x and y for the following pair of linear equations ?
99x + 101y = 499 and 101x + 99y = 501

(a) 3 and 6 (b) 3 and 2

(c) 2 and 3 (d) 6 and 3

3. The zeroes of polynomial p ^x h = ax2 + bx + c are reciprocal of each other if

(a) b = 2a (b) c = b
(c) b = a (d) c = a

4. If - 1 is a zero of the polynomial p ^x h = kx2 − 4x + k, the value of k is

(a) –4 (b) –2
(c) 2 (d) 4

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Page 2 Sample Paper 02 CBSE Maths Class 10

5. If a number x is chosen at random from the numbers - 3 , - 2 , - 1. 0, 1, 2, 3, then What is the probability
of x2 < 4 ?
(a) 4 (b) 3
7 7

(c) 1 (d) 2
7 7

6. Which of the following value of k should be selected so that the pair of equations x + 2y = 5 and
3x + ky + 15 = 0 has a unique solution ?

(a) k ! 5 (b) k ! 6
(c) k = 5 (d) k = 6

7. The quadratic equation x2 + 3x + 2 2 = 0 has

(a) two distinct real roots (b) two equal real roots
(c) no real roots (d) more than 2 real roots

8. A ladder 10 m long reaches a window 8 m above the ground. The distance of the foot of the ladder from
the base of the wall is ................ m.
(a) 8 m (b) 2 m
(c) 6 m (d) 4 m

9. The value of x for which 2x, (x + 10) and (3x + 2) are the three consecutive terms of an AP, is
(a) 6 (b) - 6
(c) 18 (d) - 18

10. If points A (- 3, 12), B (7, 6) and C (x, 9) are collinear, then the value of x is ......... .
(a) 2 (b) 3
(c) 4 (d) 5

11. If the sum of the circumferences of two circles with radii R1 and R2 is equal to the circumference of a
circle of radius R , then
(a) R1 + R2 = R (b) R1 + R2 > R
(c) R1 + R2 > R (d) R1 + R2 < R

12. The value of sin2 41º + sin2 49º will be

(a) 1 (b) 2
(c) 2 (d) 3

13. The number 7 will have -

75
(a) non-terminating repeating decimal expansion.
(b) terminating decimal expansion.
(c) non-terminating non repeating decimal expansion.
(d) terminating non repeating decimal expansion

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14. A tree casts a shadow 15 m long on the level of ground, when the angle of elevation of the sun is 45c. The
height of a tree is
(a) 10 m (b) 14 m
(c) 8 m (d) 15 m

15. The famous mathematician associated with finding the sum of the first 100 natural numbers is
(a) Pythagoras (b) Newton
(c) Gauss (d) Euclid

16. If the perimeter of one face of a cube is 20 cm, then its surface area is
(a) 120 cm2 (b) 150 cm2
(c) 125 cm2 (d) 400 cm2

17. sin2 60c − 2 tan 45c − cos2 30c = ?

(a) 2 (b) –2
(c) 1 (d) –1

18. If xi ’s are the mid-points of the class intervals of grouped data, f i ’s are the corresponding frequencies and
x is the mean, then / (f i xi - x ) is equal to
(a) 0 (b) - 1
(c) 1 (d) 2

19. Assertion : The two tangents are drawn to a circle from an external point, then they subtend equal angles
at the centre.
Reason : A parallelogram circumscribing a circle is a rhombus.
(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 but 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.

20. Assertion : The values of x are - a , a for a quadratic equation 2x2 + ax − a2 = 0 .

2
Reason : For quadratic equation ax2 + bx + c = 0
2
x = − b ! b − 4ac
2a

(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 but 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.

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Page 4 Sample Paper 02 CBSE Maths Class 10

Section - B
Section B consists of 5 questions of 2 marks each.

21. The mid-point of the line-segment AB is P (0, 4), if the coordinates of B are (- 2, 3) then find the co-
ordinates of A.

22. Two different dice are tossed together. Find the probability :
(i) that the number on each die is even.
(ii) that the sum of numbers appearing on the two dice is 5.

23. Given that HCF (306, 1314) = 18. Find LCM (306, 1314).

24. If α and β are the zeroes of a polynomial x2 − 4 3 x + 3, then find the value of α + β − αβ .

O

If one of the zeroes of the quadratic polynomial f ^x h = 14x2 − 42k2 x − 9 is negative of the other, find the
value of ‘k ’.

