Class 10 Mathematics (Standard): CBSE (Official) Sample Question Paper (2025-26) | Mathematics (Maths) Class 10 PDF Download

 Page 1


Page 1 of 8 
 
MATHEMATICS STANDARD – Code No.041 
SAMPLE QUESTION PAPER  
CLASS – X (2025-26)  
Maximum Marks: 80                                                                                                 Time: 3 hours 
 
 General Instructions: 
 
Read the following instructions carefully and follow them: 
 
1. This question paper contains 38 questions. All Questions are compulsory. 
2. This Question Paper is divided into 5 Sections A, B, C, D and E. 
3. In Section A, Question numbers 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, 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. 
8. There is no overall choice. However, an internal choice in 2 questions 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. Take ?? =
22
7
 wherever required if not stated. 
10. Use of calculators is not allowed. 
 
 
(Section A) 
Section A consists of 20 questions of 1 mark each. 
Q.No. Questions Marks 
 
1. If ?? = 2
2
× 3
?? ,?? = 2
2
× 3 × 5,?? = 2
2
× 3 × 7 and LCM (?? , ?? , ?? ) = 3780, then ?? is 
equal to 
 
(A) 1                 (B) 2                   (C) 3                (D) 0  
 
1 
2. The shortest distance (in units) of the point (2,3) from y-axis is 
 
     (A) 2                  (B) 3                  (C) 5                (D) 1 
 
1 
3. If the lines given by 3x +2ky =2 and 2x+5y +1=0 are not parallel, then k has to be 
 
    (A) 
15
4
                                         (B) ?
15
4
            
    (C) any rational number            (D) any rational number having 4 as denominator 
 
1 
*Please note that the assessment scheme of the Academic Session 2024-25 will continue in the current session i.e. 2025-26
Page 2


Page 1 of 8 
 
MATHEMATICS STANDARD – Code No.041 
SAMPLE QUESTION PAPER  
CLASS – X (2025-26)  
Maximum Marks: 80                                                                                                 Time: 3 hours 
 
 General Instructions: 
 
Read the following instructions carefully and follow them: 
 
1. This question paper contains 38 questions. All Questions are compulsory. 
2. This Question Paper is divided into 5 Sections A, B, C, D and E. 
3. In Section A, Question numbers 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, 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. 
8. There is no overall choice. However, an internal choice in 2 questions 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. Take ?? =
22
7
 wherever required if not stated. 
10. Use of calculators is not allowed. 
 
 
(Section A) 
Section A consists of 20 questions of 1 mark each. 
Q.No. Questions Marks 
 
1. If ?? = 2
2
× 3
?? ,?? = 2
2
× 3 × 5,?? = 2
2
× 3 × 7 and LCM (?? , ?? , ?? ) = 3780, then ?? is 
equal to 
 
(A) 1                 (B) 2                   (C) 3                (D) 0  
 
1 
2. The shortest distance (in units) of the point (2,3) from y-axis is 
 
     (A) 2                  (B) 3                  (C) 5                (D) 1 
 
1 
3. If the lines given by 3x +2ky =2 and 2x+5y +1=0 are not parallel, then k has to be 
 
    (A) 
15
4
                                         (B) ?
15
4
            
    (C) any rational number            (D) any rational number having 4 as denominator 
 
1 
*Please note that the assessment scheme of the Academic Session 2024-25 will continue in the current session i.e. 2025-26
Page 2 of 8 
 
4. A quadrilateral ABCD is drawn to circumscribe a circle. If BC=7cm, CD=4cm and 
AD=3cm, then the length of AB is 
 
(A) 3cm              (B) 4cm             (C) 6cm             (D) 7cm 
 
1 
5. If  ???????? + ???????? = ?? ,then ???????? - ???????? will be 
 
      (A) ??                (B) ?? 2
                  (C) 
2
??                  (D) 
1
?? 
 
1 
6. Which one of the following is not a quadratic equation? 
 
