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1 
                                                      SAMPLE QUESTION PAPER  
Class X Session 2024-25  
MATHEMATICS BASIC (Code No.241)  
TIME: 3 hours                                                                                                      MAX.MARKS: 80 
 
General Instructions: 
Read the following instructions carefully and follow them: 
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 Questions of section B, 2 
Questions of section C and 2 Questions of section D has been provided. And internal choice has 
been provided in all the 2 marks questions of Section E.  
9. Draw neat and clean figures wherever required.  
10. Take p =22/7 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. 
HCF OF (3
3
× 5
2
× 2), (3
2
× 5
3
× 2
2
) ?????? (3
4
× 5 × 2
3
) is  
(A) 450                      (B)  90                   (C) 180                              (D) 630 
1 
2. 
The system of linear equations represented by the lines l and m is  
 
(A) consistent with unique solution               (B) inconsistent  
(C) consistent with three solutions               (D) consistent with many solutions  
1 
3. 
The value of k for which the quadratic equation ?? ?? 2
- 5?? + 1 = 0 does not have 
a real solution, is  
(A) 0                      (B)  
25
4
                   (C) 
4
25
                               (D) 7 
1 
Page 2


1 
                                                      SAMPLE QUESTION PAPER  
Class X Session 2024-25  
MATHEMATICS BASIC (Code No.241)  
TIME: 3 hours                                                                                                      MAX.MARKS: 80 
 
General Instructions: 
Read the following instructions carefully and follow them: 
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 Questions of section B, 2 
Questions of section C and 2 Questions of section D has been provided. And internal choice has 
been provided in all the 2 marks questions of Section E.  
9. Draw neat and clean figures wherever required.  
10. Take p =22/7 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. 
HCF OF (3
3
× 5
2
× 2), (3
2
× 5
3
× 2
2
) ?????? (3
4
× 5 × 2
3
) is  
(A) 450                      (B)  90                   (C) 180                              (D) 630 
1 
2. 
The system of linear equations represented by the lines l and m is  
 
(A) consistent with unique solution               (B) inconsistent  
(C) consistent with three solutions               (D) consistent with many solutions  
1 
3. 
The value of k for which the quadratic equation ?? ?? 2
- 5?? + 1 = 0 does not have 
a real solution, is  
(A) 0                      (B)  
25
4
                   (C) 
4
25
                               (D) 7 
1 
2 
4. 
The distance between the points (?? , ?? ) and (-?? , -?? ) is  
(A)v?? 2
+ ?? 2
           (B)  ?? 2
+ ?? 2
            (C) 2 v?? 2
+ ?? 2
                  (D) 4v?? 2
+ ?? 2
  
1 
5. 
In the given figure, PQ and PR are tangents to a circle centred at O. If  
?QPR=35
°
 then ?QOR is equal to  
 
  (A)  70
°
                   (B)  90
°
                  (C) 135
°
                             (D) 145
°
 
1 
6. 
 If ? ?????? ~? ?????? such that 3AB = 2PQ and BC=10 cm, then length QR is 
equal to  
(A) 10 cm                 (B)  15 cm              (C) 
20
3
 cm                            (D) 30 cm 
1 
7. 
 If 3 cot?? =4, where 0° < ?? < 90°, then sec?? is equal to  
(A) 
5
4
                          (B)  
4
3
                   (C) 
5
3
                               (D) 
3
4
 
1 
8. 
In the given figure, ???????? is similar to  
 
 
(A) ????????                   (B) ????????               (C) ????????                         (D) ???????? 
1 
9. 
 If H.C.F(420,189) = 21 then L.C.M(420,189) is 
(A) 420                      (B)  1890                   (C) 3780                   (D) 3680 
1 
10. 
The  4
?? h
 term from the end of the A.P -8, -5, -2, … ,49 is  
(A) 37                      (B)  40                   (C) 1                             (D) 43 
1 
11. 
In the given figure, if ? ?????? ~? ?????? then ??????? is equal to 
1 
Page 3