25. In the given figure, G is the mid-point of the side PQ of TPQR and GH || QR. Prove that H is the mid-
point of the side PR or the triangle PQR.

O

In the figure of TABC, the points D and E are on the sides CA, CB respectively such that DE || AB,
AD = 2x, DC = x + 3, BE = 2x − 1 and CE = x. Then, find x.

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CBSE Maths Class 10 Sample Paper 02 Page 5

Section - C
Section C consists of 6 questions of 3 marks each.

26. Evaluate :
3 tan2 30º + tan2 60º + cosec 30º − tan 45º
cot2 45º

27. Prove that the rectangle circumscribing a circle is a square.

28. A solid is in the shape of a cone surmounted on a hemisphere. The radius of each of them being 3.5 cm
and the total height of the solid is 9.5 cm. Find the volume of the solid.

O

A heap of rice is in the form of a cone of base diameter 24 m and height 3.5 m. Find the volume of the
rice. How much canvas cloth is required to just cover the heap?

29. Write the smallest number which is divisible by both 306 and 657.

30. The mean of the following distribution is 48 and sum of all the frequency is 50. Find the missing
frequencies x and y .

Class 20-30 30-40 40-50 50-60 60-70

Frequency 8 6 x 11 y

O
The table below shows the daily expenditure on food of 25 households in a locality. Find the mean daily
expenditure on food.

Daily expenditure (in <) 100-150 150-200 200-250 250-300 300-350

Number of households 4 5 12 2 2

31. TABC and TBDE are two equilateral triangle such that D is the mid-point of BC . Ratio of the areas
of triangles ABC and BDE is ................. .

Section - D
Section D consists of 4 questions of 5 marks each.

32. Prove that the point ^3, 0h , ^6, 4h and ^- 1, 3h are the vertices of a right angled isosceles triangle.

33. Find the values of k for which the equation ^3k + 1h x2 + 2 ^k + 1h x + 1 has equal roots. Also find the roots.

O

A person on tour has < 4200 for his expenses. If he extends his tour for 3 days, he has to cut down his
daily expenses by < 70. Find the original duration of the tour.

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Page 6 Sample Paper 02 CBSE Maths Class 10

34. In figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC
, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, +B = 90c and
DS = 5 cm, then find the radius of the circle (in cm).

O

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the
centre of the circle.

35. In Figure, a square OABC is inscribed in a quadrant OPBQ . If OA = 15 cm , find the area of the shaded
region. (Use π = 3.14 ).

Section - E
Section E consists of 3 case study based questions of 4 marks each.

36. Eiffel Tower : The Eiffel Tower is a landmark and an early example of wrought-iron construction on a
gigantic scale. The lower section consists of four immense arched legs set on masonry piers. The legs curve
inward until they unite in a single tapered tower. Platforms, each with an observation deck, are at three
levels; on the first is also a restaurant.
The tower, constructed of about 7000 tons of iron, has stairs and elevators. A meteorological station, a
radio communications station, and a television transmission antenna, as well as a suite of rooms that were
used by Eiffel are located near the top of the tower.

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CBSE Maths Class 10 Sample Paper 02 Page 7

(i) For a person standing 324 m from the center of the base of the Eiffel Tower, the angle of elevation
to the top of the tower is 45c . How tall is the Eiffel Tower?
(ii) A car is moving at uniform speed towards the Eiffel tower. It takes 15 minutes for the angle of
depression from the top of tower to the car to change from 30c to 60c . After how much time after
this, the car will reach the base of the tower?

37. Bequests to Charity : At the time our mother left this Earth, she gave ` 90000 to her children of birth.
This we kept and each year added ` 30000 more, as a lasting memorial from the children she bore. When
` 4,20,000 is thusly attained, all goes to charity that her memory be maintained.
(i) What was the balance in the sixth year?
(ii) In what year was the goal of ` 420,000 met?

38. Double-six Dominos : It is a game played with the 28 numbered tiles shown in the diagram.

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Page 8 Sample Paper 02 CBSE Maths Class 10

The 28 dominos are placed in a bag, shuffled, and then one domino is randomly drawn. Give the following
answer.
(i) What is the probability the total number of dots on the domino is three or less ?
(ii) What is the probability the total number of dots on the domino is greater than three ?
(iii) What is the probability the total number of dots on the domino does not have a blank half ?
(iv) What is the probability the total number of dots on the domino is not a “double” (both sides the
same) ?