      (A) (?? +2)
2
 =2(?? +3)                                       (B) ?? 2
 +3?? =(- 1)(1- 3?? )
2
  
     (C) ?? 3 
- ?? 2
 +2 ?? +1 =( ?? +1)
3
                           (D) ( ?? +2)( ?? +1)  = ?? 2
+ 2?? +3 
 
1 
7. Given below is the picture of the Olympic rings made by taking five congruent circles 
of radius 1cm each, intersecting in such a way that the chord formed by joining the 
point of intersection of two circles is also of length 1cm.Total area of all the dotted 
regions (assuming the thickness of the rings to be negligible) is 
 
 
 
 
 
 
 
 
(A) 4[
?? 12
 - 
v3
4
 ] cm
2
                                    (B) [
?? 6
 - 
v3
4
 ] cm
2
     
(C) 4[
?? 6
 - 
v3
4
 ] cm
2                                                       
(D) 8[
?? 6
 - 
v3
4
 ] cm
2    
 
For Visually Impaired candidates 
 
The area of the circle that can be inscribed in a square of 6 cm is 
 
(A) 36?? cm
2 
          (B) 18?? cm
2               
(C) 12?? cm
2   
        (D) 9?? cm
2
 
 
1 
8. A pair of dice is tossed. The probability of not getting the sum eight is 
 
       (A) 
5
36
                (B) 
31
36
                 (C) 
5
18
                  (D) 
5
9
 
1 
9. 
If 2sin5?? = v3 ,0°= ?? =90
o
, then ?? is equal to  
          
        (A) 10
o
               (B) 12
o
            (C) 20
o
                 (D) 50
o
 
1 
10. The sum of two numbers is 1215 and their HCF is 81, then the possible pairs of such 
numbers are 
 
(A) 2                   (B) 3                 (C ) 4                      (D) 5 
1 
*Please note that the assessment scheme of the Academic Session 2024-25 will continue in the current session i.e. 2025-26
Page 3


Page 1 of 8 
 
MATHEMATICS STANDARD – Code No.041 
SAMPLE QUESTION PAPER  
CLASS – X (2025-26)  
Maximum Marks: 80                                                                                                 Time: 3 hours 
 
 General Instructions: 
 
Read the following instructions carefully and follow them: 
 
1. This question paper contains 38 questions. All Questions are compulsory. 
2. This Question Paper is divided into 5 Sections A, B, C, D and E. 
3. In Section A, Question numbers 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, 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. 
8. There is no overall choice. However, an internal choice in 2 questions 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. Take ?? =
22
7
 wherever required if not stated. 
10. Use of calculators is not allowed. 
 
 
(Section A) 
Section A consists of 20 questions of 1 mark each. 
Q.No. Questions Marks 
 
1. If ?? = 2
2
× 3
?? ,?? = 2
2
× 3 × 5,?? = 2
2
× 3 × 7 and LCM (?? , ?? , ?? ) = 3780, then ?? is 
equal to 
 
(A) 1                 (B) 2                   (C) 3                (D) 0  
 
1 
2. The shortest distance (in units) of the point (2,3) from y-axis is 
 
     (A) 2                  (B) 3                  (C) 5                (D) 1 
 
1 
3. If the lines given by 3x +2ky =2 and 2x+5y +1=0 are not parallel, then k has to be 
 
    (A) 
15
4
                                         (B) ?
15
4
            
    (C) any rational number            (D) any rational number having 4 as denominator 
 
1 
*Please note that the assessment scheme of the Academic Session 2024-25 will continue in the current session i.e. 2025-26
Page 2 of 8 
 
4. A quadrilateral ABCD is drawn to circumscribe a circle. If BC=7cm, CD=4cm and 
AD=3cm, then the length of AB is 
 
(A) 3cm              (B) 4cm             (C) 6cm             (D) 7cm 
 
1 
5. If  ???????? + ???????? = ?? ,then ???????? - ???????? will be 
 
      (A) ??                (B) ?? 2
                  (C) 
2
??                  (D) 
1
?? 
 
