CBSE Class 10 Sample Paper 2027 for Maths Standard

FOR CBSE CLASS 10 PREPARATION

CBSE Class 10 Sample
Paper 2027 for Maths
Standard
EXAM YEAR TYPE SUBJECT

CBSE Class 10 2027 Sample Paper Maths Standard

Notes · Sample Papers · Previous Year Papers · Mock Tests

SUBJECT: MATHEMATICS STANDARD (041)
SAMPLE QUESTION PAPER
CLASS – X (2026 – 27)
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m Time Allowed: 3 hours
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Maximum Marks: 80
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General Instructions: a
Read the following instructions very carefully and strictly follow them:
(i) This Question paper contains 38 questions. All questions are compulsory.
(ii) This Question paper is divided into five Sections – A, B, C, D and E.
(iii) In Section A, Question number 1 to 18 are Multiple Choice Questions (MCQs) and Question

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number 19 and 20 are Assertion - Reason based questions of 1 mark each.
(iv)
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In Section B, Question number 21 to 25 are Very Short Answer (VSA)-type questions, carrying
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2 marks each.
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e number 26 to 31 are Short Answer (SA)-type questions carryinggl3 marks
(v)
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In Section C, Question
a
each. ag
(vi) In Section D, Question number 32 to 35 are Long Answer (LA)-type questions carrying 5 marks
each.
(vii) In Section E, Question number 36 to 38 are case study-based questions carrying 4 marks each.
(viii) There is no overall choice. However, an internal choice has been provided in 2 questions in
Section B, 2 questions in Section C and 2 questions in Section D. An internal choice has been
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provided in all the sub parts having 2 marks of questions in section E.
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(ix) Draw neat and clean figures wherever required. Take π = 7 wherever required, if not stated.
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(x) Use of calculators is not allowed.
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agSECTION – A (20 x 1 = 20)
This section comprises of 18 multiple choice questions and two questions of assertion and
reasoning type of 1 mark each.
Q. No. Questions Marks
1. The greatest number which divides both 134 and 188, leaving remainders 4 and 6 1
respectively, is:

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(A) 13 (B) 26 (C) 39 (D) 65
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2.
c. oIf f(x) = pxq + qx + r, p ≠r0 and p + r = q, thenr one of the zeroesq ofsf(x)
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2

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is:

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p
(B)
p
(C) −
p
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ag 3. Tarun correctly solved a pair of linear equations in two variables and found their 1
only point of intersection as (5, – 1). One of the lines was x – y = 6.
Which of the following could have been the other line?
I: 3x – 3y = 18
II: 2x – 3y = 13
III: 2x – 3y = 16
(A) I only
o m (C) I and II (D) II and III
(B) II only . c
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If (1 – p) is a root of the .quadratic e m
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e(B) – 1, 1
equation x + px + 1 – p = 0, then its roots are:
2 1
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(A) 0, 1
l as (C) 0, – 1 (D) – 1, 2
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5. The middle term of the A.P.: 10, 7, 4, …, – 62 is: 1
(A) – 26 (B) – 29 (C) – 32 (D) – 35
6. The perimeters of two similar triangles are 56 cm and 70 cm respectively. If one 1
side of the first triangle is 14 cm, then the corresponding side of the second triangle
(in cm) is:
(A) 5 (B) 7.5 (C) 10 (D) 17.5
7. The point which lies on the perpendicular bisector of the line segment joining the 1
points A (– 3, – 4) and B (3, 4) is:
(A) (0, 0) (B) (0, 3) (C) (3, 0) (D) (0, 4)

8. 1 1
If tan (A + B) = √3 and tan (A – B) = , 0° < A + B < 90°, A > B, then the value
√3
of A and B respectively are:
(A) 60°, 30° (B) 60°, 45° (C) 45°, 15° (D) 60°,15°

9. T-shirts marked with numbers 4 to 99 are placed in a box. Gunika is fond of 1
numbers. She randomly takes out a T-shirt from this box. The probability that she
gets a T-shirt marked with a number that is either a perfect square or a perfect cube
is:
1 1 11 5
(A) (B) (C) (D)
12 32 96 48
10. The diameter of a car wheel is 21 cm. The number of complete revolutions it will 1
make in moving 66 km is:
(A) 104 (B) 105 (C) 106 (D) 107

11. Two cubes each of volume 64 cm3 are joined end to end to form a solid. The surface 1
area of the resultant cuboid is:
(A) 192 cm2 (B) 160 cm2 (C) 96 cm2 (D) 80 cm2

12. The mean age of a combined group of men and women is 35 years. If the mean 1
ages of the men and women are 38 years and 30 years respectively, then the
percentage of women in the group is:
(A) 15 (B) 25.5 (C) 35 (D) 37.5
13. Two dice are rolled simultaneously. The probability of getting number less than 4 1
on each die is:
1 1 1 1
(A) (B) (C) (D)
4 9 36 6