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CBSE Maths Class 10 Sample Paper 03 Page 1

Sample Paper 03
Class - 10th Exam - 2024 - 25
Mathematics - Standard
Time : 3 Hours Max. Marks : 80
General Instructions :
1. This question paper contains 38 questions.
2. This Question Paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are
Assertion - Reason based questions of 1 mark each.
4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each.
5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each.
6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each.
7. In Section E, Questions no. 36-38 are case study based questions carrying 4 marks each with sub parts
of the values of 1, 1 and 2 marks each respectively.
8. All Questions are compulsory. However, an internal choice in 2 Question of Section B, 2 Questions of
Section C and 2 Questions of Section D has been provided. An internal choice has been provided in all
the 2 marks questions of Section E.
9. Draw neat and clean figures wherever required.
10. Take π = 227 wherever required if not stated.
11. Use of calculators is not allowed.

Section - A
Section A consists of 20 questions of 1 mark each.
1. The maximum number of zeroes a cubic polynomial can have, is
(a) 1 (b) 4
(c) 2 (d) 3

2. If α and β are the zeroes of the polynomial x2 + 2x + 1, then 1

α + 1β is equal to
(a) - 2 (b) 2
(c) 0 (d) 1

3. In the given figure, PA is a tangent from an external point P to a circle with centre O . If +POB = 115c
, then perimeter of +APO is

(a) 25c (b) 20c

(c) 30c (d) 65c

4. In an AP, if d = − 4 , n = 7 and an = 4 , then a is equal to

(a) 6 (b) 7
(c) 20 (d) 28

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Page 2 Sample Paper 03 CBSE Maths Class 10

5. If the probability of an event is p , then the probability of its complementary event will be
(a) p - 1 (b) p
(c) 1 - p (d) 1 - 1
p
6. A bag contains 3 red and 2 blue marbles. If a marble is drawn at random, then the probability of drawing
a blue marble is:
2 1
(a) 5 (b) 4
3 2
(c) 5 (d) 3

7. 225 can be expressed as

(a) 5 # 32 (b) 52 # 3
(c) 52 # 32 (d) 53 # 3

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

(a) 2.4 cm (b) 2.2 cm

(c) 3.2 cm (d) 3.4 cm

9. The roots of the quadratic equation x2 − 0.04 = 0 are

(a) ! 0.2 (b) ! 0.02
(c) 0.4 (d) 2

10. Consider the following distribution :

Marks obtained Number of students

More than or equal to 0 63
More than or equal to 10 58
More than or equal to 20 55
More than or equal to 30 51
More than or equal to 40 48
More than or equal to 50 42
the frequency of the class 30-40 is :
(a) 3 (b) 4
(c) 48 (d) 51

11. From the top of a 7 m high building the angle of elevation of the top of a cable tower is 60c and the angle
of depression of its foot is 45c, then the height of the tower is
(a) 14.124 m (b) 17.124 m
(c) 19.124 m (d) 15.124 m

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12. 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. If the angle made by the rope with the ground level is 30c, then what is the height
of pole?
(a) 20 m (b) 8 m
(c) 10 m (d) 6 m

13. If triangle ABC is similar to triangle DEF such that 2AB = DE and BC = 8 cm then find EF.
(a) 16 cm (b) 14 cm
(c) 12 cm (d) 15 cm

14. A sphere is melted and half of the melted liquid is used to form 11 identical cubes, whereas the remaining
half is used to form 7 identical smaller spheres. The ratio of the side of the cube to the radius of the new
small sphere is
(a) b 3 l (b) b 3 l
4 1/3 8 1/3

(c) (3) 1/3 (d) 2

15. Ratio of volumes of two cones with same radii is

(a) h1 : h2 (b) s1 : s2
(c) r1 : r2 (d) None of these

16. If cos 9a = sin a and 9α < 90c, then the value of tan 5α is

(a) 1 (b) 3
3
(c) 1 (d) 0

In the formula x = a + h f
/ f i ui , for finding the mean of grouped frequency distribution, u
/ fi p
17. i is equal to
(a) xi + a (b) h (xi - a)
h

(c) xi - a (d) a - xi
h h

18. The distance of the point P (- 3, - 4) from the x -axis (in units) is
(a) 3 (b) - 3
(c) 4 (d) 5

19. Assertion : If the circumference of a circle is 176 cm, then its radius is 28 cm.
Reason : Circumference = 2π # radius
(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 but 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.