1 
6. Which one of the following is not a quadratic equation? 
 
      (A) (?? +2)
2
 =2(?? +3)                                       (B) ?? 2
 +3?? =(- 1)(1- 3?? )
2
  
     (C) ?? 3 
- ?? 2
 +2 ?? +1 =( ?? +1)
3
                           (D) ( ?? +2)( ?? +1)  = ?? 2
+ 2?? +3 
 
1 
7. Given below is the picture of the Olympic rings made by taking five congruent circles 
of radius 1cm each, intersecting in such a way that the chord formed by joining the 
point of intersection of two circles is also of length 1cm.Total area of all the dotted 
regions (assuming the thickness of the rings to be negligible) is 
 
 
 
 
 
 
 
 
(A) 4[
?? 12
 - 
v3
4
 ] cm
2
                                    (B) [
?? 6
 - 
v3
4
 ] cm
2
     
(C) 4[
?? 6
 - 
v3
4
 ] cm
2                                                       
(D) 8[
?? 6
 - 
v3
4
 ] cm
2    
 
For Visually Impaired candidates 
 
The area of the circle that can be inscribed in a square of 6 cm is 
 
(A) 36?? cm
2 
          (B) 18?? cm
2               
(C) 12?? cm
2   
        (D) 9?? cm
2
 
 
1 
8. A pair of dice is tossed. The probability of not getting the sum eight is 
 
       (A) 
5
36
                (B) 
31
36
                 (C) 
5
18
                  (D) 
5
9
 
1 
9. 
If 2sin5?? = v3 ,0°= ?? =90
o
, then ?? is equal to  
          
        (A) 10
o
               (B) 12
o
            (C) 20
o
                 (D) 50
o
 
1 
10. The sum of two numbers is 1215 and their HCF is 81, then the possible pairs of such 
numbers are 
 
(A) 2                   (B) 3                 (C ) 4                      (D) 5 
1 
*Please note that the assessment scheme of the Academic Session 2024-25 will continue in the current session i.e. 2025-26
Page 3 of 8 
 
11. If the area of the base of a right circular cone is 51cm
2
 and it's volume is 85cm
2
, then 
the height of the cone is given as 
 
(A) 
5
6
 cm           (B) 
5
3
cm              (C) 
5
2
cm                     (D) 5cm 
 
1 
12. If zeroes of the quadratic polynomial a?? 2 
 + b?? +c (a, c ?0) are equal, then 
 
    (A) c and b must have opposite signs         (B) c and a must have opposite signs    
    (C)  c and b must have same signs            (D) c and a must have same signs   
  
1 
13. The area (in cm
2
) of a sector of a circle of radius 21cm cut off by an arc of length 
22cm is 
 
(A) 441             (B) 321                (C) 231                    (D) 221 
 
1 
14. If ?ABC ~?DEF, AB=6cm, DE=9cm, EF=6cm and FD=12cm, then the perimeter of 
?ABC is 
 
(A) 28cm           (B) 28.5cm          (C) 18cm                 (D) 23cm 
 
1 
15. If the probability of the letter chosen at random from the letters of the word 
“Mathematics” to be a vowel is 
2
2?? +1
, then ?? is equal to 
 
    (A) 
4
11
                  (B) 
9
4
                   (C) 
11
4
                      (D) 
4
9
 
1 
16. The points A(9,0), B(9, -6) ,C(-9,0) and D(-9,6) are the vertices of a 
 
    (A) Square         (B) Rectangle     (C) Parallelogram    (D) Trapezium 
 
1 
17. The median of a set of 9 distinct observation is 20.5. If each of the observations of a 
set is increased by 2,then the median of a new set  
 
    (A) is increased by 2          
    (B) is decreased by 2    
    (C) is two times the original number     
    (D) Remains same as that of original observations 
 
1 
18. The length of a tangent drawn to a circle of radius 9 cm from a point at a distance of 
41cm from the centre of the circle is 
 
(A) 40cm         (B) 9cm                (C) 41cm                 (D) 50cm 
 
1 
 DIRECTIONS: In the question number 19 and 20, a statement of Assertion (A) is 
followed by a statement of Reason (R). 
 