14. PM is a median of Δ PQR with vertices P (5, – 6), Q (6, 4) and R (0, 0). The 1
length of PM is:
(A) 2√17 units (B) 2√15 units
(C) √101 units (D) 10 units
15. The arc of a circle is of length 6𝜋 cm and the sector it bound has an area of 24𝜋 cm2. 1
The radius of the circle is:
(A) 4 cm (B) 8 cm (C) 16 cm (D) 18 cm

16. The mean and median of the data are 35.5 and 32 respectively. The value of 1
mode for this data is:
(A) 23 (B) 26 (C) 25 (D) 30

17. A flying kite is tied to a point on the ground with the help of a string. The string 1
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makes an angle θ with the ground level such that tan θ = 5 . If the length of the
string is 52 m, then the height of the kite above the ground is:
(A) 40 m (B) 45.5 m (C) 48 m (D) 50 m

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18. 2 cards of diamonds and 4 cards of spades are missing from a pack of 52 cards. 1
A card is drawn at random from this pack. The probability of getting a card of
heart is:
13 13 11 11
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(A) (B) (C) (D)
m 52 46 52 46

m .co Assertion-Reason Based Questions
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as e Directions: Questions number 19 and 20 are Assertion and Reason based
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questions carrying 1 mark each. Two statements are given, one labelled
Assertion (A) and the other labelled Reason (R).
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Select the correct answer from the options (A), (B), (C) and (D) as given below:
(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).

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(C) Assertion (A) is true but Reason (R) is false.
(D) Assertion (A) is false but Reason (R) is true.
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19.
. co vertices of a parallelogram taken in order are (–1, –6), (2, – s1em
Assertion (A): If three

em its fourth vertex is (4,1).
5) and (7, 2), then
Reason (R):s Diagonals of a parallelogram bisect each other. g l a
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20.
a
Assertion (A): If zeroes of the polynomial (2k – 1) x2 + 4x – 3 are reciprocal of each 1
other, then k = –1.
Reason (R): If a = c, then zeroes of the polynomial ax2 + bx + c, a ≠ 0 are
reciprocal of each other.
SECTION – B (5 x 2 = 10)
This section comprises of 5 Very Short Answer (VSA) type questions of 2 marks each.
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21(A).
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A hall has a length of 9.75 m, breadth of 6.75 m and height of 5.25 m. What is the
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2

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length of the longest unmarked ruler that can exactly measure the dimensions of

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the hall?

21(B). There are three bells placed at different swings in a park, which toll at intervals of
5, 6 and 8 minutes, respectively. They all toll together when the park opens for the
visitors at 10:00 a.m.. How many more times do they all toll together till the park is
closed at 7:00 p.m.?

22(A). ABCD is a trapezium in which AB is parallel to DC and its diagonals intersect each 2
AO CO
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other at the point O. Show that = .
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22(B). In the given figure, if ∠PQR = ∠QSP, PQ = 6 cm and PS = 3 cm,
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then find

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For visually Impaired Candidates:
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In a right-angled triangle ABC, right-angled at B, a perpendicular BD is drawn to
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the hypotenuse AC. Prove that the triangle BCD is similar to the triangle ACB.
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23. 1 cosec2 θ − sec2 θ 2
If tanθ = , then find the value of .
√5 cosec2 θ + sec2 θ

24. Find the area of a sector of a circle with diameter 28 cm, If the length of the 2
corresponding arc is 22 cm.

25. Two dice are thrown simultaneously. Find the probability that the product of the 2
numbers appearing on them is a prime number.

SECTION – C (6 x 3 = 18)

This section comprises of 6 Short Answer (SA) type questions of 3 marks each.

26. Given that √3 is irrational number, prove that (2 + 3√3) is an irrational number. 3

27. If α and β are the zeroes of the quadratic polynomial 2𝑥2 − 8𝑥 + 5, then find the 3
1 1
value of (𝛼 + ) × (𝛽 + ).
𝛽 𝛼

28(A). Ridhi drew a polygon with n sides. The smallest exterior angle is 8° and each 3
subsequent exterior angle is 4° more than the previous exterior angle. Find the
number of sides of the polygon that Ridhi had drawn.

OR
28(B). Find the sum of integers between 1 and 400 that are multiples of 4 as well as of 5.

29. Prove that the parallelogram circumscribing a circle is a rhombus. 3

30. In what ratio does the x–axis divide the line segment joining the points (– 4, – 6) 3
and (–1, 7)? Also, find the coordinates of the point of division.

31(A). During a math class, Ms. Isha wrote the expression given below on the board and 3
asked the students to simplify it.
cos θ 1 − sin θ
+
1 − sin θ cos θ
Jyoti solved it in her note book as follows:
cos θ 1−sin θ
+
1−sin θ cos θ
cos θ+ 1−sinθ)2
2 (
= …. (step 1)
(1−sin θ)×cosθ
cos2 θ+cos2 θ
= …. (step 2)
(1−sin θ)×cosθ
2cos2 θ
= …. (step 3)
(1−sin θ)×cosθ
2cosθ
= …. (step 4)
(1−sin θ)
Identify the step in which Jyoti has made error(s), if any. Rectify the same and find
the correct answer.