1 
                                                      SAMPLE QUESTION PAPER  
Class X Session 2024-25  
MATHEMATICS BASIC (Code No.241)  
TIME: 3 hours                                                                                                      MAX.MARKS: 80 
 
General Instructions: 
Read the following instructions carefully and follow them: 
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 Questions of section B, 2 
Questions of section C and 2 Questions of section D has been provided. And internal choice has 
been provided in all the 2 marks questions of Section E.  
9. Draw neat and clean figures wherever required.  
10. Take p =22/7 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. 
HCF OF (3
3
× 5
2
× 2), (3
2
× 5
3
× 2
2
) ?????? (3
4
× 5 × 2
3
) is  
(A) 450                      (B)  90                   (C) 180                              (D) 630 
1 
2. 
The system of linear equations represented by the lines l and m is  
 
(A) consistent with unique solution               (B) inconsistent  
(C) consistent with three solutions               (D) consistent with many solutions  
1 
3. 
The value of k for which the quadratic equation ?? ?? 2
- 5?? + 1 = 0 does not have 
a real solution, is  
(A) 0                      (B)  
25
4
                   (C) 
4
25
                               (D) 7 
1 
2 
4. 
The distance between the points (?? , ?? ) and (-?? , -?? ) is  
(A)v?? 2
+ ?? 2
           (B)  ?? 2
+ ?? 2
            (C) 2 v?? 2
+ ?? 2
                  (D) 4v?? 2
+ ?? 2
  
1 
5. 
In the given figure, PQ and PR are tangents to a circle centred at O. If  
?QPR=35
°
 then ?QOR is equal to  
 
  (A)  70
°
                   (B)  90
°
                  (C) 135
°
                             (D) 145
°
 
1 
6. 
 If ? ?????? ~? ?????? such that 3AB = 2PQ and BC=10 cm, then length QR is 
equal to  
(A) 10 cm                 (B)  15 cm              (C) 
20
3
 cm                            (D) 30 cm 
1 
7. 
 If 3 cot?? =4, where 0° < ?? < 90°, then sec?? is equal to  
(A) 
5
4
                          (B)  
4
3
                   (C) 
5
3
                               (D) 
3
4
 
1 
8. 
In the given figure, ???????? is similar to  
 
 
(A) ????????                   (B) ????????               (C) ????????                         (D) ???????? 
1 
9. 
 If H.C.F(420,189) = 21 then L.C.M(420,189) is 
(A) 420                      (B)  1890                   (C) 3780                   (D) 3680 
1 
10. 
The  4
?? h
 term from the end of the A.P -8, -5, -2, … ,49 is  
(A) 37                      (B)  40                   (C) 1                             (D) 43 
1 
11. 
In the given figure, if ? ?????? ~? ?????? then ??????? is equal to 
1 
3 
 
   (A)  58
°
                   (B)  55
°
                  (C) 128
°
                             (D) 52
°
 
12. 
 If perimeter of given triangle is 38 cm, then length AP is equal to 
 
 (A)19 cm                    (B)  5 cm                   (C) 10 cm                         (D)8 cm 
1 
13. 
 
1-?????? 2
30
°
1+?????? 2
30
°
 is equal to 
(A) cos60
°
                       (B) sin60
°
                  (C) 1                    (D) ?????? 2
60
°
 
1 
14. 
The total surface area of solid hemisphere of radius ?? is  
(A) ?? ?? 2
                            (B) 2?? ?? 2
                    (C) 3?? ?? 2
                (D) 4?? ?? 2
 
1 
15. 
 Which of the following cannot be the probability of an event? 
(A) 0.4                             (B) 4%                      (C) 0.04%                (D) 4 
1 
16. 
The roots of quadratic equation 3?? 2
- 4v3?? + 4 = 0 are  
(A) not real                                    (B) real and equal             
(C) rational and distinct                 (D) irrational and distinct 
1 
17. 
 The following distribution shows the marks distribution of 80 students. 
 