Choose the correct option: 
 
(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 and 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. 
 
*Please note that the assessment scheme of the Academic Session 2024-25 will continue in the current session i.e. 2025-26
Page 4


Page 1 of 8 
 
MATHEMATICS STANDARD – Code No.041 
SAMPLE QUESTION PAPER  
CLASS – X (2025-26)  
Maximum Marks: 80                                                                                                 Time: 3 hours 
 
 General Instructions: 
 
Read the following instructions carefully and follow them: 
 
1. This question paper contains 38 questions. All Questions are compulsory. 
2. This Question Paper is divided into 5 Sections A, B, C, D and E. 
3. In Section A, Question numbers 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, 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. 
8. There is no overall choice. However, an internal choice in 2 questions 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. Take ?? =
22
7
 wherever required if not stated. 
10. Use of calculators is not allowed. 
 
 
(Section A) 
Section A consists of 20 questions of 1 mark each. 
Q.No. Questions Marks 
 
1. If ?? = 2
2
× 3
?? ,?? = 2
2
× 3 × 5,?? = 2
2
× 3 × 7 and LCM (?? , ?? , ?? ) = 3780, then ?? is 
equal to 
 
(A) 1                 (B) 2                   (C) 3                (D) 0  
 
1 
2. The shortest distance (in units) of the point (2,3) from y-axis is 
 
     (A) 2                  (B) 3                  (C) 5                (D) 1 
 
1 
3. If the lines given by 3x +2ky =2 and 2x+5y +1=0 are not parallel, then k has to be 
 
    (A) 
15
4
                                         (B) ?
15
4
            
    (C) any rational number            (D) any rational number having 4 as denominator 
 
1 
*Please note that the assessment scheme of the Academic Session 2024-25 will continue in the current session i.e. 2025-26
Page 2 of 8 
 
4. A quadrilateral ABCD is drawn to circumscribe a circle. If BC=7cm, CD=4cm and 
AD=3cm, then the length of AB is 
 
(A) 3cm              (B) 4cm             (C) 6cm             (D) 7cm 
 
1 
5. If  ???????? + ???????? = ?? ,then ???????? - ???????? will be 
 
      (A) ??                (B) ?? 2
                  (C) 
2
??                  (D) 
1
?? 
 
1 
6. Which one of the following is not a quadratic equation? 
 
      (A) (?? +2)
2
 =2(?? +3)                                       (B) ?? 2
 +3?? =(- 1)(1- 3?? )
2
  
     (C) ?? 3 
- ?? 2
 +2 ?? +1 =( ?? +1)
3
                           (D) ( ?? +2)( ?? +1)  = ?? 2
+ 2?? +3 
 
1 
7. Given below is the picture of the Olympic rings made by taking five congruent circles 
of radius 1cm each, intersecting in such a way that the chord formed by joining the 
point of intersection of two circles is also of length 1cm.Total area of all the dotted 
regions (assuming the thickness of the rings to be negligible) is 
 
 
 
 
 
 
 
 
(A) 4[
?? 12
 - 
v3
4
 ] cm
2
                                    (B) [
?? 6
 - 
v3
4
 ] cm
2
     
(C) 4[
?? 6
 - 
v3
4
 ] cm
2                                                       
(D) 8[
?? 6
 - 
v3
4
 ] cm
2    
 
For Visually Impaired candidates 
 
The area of the circle that can be inscribed in a square of 6 cm is 
 
(A) 36?? cm
2 
          (B) 18?? cm
2               
(C) 12?? cm
2   
        (D) 9?? cm
2
 
