NODIA APP Sample Paper 01 Page 1
Sample Paper 01
Class - 10th Exam - 2025 - 26
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. What is the common difference of an AP in which a18 − a14 = 32 ?
(a) 8 (b) - 8
(c) - 4 (d) 4
2. A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of
outcomes favourable to E is
(a) 4 (b) 13
(c) 48 (d) 51
3. The first term of AP is p and the common difference is q , then its 10th term is
(a) q + 9p
(b) p - 9q
(c) p + 9q
(d) 2p + 9q
4. Two chords AB and CD of a circle intersect at E such that AE = 2.4 cm , BE = 3.2 cm and CE = 1.6 cm
. The length of DE is
(a) 1.6 cm
(b) 3.2 cm
(c) 4.8 cm
(d) 6.4 cm
,Page 2 Sample Paper 01 CBSE Maths Class 10
5. If cos 9a = sin a and 9α < 90c, then the value oftan 5α is
(a) 1 (b) 3
3
(c) 1 (d) 0
6. The ratio of the length of a rod and its shadow is 1 : 3 then the angle of elevation of the sun is
(a) 90c (b) 45c
(c) 30c (d) 75c
7. If a circular grass lawn of 35 m in radius has a path 7 m wide running around it on the outside, then the
area of the path is
(a) 1450 m2 (b) 1576 m2
(c) 1694 m2 (d) 3368 m2
8. Two poles of height 6 m and 11 m stand vertically upright on a plane ground. If the distance between their
foot is 12 m, then distance between their tops is
(a) 12 m (b) 14 m
(c) 13 m (d) 11 m
9. 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
10. The co-ordinates of the point which is reflection of point (- 3, 5) in x -axis are
(a) (3, 5) (b) (3, - 5 )
(c) (- 3, - 5) (d) (- 3, 5)
11. C is the mid-point of PQ , if P is (4, x), C is (y, - 1) and Q is (- 2, 4), then x and y respectively are
(a) - 6 and 1
(b) - 6 and 2
(c) 6 and - 1
(d) 6 and - 2
12. Consider the following frequency distribution of the heights of 60 students of a class
Height (in cm) 150-155 155-160 160-165 165-170 170-175 175-180
Number of students 15 13 10 8 9 5
The upper limit of the median class in the given data is
(a) 165 (b) 155
(c) 160 (d) 170
Continue on next page.....
,NODIA APP Sample Paper 01 Page 3
13. If one zero of a quadratic polynomial (kx2 + 3x + k) is 2, then the value of k is
(a) 5 (b) - 5
6 6
(c) 6 (d) - 6
5 5
14. The centroid of the triangle whose vertices are (3, - 7), (- 8, 6) and (5, 10) is
(a) (0, 9) (b) (0, 3)
(c) (1, 3) (d) (3, 5)
15. The zeroes of the polynomial x2 − 3x − m (m + 3) are
(a) m, m + 3
(b) − m, m + 3
(c) m, − (m + 3)
(d) − m, − (m + 3)
16. The value of k for which the system of equations x + y − 4 = 0 and 2x + ky = 3 , has no solution, is
(a) - 2 (b) ! 2
(c) 3 (d) 2
17. If one root of the quadratic equation ax2 + bx + c = 0 is the reciprocal of the other, then
(a) b = c (b) a = b
(c) ac = 1 (d) a = c
18. The pair of equations 3x + y = 81, 81x − y = 3 has
(a) no solution
(b) unique solution
(c) infinitely many solutions
(d) x = 2 1 , y = 1 7
8 8
19. Assertion : 4x2 − 12x + 9 = 0 has repeated roots.
Reason : The quadratic equation ax2 + bx + c = 0 have repeated roots if discriminant D > 0 .
(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 HCF of two numbers is 5 and their product is 150, then their LCM is 30
Reason : For any two positive integers a and b, HCF ^a, b h + LCM ^a, b h = a # b .
(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.
, Page 4 Sample Paper 01 CBSE Maths Class 10
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.
