CBSE Class 10 Sample Paper 2027 for Maths Basic

FOR CBSE CLASS 10 PREPARATION

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

CBSE Class 10 2027 Sample Paper Maths

Notes · Sample Papers · Previous Year Papers · Mock Tests

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SUBJECT: MATHEMATICS BASIC
SAMPLE QUESTION PAPER
CLASS - X (2026 - 27)

Maximum Marks: 80 Time Allowed: 3 hours

General Instructions
Read the following instructions carefully and follow them:
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1. This question paper contains 38 questions. All questions are compulsory.
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2. This question Paper is divided into 5 Sections A, B, C, D and E.
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3. In Section A, Question numbers 1-18 are multiple choice questions (MCQs) and question
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no.19 and 20 are Assertion- Reason based questions of 1 mark each.
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4. In Section B, Question numbers 21-25 are very short answer (VSA) type questions, carrying 02
marks each.
5. In Section C, Question numbers 26-31 are short answer (SA) type questions, carrying 03 marks
each.
6. In Section D, Question numbers 32-35 are long answer (LA) type questions, carrying 05 marks
each.
7. In Section E, Question numbers 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.
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8. There is no overall choice. However, an internal choice in 2 questions of Section B, 2 questions

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of Section C and 2 questions of Section D has been provided. An internal choice has
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s Take 𝝅 = 22 wherever required if not stated.
been provided in all 2 marks questions of Section E.

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9. Draw neat and clean figures wherever required.
10. Use of calculators is not allowed.
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SECTION – A (20 × 1 = 20)
This section comprises of 18 multiple choice questions and two assertion and reason type
questions of 1 mark each.

Q.No. Question Marks
If HCF (2520, 6600) = 40 and LCM (2520, 6600) = 252 × k, then the value of k is
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Q1.
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(A) 165 (B) 1600 (C)1625 (D)1650 1

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2

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𝟐

las (A) 4 (B) 6 (C) 14
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(D)
1

ag For what value of 𝑝 does the pair of Linear equations 4𝑥 + 𝑝𝑦 + 8 = 0 and
Q3. 1
2𝑥 +2𝑦 + 2 = 0 has a unique solution
(A) 𝑝 = 4 only (B) 𝑝 = 2 only (C) 𝑝 ≠ 4 (D)𝑝 ≠ 2

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The sum of the numerator and denominator of a fraction is 11. If the denominator
Q4. 1 1
is increased by 1, the fraction becomes , then the fraction is
2
2 3 4 5
(A) (B) (C) (D)
9 8 7 6
If one root of the quadratic equation 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 is the reciprocal of the
Q5. other, then 1
(A) 𝑏 = 𝑐 (B) 𝑎 = 𝑏 (C) 𝑎𝑐 = 1 (D) 𝑎 = 𝑐

The first term of AP is 𝑝 and the common difference is 𝑞 , then its 10th term is
Q6. 1
(A) 𝑞 + 10𝑝 (B) 𝑝 − 9𝑞 (C) 𝑝 + 9𝑞 (D) 𝑝 + 10q
Which term of the AP: 21, 42, 63, 84 ... is 210?
Q7. 1
(A) 9th (B) 10th (C) 11th (D) 12th
If the point P (5, 2) divides the line segment joining A( 8, 5) and B( 4, 𝒚) in the
Q8. 1
ratio 3 : 1, then the value of 𝒚 is
(A) 4 (B) 3 (C) 2 (D) 1
A letter from the word INDEPENDENCE is selected at random. What is the
Q9. probability that the letter selected is a vowel which occurs the maximum number 1
of times in the given word?
1 1 1 5
(A) (B) (C) (D)
12 4 3 12
For the following distribution
Q10. 1
Class 0-5 5-10 10-15 15-20 20-25

Frequency 10 15 12 20 9
The lower limit of the median class is
(A) 5 (B) 10 (C) 15 (D) 20
The length of a tangent drawn from a point at a distance of 10 cm from the
Q11. centre of the circle is 8 cm. The radius of the circle is 1
(A) 4 cm (B) 5 cm (C) 6 cm (D) 7 cm
Mean and median of certain data are 32 and 30 respectively. Using empirical
Q12. 1
formula, the value of mode is
(A) 36 (B) 26 (C) 30 (D) 20

A ladder 15 m long reaches a window 12 m above the ground. The distance of the
Q13. 1
foot of the ladder from the base of the wall is
(A) 8 m (B) 9 m (C) 10 m (D) 13 m