 
1 
8. A pair of dice is tossed. The probability of not getting the sum eight is 
 
       (A) 
5
36
                (B) 
31
36
                 (C) 
5
18
                  (D) 
5
9
 
1 
9. 
If 2sin5?? = v3 ,0°= ?? =90
o
, then ?? is equal to  
          
        (A) 10
o
               (B) 12
o
            (C) 20
o
                 (D) 50
o
 
1 
10. The sum of two numbers is 1215 and their HCF is 81, then the possible pairs of such 
numbers are 
 
(A) 2                   (B) 3                 (C ) 4                      (D) 5 
1 
*Please note that the assessment scheme of the Academic Session 2024-25 will continue in the current session i.e. 2025-26
Page 3 of 8 
 
11. If the area of the base of a right circular cone is 51cm
2
 and it's volume is 85cm
2
, then 
the height of the cone is given as 
 
(A) 
5
6
 cm           (B) 
5
3
cm              (C) 
5
2
cm                     (D) 5cm 
 
1 
12. If zeroes of the quadratic polynomial a?? 2 
 + b?? +c (a, c ?0) are equal, then 
 
    (A) c and b must have opposite signs         (B) c and a must have opposite signs    
    (C)  c and b must have same signs            (D) c and a must have same signs   
  
1 
13. The area (in cm
2
) of a sector of a circle of radius 21cm cut off by an arc of length 
22cm is 
 
(A) 441             (B) 321                (C) 231                    (D) 221 
 
1 
14. If ?ABC ~?DEF, AB=6cm, DE=9cm, EF=6cm and FD=12cm, then the perimeter of 
?ABC is 
 
(A) 28cm           (B) 28.5cm          (C) 18cm                 (D) 23cm 
 
1 
15. If the probability of the letter chosen at random from the letters of the word 
“Mathematics” to be a vowel is 
2
2?? +1
, then ?? is equal to 
 
    (A) 
4
11
                  (B) 
9
4
                   (C) 
11
4
                      (D) 
4
9
 
1 
16. The points A(9,0), B(9, -6) ,C(-9,0) and D(-9,6) are the vertices of a 
 
    (A) Square         (B) Rectangle     (C) Parallelogram    (D) Trapezium 
 
1 
17. The median of a set of 9 distinct observation is 20.5. If each of the observations of a 
set is increased by 2,then the median of a new set  
 
    (A) is increased by 2          
    (B) is decreased by 2    
    (C) is two times the original number     
    (D) Remains same as that of original observations 
 
1 
18. The length of a tangent drawn to a circle of radius 9 cm from a point at a distance of 
41cm from the centre of the circle is 
 
(A) 40cm         (B) 9cm                (C) 41cm                 (D) 50cm 
 
1 
 DIRECTIONS: In the question number 19 and 20, a statement of Assertion (A) is 
followed by a statement of Reason (R). 
 
Choose the correct option: 
 
(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 and 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. 
 
*Please note that the assessment scheme of the Academic Session 2024-25 will continue in the current session i.e. 2025-26
Page 4 of 8 
 
19. Assertion (A): The number 5
n
 cannot end with the digit 0, where n is a natural 
number 
Reason (R): A number ends with 0, if its prime factorization contains both 2 and 5 
 
1 
20. Assertion (A): If cosA + cos
2
A=1, then sin
2
A + sin
4
A =1 
Reason (R):  sin
2
A + cos
2
A =1 
 
1 
                                                                (Section – B) 
Section B consists of 5 questions of 2 marks each. 
21.(A) 
 
 
(B) 
The A.P 8, 10, 12,……. has 60 terms. Find the sum of last 10 terms. 
 
                                         OR 
 
Find the middle term of A.P 6,13, 20, ……., 230 
2 
22. 
If ?????? (?? + ?? ) = 1 and ?????? (?? - ?? ) = 
v3
2
 ,0° < ?? , ?? < 90°, find the measure of 
angles ?? and ?? . 
2 
23. If AP and DQ are medians of triangles ABC and DEF respectively, where  
?ABC~ ?DEF, then prove that 
????
????
   = 
????
????
      