OR
31(B). 1 cosec 𝑥 1 2 sec2 𝑥
If = , then prove that ( ) =
sin 𝑥 − cos 𝑥 √2 sin 𝑥 + cos 𝑥 2

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SECTION – D (4 x 5= 20)

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This section comprises of 4 Long Answer (LA) type questions of 5 marks each.

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In a rectangular park measuring 50 m × 40 m, the gram panchayat plans to
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32. 5

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construct a rectangular swimming pool in the middle, surrounded by a uniform-
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width grass strip throughout the park. Find the dimensions of the swimming pool, if
as the area of the grassy strip is 1184 m².
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33. Prove that a line drawn parallel to one side of a triangle to intersect the other two 5
sides in distinct points, divides the other two sides in the same ratio.
Using the above theorem solve the following:
PQRS is a trapezium with PQ || SR. X and Y are points on non-parallel sides PS
PX QY
and QR respectively such that XY || PQ. Show that = .
XS YR

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34(A). A tent is in the shape of a cylinder surmounted by a conical top. If the height and 5

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radius of the cylindrical part are 3 m and 14 m respectively, and the total height of
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the tent is 13.5 m, then find the area of the canvas required for making the tent,
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keeping a provision of 26 m2 of canvas for stitching and wastage. Also, find the cost

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of the canvas to be purchased at the rate of ₹ 250 per m2.
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34(B). A solid wooden toy is in the form of a hemisphere surmounted by a cone of the
same radius. The radius of hemisphere is 3.5 cm and the total wood used in making
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the toy is 166 cm3. Find the height of the conical part. Also, find the cost of painting
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the hemispherical part of the toy at the rate of ₹ 15 per cm2.

Manish is standing on level ground and observes a kite flying 200 m away from
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35(A). 5
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him at an angle of elevation of 300. Mahesh, standing on the roof of a 50 m high
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building on the opposite side of the kite, observes the same kite at an angle of
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elevation of 450. Find the distance between the kite and Mahesh.
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35(B). The angles of depression of two ships from the top of a lighthouse and on the same
side of it are found to be 450 and 300. If the ships are 200m apart and one ship is
exactly behind the other then find the height of lighthouse.

SECTION – E (3 x 4 = 12)

This section comprises of 3 case-study-based questions of 4 marks each with sub parts.
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Each case study questions has three sub parts (i), (ii), (iii) of marks 1, 1, 2 respectively.
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c. oA student entrepreneur started a company that manufactures sanitizers
36.
s e min two sizes
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small and large. The cost of a small bottle of sanitizer is ₹10 and that of a large
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is ₹15. In June, the company sold 1000 bottles and recorded
ag ₹12,750. Seeing the increased demand, the company decided to increase the price
of both sanitizer bottles by ₹2 each. In the next month, the company sold 2500
bottles and recorded a total sale of ₹34,250.
Based on the above information, answer the following questions:
(i) Form a linear equation in two variables representing the sale for June. 1
(ii) Form a linear equation in two variables representing the sale for July. 1
(iii) (A) How many sanitizer bottles of each type were actually sold in June? 2

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(B) How many sanitizer bottles of each type were sold in July? 2
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37. In a technology park in Hyderabad, a company installed a circular meditation
garden for its employees as shown in the figure.

Arjun, a designer, stood at a point P outside the garden and drew two tangents PA
and PB to the circular boundary. The radius of the garden is 9 m, and the distance
of point P from the centre O is 18 m. For preparing safety guidelines, Arjun needed
the lengths of the tangents. During a demonstration to interns, he asked them to
compute the angle formed between the two tangents using the properties of circle.

Based on the above information, answer the following questions:
(i) What is the measure of ∠OAP?
(ii) Calculate the length of the tangent PA. 1
(iii) (A) Calculate the measure of ∠AOB. 1
2
OR
(iii) (B) In the above design, if PA and PB were inclined at 60°, then what
would be their length? 2

38. A school conducted a weekly test for Class X students, before the commencement
of the pre-board examination and recorded their scores (out of 50). To analyse
performance patterns, the academic coordinator grouped the marks into intervals.
The grouped frequency distribution is as below:

Marks Obtained 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50
Number of students 3 6 12 15 14

The academic coordinator computed the central tendencies to judge overall
learning level, the most common performance range and to understand consistency
across the batch for planning the remedial sessions.
Based on the above information, answer the following questions:
(i) Identify the class with the most common performance range. 1
(ii) Find the class interval containing the median. 1
(iii) (A) What is the average performance of the students? 2
OR
(iii) (B) Find the mode of the data. 2

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