20. Assertion : Pair of linear equations : 9x + 3y + 12 = 0, 8x + 6y + 24 = 0 have infinitely many solutions.

Reason : Pair of linear equations a1 x + b1 y + c1 = 0 and a2 x + b2 y + c2 = 0 have infinitely many solutions,
if a1 = b1 = c1
a2 b2 c2

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(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 but 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.

Section - B
Section B consists of 5 questions of 2 marks each.

21. If 3 sin θ − cos θ = 0 and 0º < θ < 90º, find the value of θ.

22. In the given figure, if ABCD is a trapezium in which AB || CD || EF, then prove that AE
ED = BF
FC

23. A box contains cards numbered 11 to 123. A card is drawn at random from the box. Find the probability
that the number of the drawn card is
(i) A perfect square number
(ii) A multiple of 7.


O
A letter of English alphabet is chosen at random, find the probability that the letter so chosen is :
(i) a vowel,
(ii) a consonant.

24. In Figure +D = +E and AD = AE , prove that

DB EC
TBAC is an isosceles triangle.

O
ABC is a right triangle right angled at C. Let BC = a, CA = b, AB = c PQR, ST || QR and p be the
length of perpendicular from C to AB . Prove that cp = ab .

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CBSE Maths Class 10 Sample Paper 03 Page 5

25. In the given figure, from a point P , two tangents PT and PS are drawn to a circle with centre O such
that +SPT = 120c, Prove that OP = 2PS .

Section - C
Section C consists of 6 questions of 3 marks each.

26. Find whether the following pair of linear equations has a unique solutions. If yes, find the solution :
7x - 4y = 49, 5x − 6y = 57 .

27. In given figure TABC~TDEF. AP bisects +CAB and DQ bisects +FDE.

Prove that :
(1) AP = AB (2) TCAP~TFDQ.
DQ DE


O
In the given figure, DE | | AC and DF | | AE. Prove that BE = BE .
FE EC

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Page 6 Sample Paper 03 CBSE Maths Class 10

28. A conical vessel, with base radius 5 cm height 24 cm, is full of water. This water emptied into a cylindrical
vessel, of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel. Use
π = 227


O
504 cones, each of diameter 3.5 cm and height 3 cm, are melted and recast into a metallic sphere. Find
the diameter of the sphere and hence find its surface area. Use π = 227

29. Quadratic polynomial 2x2 − 3x + 1 has zeroes as α and β . Now form a quadratic polynomial whose zeroes
are 3α and 3β .

30. Three bells toll at intervals of 9, 12, 15 minutes respectively. If they start tolling together, after what time
will they next toll together?

31. If cos ^40º + x h = sin 30º, find the value of x .

Section - D
Section D consists of 4 questions of 5 marks each.

32. Find for x : 1 + 2 = 6 ; x ! 0, 1, 2

x−2 x−1 x


O
Find the values of k for which the equation ^3k + 1h x2 + 2 ^k + 1h x + 1 has equal roots. Also find the roots.

33. In figure O is the centre of a circle of radius 5 cm. T is a point such that OT = 13 cm and OT intersects
circle at E . If AB is a tangent to the circle at E , find the length of AB , where TP and TQ are two
tangents to the circle.

34. Find the mode of the following frequency distribution

Class Interval 25-30 30-35 35-40 40-45 45-50 50-55

Frequency 25 34 50 42 38 14

O
On the sports day of a school, 300 students participated. Their ages are given in the following distribution:

Age (in years) 5-7 7-9 9-11 11-13 13-15 15-17 17-19
Number of students 67 33 41 95 36 13 15
Find the mean and mode of the data.

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CBSE Maths Class 10 Sample Paper 03 Page 7

35. Find the ratio in which the line x − 3y = 0 divides the line segment joining the points ^- 2, - 5h and ^6, 3h
. Find the coordinates of the point of intersection.

Section - E
Section E consists of 3 case study based questions of 4 marks each.

36. Conical Tank : The advantages of cone bottom tanks are found in nearly every industry, especially where
getting every last drop from the tank is important. This type of tank has excellent geometry for draining,
especially with high solids content slurries as these cone tanks provide a better full-drain solution. The
conical tank eliminates many of the problems that flat base tanks have as the base of the tank is sloped
towards the centre giving the greatest possible full-drain system in vertical tank design.