Marks Below 10 Below 20 Below 30 Below 40 Below 50 Below 60 
No. of 
students 
2 12 28 56 76 80 
 
The median class is  
(A) 20-30                      (B) 40-50                    (C) 30-40                   (D) 10-20 
1 
18. 
A quadratic polynomial whose zeroes are 
2
5
 ?????? 
-1
5
 is 
(A) 25?? 2
+ 5?? - 2                       (B) 5?? 2
- 2?? + 1 
(C) 5?? 2
+ 2?? - 1                        (D) 25?? 2
- 5?? - 2 
1 
Page 4


1 
                                                      SAMPLE QUESTION PAPER  
Class X Session 2024-25  
MATHEMATICS BASIC (Code No.241)  
TIME: 3 hours                                                                                                      MAX.MARKS: 80 
 
General Instructions: 
Read the following instructions carefully and follow them: 
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 Questions of section B, 2 
Questions of section C and 2 Questions of section D has been provided. And internal choice has 
been provided in all the 2 marks questions of Section E.  
9. Draw neat and clean figures wherever required.  
10. Take p =22/7 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. 
HCF OF (3
3
× 5
2
× 2), (3
2
× 5
3
× 2
2
) ?????? (3
4
× 5 × 2
3
) is  
(A) 450                      (B)  90                   (C) 180                              (D) 630 
1 
2. 
The system of linear equations represented by the lines l and m is  
 
(A) consistent with unique solution               (B) inconsistent  
(C) consistent with three solutions               (D) consistent with many solutions  
1 
3. 
The value of k for which the quadratic equation ?? ?? 2
- 5?? + 1 = 0 does not have 
a real solution, is  
(A) 0                      (B)  
25
4
                   (C) 
4
25
                               (D) 7 
1 
2 
4. 
The distance between the points (?? , ?? ) and (-?? , -?? ) is  
(A)v?? 2
+ ?? 2
           (B)  ?? 2
+ ?? 2
            (C) 2 v?? 2
+ ?? 2
                  (D) 4v?? 2
+ ?? 2
  
1 
5. 
In the given figure, PQ and PR are tangents to a circle centred at O. If  
?QPR=35
°
 then ?QOR is equal to  
 
  (A)  70
°
                   (B)  90
°
                  (C) 135
°
                             (D) 145
°
 
1 
6. 
 If ? ?????? ~? ?????? such that 3AB = 2PQ and BC=10 cm, then length QR is 
equal to  
(A) 10 cm                 (B)  15 cm              (C) 
20
3
 cm                            (D) 30 cm 
1 
7. 
 If 3 cot?? =4, where 0° < ?? < 90°, then sec?? is equal to  
(A) 
5
4
                          (B)  
4
3
                   (C) 
5
3
                               (D) 
3
4
 
1 
8. 
In the given figure, ???????? is similar to  
 
 
(A) ????????                   (B) ????????               (C) ????????                         (D) ???????? 
1 
9. 
 If H.C.F(420,189) = 21 then L.C.M(420,189) is 
(A) 420                      (B)  1890                   (C) 3780                   (D) 3680 
1 
10. 
The  4
?? h
 term from the end of the A.P -8, -5, -2, … ,49 is  
(A) 37                      (B)  40                   (C) 1                             (D) 43 
1 
11. 
In the given figure, if ? ?????? ~? ?????? then ??????? is equal to 
1 
3 
 
   (A)  58
°
                   (B)  55
°
                  (C) 128
°
                             (D) 52
°
 
12. 
 If perimeter of given triangle is 38 cm, then length AP is equal to 
 
 (A)19 cm                    (B)  5 cm                   (C) 10 cm                         (D)8 cm 
1 
13. 
 
1-?????? 2
30
°
1+?????? 2
30
°
 is equal to 
(A) cos60
°
                       (B) sin60
°
                  (C) 1                    (D) ?????? 2
60
°
 
1 
14. 
The total surface area of solid hemisphere of radius ?? is  
(A) ?? ?? 2
                            (B) 2?? ?? 2
                    (C) 3?? ?? 2
                (D) 4?? ?? 2
 
1 
15. 
 Which of the following cannot be the probability of an event? 
(A) 0.4                             (B) 4%                      (C) 0.04%                (D) 4 
1 
16. 
The roots of quadratic equation 3?? 2
- 4v3?? + 4 = 0 are  
(A) not real                                    (B) real and equal             
(C) rational and distinct                 (D) irrational and distinct 
1 
17. 
 The following distribution shows the marks distribution of 80 students. 
 