 
2 
24. 
(A) 
 
 
 
(B) 
A horse, a cow and a goat are tied, each by ropes of length 14m, at the corners A, B 
and C respectively, of a grassy triangular field ABC with sides of lengths 35m, 40m 
and 50 m. Find the area of grass field that can be grazed by them. 
 
                                                   OR 
Find the area of the major segment (in terms of ?? ) of a circle of radius 5cm, formed 
by a chord subtending an angle of 90° at the centre. 
 
2 
25. 
 
 
A ?ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD 
and DC are of lengths 10 cm and 8 cm respectively. Find the lengths of the sides AB 
and AC, if it is given that ar(?ABC) = 90cm
2 
 
For Visually Impaired candidates: 
 
A circle is inscribed in a right-angled triangle ABC, right angled at B. If BC=7cm and 
AB=24cm, find the radius of the circle 
2 
*Please note that the assessment scheme of the Academic Session 2024-25 will continue in the current session i.e. 2025-26
Page 5


Page 1 of 8 
 
MATHEMATICS STANDARD – Code No.041 
SAMPLE QUESTION PAPER  
CLASS – X (2025-26)  
Maximum Marks: 80                                                                                                 Time: 3 hours 
 
 General Instructions: 
 
Read the following instructions carefully and follow them: 
 
1. This question paper contains 38 questions. All Questions are compulsory. 
2. This Question Paper is divided into 5 Sections A, B, C, D and E. 
3. In Section A, Question numbers 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, 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. 
8. There is no overall choice. However, an internal choice in 2 questions 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. Take ?? =
22
7
 wherever required if not stated. 
10. Use of calculators is not allowed. 
 
 
(Section A) 
Section A consists of 20 questions of 1 mark each. 
Q.No. Questions Marks 
 
1. If ?? = 2
2
× 3
?? ,?? = 2
2
× 3 × 5,?? = 2
2
× 3 × 7 and LCM (?? , ?? , ?? ) = 3780, then ?? is 
equal to 
 
(A) 1                 (B) 2                   (C) 3                (D) 0  
 
1 
2. The shortest distance (in units) of the point (2,3) from y-axis is 
 
     (A) 2                  (B) 3                  (C) 5                (D) 1 
 
1 
3. If the lines given by 3x +2ky =2 and 2x+5y +1=0 are not parallel, then k has to be 
 
    (A) 
15
4
                                         (B) ?
15
4
            
    (C) any rational number            (D) any rational number having 4 as denominator 
 
1 
*Please note that the assessment scheme of the Academic Session 2024-25 will continue in the current session i.e. 2025-26
Page 2 of 8 
 
4. A quadrilateral ABCD is drawn to circumscribe a circle. If BC=7cm, CD=4cm and 
AD=3cm, then the length of AB is 
 
(A) 3cm              (B) 4cm             (C) 6cm             (D) 7cm 
 
1 
5. If  ???????? + ???????? = ?? ,then ???????? - ???????? will be 
 
      (A) ??                (B) ?? 2
                  (C) 
2
??                  (D) 
1
?? 
 
1 
6. Which one of the following is not a quadratic equation? 
 
      (A) (?? +2)
2
 =2(?? +3)                                       (B) ?? 2
 +3?? =(- 1)(1- 3?? )
2
  
     (C) ?? 3 
- ?? 2
 +2 ?? +1 =( ?? +1)
3
                           (D) ( ?? +2)( ?? +1)  = ?? 2
+ 2?? +3 
 
1 
7. Given below is the picture of the Olympic rings made by taking five congruent circles 
of radius 1cm each, intersecting in such a way that the chord formed by joining the 
point of intersection of two circles is also of length 1cm.Total area of all the dotted 
regions (assuming the thickness of the rings to be negligible) is 
 
 
 
 
 
 
 