Rajesh has been given the task of designing a conical bottom tank for his client. Height of conical part
is equal to its radius. Length of cylindrical part is the 3 times of its radius. Tank is closed from top. The
cross section of conical tank is given below.

(i) If radius of cylindrical part is taken as 3 meter, what is the volume of above conical tank ?
(ii) What is the area of metal sheet used to make this conical tank ? Assume that tank is covered from
top.
(iii) What is the ratio of volume of cylindrical part to the volume of conical part?
(iv) The cost of metal sheet is ` 2000 per square meter and fabrication cost is 1000 per square meter.
What is the total cost of tank ?

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Page 8 Sample Paper 03 CBSE Maths Class 10

37. Volume of a Bird Cage. A company makes rectangular shaped bird cages with height b inches and square
bottoms. The volume of these cages is given by the function V = b 3 − 6b2 + 9b .
(i) Find an expression for the length of each side of the square bottom.
(ii) Use the function to find the volume of a cage with a height of 18 inches.
(iii) Use the remainder theorem to find the volume of a cage with a height of 15 inches.
(iv) Verify the result of (iii) using function ?

38. Dipesh bought 3 notebooks and 2 pens for ` 80. His friend Ramesh said that price of each notebook could
be ` 25. Then three notebooks would cost ` 75, the two pens would cost ` 5 and each pen could be for
` 2.50. Another friend Amar felt that ` 2.50 for one pen was too little. It should be at least ` 16. Then
the price of each notebook would also be ` 16.

Aditya also bought the same types of notebooks and pens as Dipesh. He paid 110 for 4 notebooks and 3
pens.
(i) Whether the estimation of Ramesh and Amar is applicable for Aditya?
(ii) Let the cost of one notebook be x and that of pen be y . Which of the following set describe the
given problem ?
(iii) What is the exact cost of the notebook?
(iv) What is the exact cost of the pen? What is the total cost if they purchase the same type of 15
notebooks and 12 pens.


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CBSE Maths Class 10 Sample Paper 04 Page 1

Sample Paper 04
Class - 10th Exam - 2024 - 25
Mathematics - Standard
Time : 3 Hours Max. Marks : 80
General Instructions :
1. This question paper contains 38 questions.
2. This Question Paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are
Assertion - Reason based questions of 1 mark each.
4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each.
5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each.
6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each.
7. In Section E, Questions no. 36-38 are case study based questions carrying 4 marks each with sub parts
of the values of 1, 1 and 2 marks each respectively.
8. All Questions are compulsory. However, an internal choice in 2 Question of Section B, 2 Questions of
Section C and 2 Questions of Section D has been provided. An internal choice has been provided in all
the 2 marks questions of Section E.
9. Draw neat and clean figures wherever required.
10. Take π = 227 wherever required if not stated.
11. Use of calculators is not allowed.

Section - A
Section A consists of 20 questions of 1 mark each.

1. Each root of x2 − bx + c = 0 is decreased by 2. The resulting equation is x2 − 2x + 1 = 0 , then

(a) b = 6, c = 9 (b) b = 3, c = 5
(c) b = 2, c = − 1 (d) b = − 4, c = 3

2. If the mean of a , b , c is M and ab + bc + ca = 0 , the mean of a2 , b2 and c2 is KM2 , then K is equal to

(a) 3 (b) 9
(c) 6 (d) 4

3. The 2 digit number which becomes 56 th of itself when its digits are reversed. The difference in the digits
of the number being 1, then the two digits number is
(a) 45 (b) 54
(c) 36 (d) None of these

4. If the nth term of an AP is given by an = 5n − 3 , then the sum of first 10 terms if

(a) 225 (b) 245
(c) 255 (d) 270

5. If the perimeter of one face of a cube is 20 cm, then its surface area is
(a) 120 cm2 (b) 150 cm2
(c) 125 cm2 (d) 400 cm2

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6. The HCF and the LCM of 12, 21, 15 respectively are

(a) 3, 140 (b) 12, 420
(c) 3, 420 (d) 420, 3

7. From an external point Q , the length of tangent to a circle is 12 cm and the distance of Q from the centre
of circle is 13 cm. The radius of circle (in cm) is
(a) 10 (b) 5
(c) 12 (d) 7

8. One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the
selected ticket has a number which is a multiple of 5 is
(a) 1 (b) 3
5 5