Marks Below 10 Below 20 Below 30 Below 40 Below 50 Below 60 
No. of 
students 
2 12 28 56 76 80 
 
The median class is  
(A) 20-30                      (B) 40-50                    (C) 30-40                   (D) 10-20 
1 
18. 
A quadratic polynomial whose zeroes are 
2
5
 ?????? 
-1
5
 is 
(A) 25?? 2
+ 5?? - 2                       (B) 5?? 2
- 2?? + 1 
(C) 5?? 2
+ 2?? - 1                        (D) 25?? 2
- 5?? - 2 
1 
4 
 DIRECTION: 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.  
 
19. 
Assertion(A): The sequence -1, -1 - 1, . . . , -1 is an AP. 
Reason(R): In an AP, ?? ?? - ?? ?? -1
 is constant where ?? = 2 and ?? ? ?? 
1 
20. 
Assertion(A): (2 + v3)v3 is an irrational number. 
Reason(R): Product of two irrational numbers is always irrational. 
1 
 
                                              Section B 
 
 
                            Section B consists of 5 questions of 2 marks each.  
 
21 (A). 
 
?? (?? , ?? ) is a point equidistant from the points ?? (4,3) and ?? (3,4). Prove that ?? -
?? = 0. 
2 
 
OR 
 
21 (B). 
In the given figure, ???????? is an equilateral triangle. Coordinates of vertices A 
and B are (0,3) and (0, -3) respectively. Find the coordinates of points C. 
                             
 
22. 
In two concentric circles, a chord of length 8 cm of the larger circle touches the 
smaller circle. If the radius of the larger circle is 5 cm, then find the radius of the 
smaller circle. 
2 
23 (A). 
 
The sum of the first 12 terms of an A.P. is 900. If its first term is 20 then find the 
common difference and 12
th
 term. 
2 
 
OR 
 
23 (B). 
The sum of first ?? terms of an A.P. is represented by ?? ?? = 6?? - ?? 2
. Find the 
common difference. 
 
24. 
If ?????? (?? - ?? ) =
1
2
 ?????? ?????? (?? + ?? ) =
1
2
, 0
°
< ?? + ?? < 90
°
 ?????? ?? > ?? , then find the 
values of ?? and ?? . 
2 
Page 5


1 
                                                      SAMPLE QUESTION PAPER  
Class X Session 2024-25  
MATHEMATICS BASIC (Code No.241)  
TIME: 3 hours                                                                                                      MAX.MARKS: 80 
 
General Instructions: 
Read the following instructions carefully and follow them: 
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 Questions of section B, 2 
Questions of section C and 2 Questions of section D has been provided. And internal choice has 
been provided in all the 2 marks questions of Section E.  
9. Draw neat and clean figures wherever required.  
10. Take p =22/7 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. 
HCF OF (3
3
× 5
2
× 2), (3
2
× 5
3
× 2
2
) ?????? (3
4
× 5 × 2
3
) is  
(A) 450                      (B)  90                   (C) 180                              (D) 630 
1 
2. 
The system of linear equations represented by the lines l and m is  
 
(A) consistent with unique solution               (B) inconsistent  
(C) consistent with three solutions               (D) consistent with many solutions  
1 
3. 
The value of k for which the quadratic equation ?? ?? 2
- 5?? + 1 = 0 does not have 
a real solution, is  
(A) 0                      (B)  
25
4
                   (C) 
4
25
                               (D) 7 
1 
2 
4. 
The distance between the points (?? , ?? ) and (-?? , -?? ) is  
(A)v?? 2
+ ?? 2
           (B)  ?? 2
+ ?? 2
            (C) 2 v?? 2
+ ?? 2
                  (D) 4v?? 2
+ ?? 2
  