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 .
Sample Paper 01
Class - 10th Exam - 2025 - 26
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. What is the common difference of an AP in which a18 − a14 = 32 ?
(a) 8 (b) - 8
(c) - 4 (d) 4
2. A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of
outcomes favourable to E is
(a) 4 (b) 13
(c) 48 (d) 51
3. The first term of AP is p and the common difference is q , then its 10th term is
(a) q + 9p
(b) p - 9q
(c) p + 9q
(d) 2p + 9q
4. Two chords AB and CD of a circle intersect at E such that AE = 2.4 cm , BE = 3.2 cm and CE = 1.6 cm
. The length of DE is
(a) 1.6 cm
(b) 3.2 cm
(c) 4.8 cm
(d) 6.4 cm
,Page 2 Sample Paper 01 CBSE Maths Class 10
5. If cos 9a = sin a and 9α < 90c, then the value oftan 5α is
(a) 1 (b) 3
3
(c) 1 (d) 0
6. The ratio of the length of a rod and its shadow is 1 : 3 then the angle of elevation of the sun is
(a) 90c (b) 45c
(c) 30c (d) 75c
7. If a circular grass lawn of 35 m in radius has a path 7 m wide running around it on the outside, then the
area of the path is
(a) 1450 m2 (b) 1576 m2
(c) 1694 m2 (d) 3368 m2
8. Two poles of height 6 m and 11 m stand vertically upright on a plane ground. If the distance between their
foot is 12 m, then distance between their tops is
(a) 12 m (b) 14 m
(c) 13 m (d) 11 m
9. 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
10. The co-ordinates of the point which is reflection of point (- 3, 5) in x -axis are
(a) (3, 5) (b) (3, - 5 )
(c) (- 3, - 5) (d) (- 3, 5)
11. C is the mid-point of PQ , if P is (4, x), C is (y, - 1) and Q is (- 2, 4), then x and y respectively are
(a) - 6 and 1
(b) - 6 and 2
(c) 6 and - 1
(d) 6 and - 2
12. Consider the following frequency distribution of the heights of 60 students of a class
Height (in cm) 150-155 155-160 160-165 165-170 170-175 175-180
Number of students 15 13 10 8 9 5
The upper limit of the median class in the given data is
(a) 165 (b) 155
(c) 160 (d) 170
Continue on next page.....
,NODIA APP Sample Paper 01 Page 3
13. If one zero of a quadratic polynomial (kx2 + 3x + k) is 2, then the value of k is
(a) 5 (b) - 5
6 6
(c) 6 (d) - 6
5 5
14. The centroid of the triangle whose vertices are (3, - 7), (- 8, 6) and (5, 10) is
(a) (0, 9) (b) (0, 3)
(c) (1, 3) (d) (3, 5)
15. The zeroes of the polynomial x2 − 3x − m (m + 3) are
(a) m, m + 3
(b) − m, m + 3
(c) m, − (m + 3)
(d) − m, − (m + 3)
16. The value of k for which the system of equations x + y − 4 = 0 and 2x + ky = 3 , has no solution, is
(a) - 2 (b) ! 2
(c) 3 (d) 2
17. If one root of the quadratic equation ax2 + bx + c = 0 is the reciprocal of the other, then
(a) b = c (b) a = b
(c) ac = 1 (d) a = c
18. The pair of equations 3x + y = 81, 81x − y = 3 has
(a) no solution
(b) unique solution
(c) infinitely many solutions
(d) x = 2 1 , y = 1 7
8 8
19. Assertion : 4x2 − 12x + 9 = 0 has repeated roots.
Reason : The quadratic equation ax2 + bx + c = 0 have repeated roots if discriminant D > 0 .
(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 HCF of two numbers is 5 and their product is 150, then their LCM is 30
Reason : For any two positive integers a and b, HCF ^a, b h + LCM ^a, b h = a # b .
(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.
, Page 4 Sample Paper 01 CBSE Maths Class 10
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.
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 .