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a The value of sin2 60° − 2 tan2 45° − cos230° is ag
Q14. (A) −2 (B) −1 (C) 1 (D) 2 1

The perimeter of two similar triangles is 28 cm and 35 cm respectively. If one
Q15. side of the first triangle is 8cm, then the corresponding side of the second triangle 1
is
(A) 10 cm (B) 12cm (C) 14cm (D) 16cm

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If in ∆ABC and ∆PQR , ∠B = ∠Q, ∠R = ∠C and AB = 2PQ, then the two triangles
Q16. are
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(A) Congruent but not similar
econgruent
(B) Similar but not congruent
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laPA and PB from a point P to a circle with centre O and respective pointa
(C)Neither nor similar (D) Congruent as well as similar
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If tangents
Q17. of contacts as A and B, are inclined to each other at angle of 80°, then ∠AOB is 1
equal to
(A) 60° (B) 70° (C) 80° (D)100°
Two cubes each of volume 64cm3 are joined end to end to form a cuboid. The
Q18. 1
total surface area of the resulting cuboid is
(A) 128 cm2 (B) 160 cm2
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(C) 176 cm2 (D) 192 cm2
Assertion-Reason Based Questions
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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
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Assertion (A) and the other labelled Reason (R).
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 (R) is the correct
explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but (R) is not the correct
explanation of Assertion (A).
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c. o (D) Assertion (A) is false but Reason (R) is true. m .co
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s emQ1. ASSERTION (A): The probability of getting number 8 on rollingglaadie is zero (0)
g la Q19.Q2. REASON (R): The probability of an impossible event is zeroa(0) 1
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Q3. ASSERTION (A): If a line divides any two sides of a triangle in the same ratio,
Q20. 1
then the line is parallel to the third side.
REASON (R): Line drawn from midpoint of one side of triangle parallel to another
will bisect the third side.

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SECTION – B (5 x 2 = 10)

This section comprises of 5 very short answer (VSA) type questions of 2 marks each.

Q21(A) Find the smallest number which when increased by 17 is exactly divisible by both
520 and 468.

OR 2

Q21(B) Show that (25)n will never end with digit zero for any natural number n.

Q22. If 3sin𝜃 = 4cos𝜃 , find the value of sin𝜃 + cos 2 𝜃 − 1; 2
If one zero of the quadratic polynomial 2𝑥 2 − 3𝑥 + 𝑝 is 3, find the value of 𝑝. 2
Q23.
Also, find the other zero.

Q24. In the given figure, PA is a common 2
tangent and QB and PC are the tangents
from Q and P to the smaller and larger
circle respectively. If QB = 5cm and PC =
9cm, then evaluate length of PQ.

For Visually Impaired Candidates
Two concentric circles are of radii 5cm and 3cm. Find the length of the chord of
the larger circle which touches the smaller circle.

Q25(A) Points A (3,1), B (5, 1), C (a, b) and D (4, 3) are vertices of a parallelogram
ABCD. Find the values of a and b.

OR
2
Q25(B) Find a linear relation between x and y such that P (x, y) is equidistant from the
points A (1, 4) and B (–1, 2).

SECTION – C (6 x 3 = 18)

This section comprises of 6 short answer (SA) type questions of 3 marks each.

Q26. Given that √𝟓 is irrational, prove that 2 + 3√5 is irrational. 3

Q27. In the given figure, AX, AY and BC are tangents to the circle with P, R and Q
(A) 1
respective point of contacts. Prove that AP = (AB + BC + CA)
2
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For Visually Impaired
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Prove that a
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a parallelogram circumscribing a circle is a rhombus.
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Q27. Two tangents PA and PB are drawn to a circle with centre O from an external
(B) point P. Prove that ∠APB = 2∠OAB
Q28. Determine the ratio in which the point (– 6, y) divides the line segment joining the 3
points A (–3, –1) and B (– 8, 9). Also, find the value of y.
Q29. Consider ∆ ACB, right-angled at C, in which AB = 29 units, BC = 21 units and 3
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∠ABC = θ. Determine the values of
i. 1 + tan2θ
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ii. cos θ – sin θ
2 2
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ag is 48 and sum of all the frequencies is 50.
Q30. The mean of the following distribution
(A)
Find the missing frequencies x and y.