1 
5. 
In the given figure, PQ and PR are tangents to a circle centred at O. If  
?QPR=35
°
 then ?QOR is equal to  
 
  (A)  70
°
                   (B)  90
°
                  (C) 135
°
                             (D) 145
°
 
1 
6. 
 If ? ?????? ~? ?????? such that 3AB = 2PQ and BC=10 cm, then length QR is 
equal to  
(A) 10 cm                 (B)  15 cm              (C) 
20
3
 cm                            (D) 30 cm 
1 
7. 
 If 3 cot?? =4, where 0° < ?? < 90°, then sec?? is equal to  
(A) 
5
4
                          (B)  
4
3
                   (C) 
5
3
                               (D) 
3
4
 
1 
8. 
In the given figure, ???????? is similar to  
 
 
(A) ????????                   (B) ????????               (C) ????????                         (D) ???????? 
1 
9. 
 If H.C.F(420,189) = 21 then L.C.M(420,189) is 
(A) 420                      (B)  1890                   (C) 3780                   (D) 3680 
1 
10. 
The  4
?? h
 term from the end of the A.P -8, -5, -2, … ,49 is  
(A) 37                      (B)  40                   (C) 1                             (D) 43 
1 
11. 
In the given figure, if ? ?????? ~? ?????? then ??????? is equal to 
1 
3 
 
   (A)  58
°
                   (B)  55
°
                  (C) 128
°
                             (D) 52
°
 
12. 
 If perimeter of given triangle is 38 cm, then length AP is equal to 
 
 (A)19 cm                    (B)  5 cm                   (C) 10 cm                         (D)8 cm 
1 
13. 
 
1-?????? 2
30
°
1+?????? 2
30
°
 is equal to 
(A) cos60
°
                       (B) sin60
°
                  (C) 1                    (D) ?????? 2
60
°
 
1 
14. 
The total surface area of solid hemisphere of radius ?? is  
(A) ?? ?? 2
                            (B) 2?? ?? 2
                    (C) 3?? ?? 2
                (D) 4?? ?? 2
 
1 
15. 
 Which of the following cannot be the probability of an event? 
(A) 0.4                             (B) 4%                      (C) 0.04%                (D) 4 
1 
16. 
The roots of quadratic equation 3?? 2
- 4v3?? + 4 = 0 are  
(A) not real                                    (B) real and equal             
(C) rational and distinct                 (D) irrational and distinct 
1 
17. 
 The following distribution shows the marks distribution of 80 students. 
 
Marks Below 10 Below 20 Below 30 Below 40 Below 50 Below 60 
No. of 
students 
2 12 28 56 76 80 
 
The median class is  
(A) 20-30                      (B) 40-50                    (C) 30-40                   (D) 10-20 
1 
18. 
A quadratic polynomial whose zeroes are 
2
5
 ?????? 
-1
5
 is 
(A) 25?? 2
+ 5?? - 2                       (B) 5?? 2
- 2?? + 1 
(C) 5?? 2
+ 2?? - 1                        (D) 25?? 2
- 5?? - 2 
1 
4 
 DIRECTION: 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.  
 
19. 
Assertion(A): The sequence -1, -1 - 1, . . . , -1 is an AP. 
Reason(R): In an AP, ?? ?? - ?? ?? -1
 is constant where ?? = 2 and ?? ? ?? 
1 
20. 
Assertion(A): (2 + v3)v3 is an irrational number. 
Reason(R): Product of two irrational numbers is always irrational. 
1 
 
                                              Section B 
 
 
                            Section B consists of 5 questions of 2 marks each.  
 
21 (A). 
 
?? (?? , ?? ) is a point equidistant from the points ?? (4,3) and ?? (3,4). Prove that ?? -
?? = 0. 
2 
 
OR 
 
21 (B). 
In the given figure, ???????? is an equilateral triangle. Coordinates of vertices A 
and B are (0,3) and (0, -3) respectively. Find the coordinates of points C. 
                             
 
22. 
In two concentric circles, a chord of length 8 cm of the larger circle touches the 
smaller circle. If the radius of the larger circle is 5 cm, then find the radius of the 
smaller circle. 
2 
23 (A). 
 
