SUBJECT: MATHEMATICS STANDARD (041)
SAMPLE QUESTION PAPER
CLASS – X (2026 – 27)
Maximum Marks: 80 Time Allowed: 3 hours
General Instructions:
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
number 19 and 20 are Assertion - Reason based questions of 1 mark each.
(iv) In Section B, Question number 21 to 25 are Very Short Answer (VSA)-type questions, carrying
2 marks each.
(v) In Section C, Question number 26 to 31 are Short Answer (SA)-type questions carrying 3 marks
each.
(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
provided in all the sub parts having 2 marks of questions in section E.
22
(ix) Draw neat and clean figures wherever required. Take π = wherever required, if not stated.
7
(x) Use of calculators is not allowed.
SECTION – 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:
(A) 13 (B) 26 (C) 39 (D) 65
2. If f(x) = px2 + qx + r, p ≠ 0 and p + r = q, then one of the zeroes of f(x) is: 1
q r r q
(A) (B) (C) − (D) −
p p p p
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 (B) II only (C) I and II (D) II and III
4. If (1 – p) is a root of the quadratic equation x2 + px + 1 – p = 0, then its roots are: 1
(A) 0, 1 (B) – 1, 1 (C) 0, – 1 (D) – 1, 2
*There is no change in the Question Paper Design and Assessment Pattern for Academic Session 2026-27
Page 1 of 6
, 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
12
makes an angle θ with the ground level such that tan θ = . If the length of the
5
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
*There is no change in the Question Paper Design and Assessment Pattern for Academic Session 2026-27
Page 2 of 6
SAMPLE QUESTION PAPER
CLASS – X (2026 – 27)
Maximum Marks: 80 Time Allowed: 3 hours
General Instructions:
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
number 19 and 20 are Assertion - Reason based questions of 1 mark each.
(iv) In Section B, Question number 21 to 25 are Very Short Answer (VSA)-type questions, carrying
2 marks each.
(v) In Section C, Question number 26 to 31 are Short Answer (SA)-type questions carrying 3 marks
each.
(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
provided in all the sub parts having 2 marks of questions in section E.
22
(ix) Draw neat and clean figures wherever required. Take π = wherever required, if not stated.
7
(x) Use of calculators is not allowed.
SECTION – 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:
(A) 13 (B) 26 (C) 39 (D) 65
2. If f(x) = px2 + qx + r, p ≠ 0 and p + r = q, then one of the zeroes of f(x) is: 1
q r r q
(A) (B) (C) − (D) −
p p p p
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 (B) II only (C) I and II (D) II and III
4. If (1 – p) is a root of the quadratic equation x2 + px + 1 – p = 0, then its roots are: 1
(A) 0, 1 (B) – 1, 1 (C) 0, – 1 (D) – 1, 2
*There is no change in the Question Paper Design and Assessment Pattern for Academic Session 2026-27
Page 1 of 6
, 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
12
makes an angle θ with the ground level such that tan θ = . If the length of the
5
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
*There is no change in the Question Paper Design and Assessment Pattern for Academic Session 2026-27
Page 2 of 6