Class 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70

Frequency 8 6 x 11 y
3

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OR
Q30. oThe distribution below gives the weight of 50 students of class X. Find . c
(B) .
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weight of the students.
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35 – 45 45 – 55 55 – 65 65a– 75 75 – 85
ag Weight ( in kg )

Number of 5 10 20 12 3
students

Q31. The sum of the digits of a two-digit number is 9. Also, nine times this number is 3
twice the number obtained by reversing the order of the digits. Find the number.

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SECTION – D (4 x 5 = 20)

This section comprises of 4 long answer (LA) type questions of 5 marks each.
Q32. Prove that if a line is drawn parallel to one side of a triangle intersecting the other 5
two sides in distinct points, then the other two sides are divided in the same ratio.

Q33. A train travels a distance of 360 km at a uniform speed. If the speed had been 5
(A)
km/h more, then it would have taken 1 hour less to cover the same distance. Find
the speed of the train.

5
OR
Q33. John and Jivanti together have 45 marbles. Both of them lost 5 marbles each,
(B)
and the product of the number of marbles they now have is 124. Find the
number of marbles they had with them in the beginning.

Q34. The largest possible hemisphere is drilled out of a wooden cubical block of side 5
21cm such that the base of the hemisphere is on one of the faces of the cube.
Then, find
i. the volume of the wood left in the block.
ii. the total surface area of the remaining solid.

Q35. To assist an ambulance, a drone is hovering over an accident site at a constant
(A)
height on a highway. The angle of depression of the ambulance, approaching the
accident site, observed from drone is 30°. Twelve minutes later, the angle of
depression of the ambulance is found to be 60°. If the ambulance is moving at a
constant speed then, find the total time taken by the ambulance to reach the site
of accident.
5

OR
Q35.
(B) A statue standing on a pedestal, is 1.6 m tall. From a point on the ground, the
angles of elevation of the top and bottom of the statue are 60° and 45°
respectively. Find the height of the pedestal.

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a SECTION – E ag (3 x 4 = 12)
This section comprises of 3 case-study/passage-based questions of 4 marks each with sub
parts. The first two case study questions have three sub parts (i), (ii), (iii) of marks 1, 1, 2
respectively.
Q36. An Art and craft teacher prepared a fan which looked like the sector of a circle

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using ice-cream sticks and black sheet as shown in the given figure:
(i) The angle subtended at the centre of the sector is 60⁰. Find the area of
1
one face of the fan.
(ii) With the given sector angle of 60⁰ at the centre, find area of black sheet 1
used in the fan.

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(iii)(A) The boundary of the black sheet region on one face is to be covered
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by a designer tape. What length of tape 2

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OR

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(iii)(B) If 29.6 cm of designer tape
black sheet region on one face of the fan, then evaluate the central angle
of the sector.
For Visually Impaired Candidates
A motion sensor (or motion detector) is an electronic device that is designed to
detect and measure movement. The motion detector can detect movement over a
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sector of angle θ = 70° to a distance of 24m.
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(i) Derive a relation between length of arc(l) and the area of the sector(A) 1

las enclosed by it?
(ii) How much area is monitored by motion detector? a
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ag (iii) (A) To increase the area to be monitored by 50% with same range of
1

distance covered, what should be the angle?
2
OR
(iii) (B) For θ = 91°, what range of distance is required for the detector to
monitor 30% more area?

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Delhi's pollution is a severe, often seasonal issue caused by a combination of
Q37. factors like high vehicular and industrial emissions, dust from construction, and
crop burning in surrounding states. In a school, students of classes I to XII
thought of planting trees in and around the school to reduce air pollution.

It was decided that the number of trees that each section of each class will plant
be three more than the double of the class in which they are studying, e.g., a
section of class IV will plant 11 trees. If in the given school, there are two sections
of each class, then answer the following questions:
(i) If number of trees planted by students class-wise follow arithmetic
progression, then find the common difference. 1
(ii) What is the number of trees planted by students of class VI?
1
(iii) (A) What is the total number of trees planted by the students of given
school?
OR 2
(iii) (B) Identify the class that planted 34 trees.
Q38. A labourer prints 400 T-shirts in a day. The supervisor checked the T-shirts and
found that 312 prints were good, 54 prints were with minor defects and rest of the
prints were of major defects.

Harish, a customer will buy a T-shirt only if it is good but a trader will buy, if it has
no major defect. If a random T-shirt is picked, then

(i) find the probability that Harish will buy a T-shirt.
(ii) find the probability that a trader will buy the T-shirt. 1
(iii) (A) find the probability that the T-shirt is not good. 1
OR 2
(iii) (B) find the probability that neither Harish nor trader buy the T-shirt.

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