 
(A) 4[
?? 12
 - 
v3
4
 ] cm
2
                                    (B) [
?? 6
 - 
v3
4
 ] cm
2
     
(C) 4[
?? 6
 - 
v3
4
 ] cm
2                                                       
(D) 8[
?? 6
 - 
v3
4
 ] cm
2    
 
For Visually Impaired candidates 
 
The area of the circle that can be inscribed in a square of 6 cm is 
 
(A) 36?? cm
2 
          (B) 18?? cm
2               
(C) 12?? cm
2   
        (D) 9?? cm
2
 
 
1 
8. A pair of dice is tossed. The probability of not getting the sum eight is 
 
       (A) 
5
36
                (B) 
31
36
                 (C) 
5
18
                  (D) 
5
9
 
1 
9. 
If 2sin5?? = v3 ,0°= ?? =90
o
, then ?? is equal to  
          
        (A) 10
o
               (B) 12
o
            (C) 20
o
                 (D) 50
o
 
1 
10. The sum of two numbers is 1215 and their HCF is 81, then the possible pairs of such 
numbers are 
 
(A) 2                   (B) 3                 (C ) 4                      (D) 5 
1 
*Please note that the assessment scheme of the Academic Session 2024-25 will continue in the current session i.e. 2025-26
Page 3 of 8 
 
11. If the area of the base of a right circular cone is 51cm
2
 and it's volume is 85cm
2
, then 
the height of the cone is given as 
 
(A) 
5
6
 cm           (B) 
5
3
cm              (C) 
5
2
cm                     (D) 5cm 
 
1 
12. If zeroes of the quadratic polynomial a?? 2 
 + b?? +c (a, c ?0) are equal, then 
 
    (A) c and b must have opposite signs         (B) c and a must have opposite signs    
    (C)  c and b must have same signs            (D) c and a must have same signs   
  
1 
13. The area (in cm
2
) of a sector of a circle of radius 21cm cut off by an arc of length 
22cm is 
 
(A) 441             (B) 321                (C) 231                    (D) 221 
 
1 
14. If ?ABC ~?DEF, AB=6cm, DE=9cm, EF=6cm and FD=12cm, then the perimeter of 
?ABC is 
 
(A) 28cm           (B) 28.5cm          (C) 18cm                 (D) 23cm 
 
1 
15. If the probability of the letter chosen at random from the letters of the word 
“Mathematics” to be a vowel is 
2
2?? +1
, then ?? is equal to 
 
    (A) 
4
11
                  (B) 
9
4
                   (C) 
11
4
                      (D) 
4
9
 
1 
16. The points A(9,0), B(9, -6) ,C(-9,0) and D(-9,6) are the vertices of a 
 
    (A) Square         (B) Rectangle     (C) Parallelogram    (D) Trapezium 
 
1 
17. The median of a set of 9 distinct observation is 20.5. If each of the observations of a 
set is increased by 2,then the median of a new set  
 
    (A) is increased by 2          
    (B) is decreased by 2    
    (C) is two times the original number     
    (D) Remains same as that of original observations 
 
1 
18. The length of a tangent drawn to a circle of radius 9 cm from a point at a distance of 
41cm from the centre of the circle is 
 
(A) 40cm         (B) 9cm                (C) 41cm                 (D) 50cm 
 
1 
 DIRECTIONS: In the question number 19 and 20, a statement of Assertion (A) is 
followed by a statement of Reason (R). 
 
Choose the correct option: 
 
(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 and 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. 
 
*Please note that the assessment scheme of the Academic Session 2024-25 will continue in the current session i.e. 2025-26
Page 4 of 8 
 
19. Assertion (A): The number 5
n
 cannot end with the digit 0, where n is a natural 
number 
Reason (R): A number ends with 0, if its prime factorization contains both 2 and 5 
 
1 
20. Assertion (A): If cosA + cos
2
A=1, then sin
2
A + sin
4
A =1 
Reason (R):  sin
2
A + cos
2
A =1 
 
1 
                                                                (Section – B) 
Section B consists of 5 questions of 2 marks each. 
21.(A) 
 
 
(B) 
The A.P 8, 10, 12,……. has 60 terms. Find the sum of last 10 terms. 
 