(c) 4 (d) 1
5 3

9. The length of a string between a kite and a point on the ground is 85 m. If the string makes an angle θ
with level ground such that tan θ = 158 , then the height of kite is
(a) 75 m (b) 78.05 m
(c) 226 m (d) None of these

10. A tree casts a shadow 15 m long on the level of ground, when the angle of elevation of the sun is 45c.
Find the height of a tree.
(a) 15 m (b) 10 m
(c) 7.5 m (d) 12 m

11. In the given figure, x is

(a) ab (b) ac
a+b b+c
(c) bc (d) ac
b+c a+c

12. If the sum of the circumferences of two circles with radii R1 and R2 is equal to the circumference of a
circle of radius R , then
(a) R1 + R2 = R (b) R1 + R2 > R
(c) R1 + R2 > R (d) R1 + R2 < R

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CBSE Maths Class 10 Sample Paper 04 Page 3

13. In the given figure, if +A = 90º, +B = 90º, OB = 4.5 cm OA = 6 cm and AP = 4 cm then find QB.

(a) 3 cm (b) 6 cm
(c) 4.5 cm (d) 3.5 cm

14. Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm
and height 16 cm. The diameter of each sphere is
(a) 4 cm (b) 3 cm
(c) 2 cm (d) 6 cm

15. Consider the following frequency distribution

Class 0-5 6-11 12-17 18-23 24-29

Frequency 13 10 15 8 11

The upper limit of the median class is

(a) 17 (b) 17.5
(c) 18 (d) 18.5

16. The probability that a number selected at random from the numbers 1, 2, 3, ......, 15 is a multiple of 4 is
(a) 4 (b) 2
15 15

(c) 1 (d) 1
15 5

17. The zeroes of the quadratic polynomial x2 + kx + k where k ! 0 ,

(a) cannot both be positive (b) cannot both be negative
(c) are always unequal (d) are always equal

18. If the point P (6, 2) divides the line segment joining A (6, 5) and B (4, y) in the ratio 3 : 1 then the value
of y is
(a) 4 (b) 3
(c) 2 (d) 1

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19. Assertion : The value of sec2 10c - cot2 80c is 1.

Reason : The value of sin 30c = 12 .
(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 but 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.

20. Assertion : x3 + x has only one real zero.

Reason : A polynomial of n th degree must have n real zeroes.
(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 but 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.

Section - B
Section B consists of 5 questions of 2 marks each.

21. In the given figure, BOA is a diameter of a circle and the tangent at a point P meets BA when produced
at T. If +PBO = 30º , what is the measure of +PTA ?

22. A bag contains 5 red, 8 green and 7 white balls. One ball is drawn at random from the bag, find the
probability of getting :
(i) not a white ball,
(ii) neither a green nor a red ball.


O
Two coins are tossed together. Find the probability of getting both heads or both tails.

23. If tan 2A = cot (A − 18c), where 2A is an acute angle, find the value of A.

24. In TABC, AD = BC, such that AD2 = BD # CD. Prove that TABC is right angled at A.

O

In the figure of TABC, the points D and E are on the sides CA, CB respectively such that DE | | AB,
AD = 2x, DC = x + 3, BE = 2x − 1 and CE = x. Then, find x.

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O

In the figure of TABC, DE | | AB. If AD = 2x, DC = x + 3, BE = 2x − 1 and CE = x, then find the value
of x.

25. In the given figure, TABC ~TPQR. Find the value of y + z.

Section - C
Section C consists of 6 questions of 3 marks each.

26. The 34 th part of a conical vessel of internal radius 5 cm and height 24 cm is full of water. The water
emptied into a cylindrical vessel with internal radius 10 cm. Find the height of water in cylindrical vessel.

27. Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial f (x) = ax2 + bx + c
, a ! 0, c ! 0.

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Page 6 Sample Paper 04 CBSE Maths Class 10

28. Two right triangles ABC and DBC are drawn on the same hypotenuse BC and on the same side of BC
. If AC and BD intersect at P , prove that AP # PC = BP # DP .

O

In the given figure, two triangles ABC and DBC lie on the same side of BC such that PQ || BA and
PR | | BD. Prove that QR | | AD.

29. The rod of TV disc antenna is fixed at right angles to wall AB and a rod CD is supporting the disc as
shown in Figure. If AC = 1.5 m long and CD = 3 m ,
Find (i) tan θ (ii) sec θ + cosec θ .