                                         OR 
 
Find the middle term of A.P 6,13, 20, ……., 230 
2 
22. 
If ?????? (?? + ?? ) = 1 and ?????? (?? - ?? ) = 
v3
2
 ,0° < ?? , ?? < 90°, find the measure of 
angles ?? and ?? . 
2 
23. If AP and DQ are medians of triangles ABC and DEF respectively, where  
?ABC~ ?DEF, then prove that 
????
????
   = 
????
????
      
 
2 
24. 
(A) 
 
 
 
(B) 
A horse, a cow and a goat are tied, each by ropes of length 14m, at the corners A, B 
and C respectively, of a grassy triangular field ABC with sides of lengths 35m, 40m 
and 50 m. Find the area of grass field that can be grazed by them. 
 
                                                   OR 
Find the area of the major segment (in terms of ?? ) of a circle of radius 5cm, formed 
by a chord subtending an angle of 90° at the centre. 
 
2 
25. 
 
 
A ?ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD 
and DC are of lengths 10 cm and 8 cm respectively. Find the lengths of the sides AB 
and AC, if it is given that ar(?ABC) = 90cm
2 
 
For Visually Impaired candidates: 
 
A circle is inscribed in a right-angled triangle ABC, right angled at B. If BC=7cm and 
AB=24cm, find the radius of the circle 
2 
*Please note that the assessment scheme of the Academic Session 2024-25 will continue in the current session i.e. 2025-26
Page 5 of 8 
 
(Section – C)  
Section C consists of 6 questions of 3 marks each. 
26. In Figure, XY and X'Y' are two parallel tangents to a 
circle with centre O and another tangent AB with 
point of contact C intersecting XY at A and X'Y' at B.  
Prove that ? AOB = 90° 
 
 
 
 
For Visually Impaired candidates: 
 
Two tangents PA and PB are drawn to a circle with centre O from an external point 
P. Prove that ?APB= 2(?OAB) 
 
3 
27. In a workshop, the number of teachers of English, Hindi and Science are 36, 60 and 
84 respectively. Find the minimum number of rooms required, if in each room the 
same number of teachers are to be seated and all of them being of the same subject.  
3 
28. 
Find the zeroes of the quadratic polynomial 2?? 2
 – (1 + 2v2) ?? + v2 and verify the 
relationship between the zeroes and coefficents of the polynomial. 
3 
29. 
If ???????? + ???????? = v3 ,then prove that ???????? + ???????? = 1 
                                   OR 
Prove that 
???????? -???????? +1
???????? +???????? -1
 =cosecA + cotA  
3 
30. On a particular day, Vidhi and Unnati couldn’t decide on who would get to drive the 
car. They had one coin each and flipped their coin exactly three times. The following 
was agreed upon: 
 
1. If Vidhi gets two heads in a row, she would drive the car 
2. If Unnati gets a head immediately followed by a tail, she would drive the car. 
 
Who has greater probability to drive the car that day? Justify your answer. 
 
3 
31.(A) 
 
 
 
 
(B) 
 The monthly income of Aryan and Babban are in the ratio 3:4 and their monthly 
expenditures are in ratio 5:7. If each saves ? 15,000 per month, find their monthly 
incomes. 
                                                   OR  
 
Solve the following system of equations graphically: 
 
2?? + ?? =6, 2 ?? – ?? – 2=0. Find the area of the triangle so formed by two lines and ?? -
axis.     
 
For Visually Impaired candidates:  
 
Five years hence, fathers age will be three times the age of son. Five years ago, 
father was seven times as old as his son. Find their present ages.                                            
3 
*Please note that the assessment scheme of the Academic Session 2024-25 will continue in the current session i.e. 2025-26