30. A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder of same diameter. The
diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the total
surface area of the vessel. Use π = 227

O

A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the
sphere is completely submerged in water, the water level into the cylindrical vessel rises by 3 5 cm. Find
9
the diameter of the cylindrical vessel.

31. Solve the following pair of linear equations :

8x + 5y = 9
3x + 2y = 4

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CBSE Maths Class 10 Sample Paper 04 Page 7

Section - D
Section D consists of 4 questions of 5 marks each.

Solve for x : b 2x l + b 2x l − 24 = 0, x ! 5
2
32.
x−5 x−5


O

Solve for x : x + 3 − 1 − x = 17 ; x ! 0, 2
x−2 x 4

33. To conduct Sports Day activities, in your rectangular school ground ABCD , lines have been drawn with
chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each
other along AD , as shown in Figure. Niharika runs ¼th the distance AD on the 2nd line and posts a green
flag. Preet runs 15 th distance AD on the eighth line and posts a red flag.
(i) What is the distance between the two flags?
(ii) If Rashmi has to post a blue flag exactly half way between the line segment joining the two flags,
where should she post the blue flag?

34. If the angle between two tangents drawn from an external point P to a circle of radius a and centre O,
is 60º, then find the length of OP.

35. The median of the following data is 525. Find the values of x and y , if total frequency is 100 :

Class Frequency
0-100 2

100-200 5

200-300 x

300-400 12

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Page 8 Sample Paper 04 CBSE Maths Class 10

Class Frequency
400-500 17

500-600 20

600-700 y

700-800 9

800-900 7

900-1000 4

O

On annual day of a school, 400 students participated in the function. Frequency distribution showing their
ages is as shown in the following table :

Ages (in years) 05-07 07-09 09-11 11-13 13-15 15-17 17-19

Number of students 70 120 32 100 45 28 5

Find mean and median of the above data.

Section - E
Section E consists of 3 case study based questions of 4 marks each.

36. Box : For the box to satisfy certain requirements, its length must be three unit greater than the width,
and its height must be two unit less than the width.

(i) If width is taken as x , find the polynomial that represent volume of box.
(ii) Find the polynomial that represent the area of paper sheet used to make box.
(iii) If it must have a volume of 18 unit, what must be its length and height ?


O
(iv) If box is made of a paper sheet which cost is Rs 100 per square unit, what is the cost of paper?

37. MASK : Masks are an additional step to help prevent people from getting and spreading COVID-19.
They provide a barrier that keeps respiratory droplets from spreading. Wear a mask and take every day
preventive actions in public settings.

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CBSE Maths Class 10 Sample Paper 04 Page 9

Due to ongoing Corona virus outbreak, Wellness Medical store has started selling masks of decent quality.
The store is selling two types of masks currently type A and type B .

The cost of type A mask is `15 and of type B mask is` 20. In the month of April, 2020, the store sold
100 masks for total sales of ` 1650.
(i) How many masks of each type were sold in the month of April? If the store had sold 50 masks of
each type, what would be its sales in the month of April?
(ii) Due to great demand and short supply, the store has increased the price of each type by ` 5 from
May 1, 2020. In the month of May, 2020, the store sold 310 masks for total sales of ` 6875. How
many masks of each type were sold in the month of May?
(iii) What percent of masks of each type sale was increased in the month of May, compared with the sale
of month April?


O
(iv) What extra profit did store earn by increasing price in May month.

38. In a toys manufacturing company, wooden parts are assembled and painted to prepare a toy. For the
wood processing activity center, the wood is taken out of storage to be sawed, after which it undergoes
rough polishing, then is cut, drilled and has holes punched in it. It is then fine polished using sandpaper.
For the retail packaging and delivery activity center, the polished wood sub-parts are assembled together,
then decorated using paint.

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Page 10 Sample Paper 04 CBSE Maths Class 10

One specific toy is in the shape of a cone mounted on a cylinder. The total height of the toy is 110 mm
and the height of its conical part is 77 mm. The diameters of the base of the conical part is 72 mm and
that of the cylindrical part is 40 mm.
(i) If its cylindrical part is to be painted red, what is the surface area need to be painted ?
(ii) If its conical part is to be painted blue, what is the surface area need to be painted ?
(iii) How much of the wood have been used in making the toy ?


O
(iv) If the cost of painting the toy is 2 paise for 8π mm2 , then what is the cost of painting of a box of
100 toys?

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