The sum of the first 12 terms of an A.P. is 900. If its first term is 20 then find the 
common difference and 12
th
 term. 
2 
 
OR 
 
23 (B). 
The sum of first ?? terms of an A.P. is represented by ?? ?? = 6?? - ?? 2
. Find the 
common difference. 
 
24. 
If ?????? (?? - ?? ) =
1
2
 ?????? ?????? (?? + ?? ) =
1
2
, 0
°
< ?? + ?? < 90
°
 ?????? ?? > ?? , then find the 
values of ?? and ?? . 
2 
5 
25. 
Calculate mode of the following distribution: 
 
Class  5-10 10-15 15-20 20-25 25-30 30-35 
Frequency  5 6 15 10 5 4 
 
 
2 
 
Section C 
 
 
Section C consists of 6 questions of 3 marks each. 
 
26. 
 Prove that v5 is an irrational number. 
 
3 
27 (A). 
 
Find the ratio in which the y-axis divides the line segment joining the points 
(4, -5) and (-1,2). Also find the point of intersection. 
3 
 
OR 
 
27 (B). 
Line 4?? + ?? = 4 divides the line segment joining the points (-2, -1) and (3,5) 
in a certain ratio. Find the ratio. 
 
28. 
Prove that: (???????????? - ???????? )(???????? - ???????? ) =
1
tan ?? +cot ?? . 
3 
29. 
Find the mean using the step deviation method. 
 
Class 0-10 10-20 20-30 30-40 40-50 
Frequency 6 10 15 9 10 
 
3 
30. (A) 
 
 
In the given figure, PA and PB are tangents to a circle centred at O. Prove that 
 (i) OP bisects ???????  (ii) OP is the right bisector of AB.                
                            
                                                                  
3 
 
OR 
 
30 (B). Prove that the lengths of tangents drawn from an external point to a circle are 
equal.  
3 
31. 
The sum of a two-digit number and the number obtained by reversing the order 
of its digits is 99. If ten’s digit is 3 more than the unit’s digit, then find the number. 
3 
 
Section -D 
 
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FAQs on Class 10 Mathematics (Basic): CBSE (Official) Sample Question Paper (2024-25) - Mathematics (Maths) Class 10

1. What are the key topics covered in the Class 10 Mathematics (Basic) syllabus?
Ans. The Class 10 Mathematics (Basic) syllabus typically includes key topics such as real numbers, polynomials, pair of linear equations in two variables, quadratic equations, arithmetic progressions, triangles, coordinate geometry, statistics, and probability. Each of these topics aims to build a solid foundation in mathematical concepts and problem-solving skills.
2. How is the marking scheme structured for the Class 10 Mathematics (Basic) exam?
Ans. The marking scheme for the Class 10 Mathematics (Basic) exam usually consists of a total of 80 marks, divided between theory and practical assessments. The theory part typically includes multiple-choice questions, short-answer questions, and long-answer questions. Additionally, internal assessments and project work may contribute to the overall score, ensuring a comprehensive evaluation of the student's understanding.
3. What types of questions can students expect in the Class 10 Mathematics (Basic) sample question paper?
Ans. Students can expect a variety of question types in the Class 10 Mathematics (Basic) sample question paper, including multiple-choice questions, fill in the blanks, short answer questions, and long answer questions. These questions are designed to test conceptual understanding, application of formulas, and problem-solving abilities across different mathematical topics.
4. How should students prepare for the Class 10 Mathematics (Basic) exam effectively?
Ans. Effective preparation for the Class 10 Mathematics (Basic) exam involves several strategies, such as understanding the syllabus, practicing previous years' question papers, and working on sample papers. Students should focus on clearing concepts, create a study timetable, and regularly revise important formulas and theorems. Group study sessions can also be beneficial for discussing complex topics and solving problems collaboratively.
5. What are the benefits of practicing sample question papers for the Class 10 Mathematics (Basic) exam?
Ans. Practicing sample question papers for the Class 10 Mathematics (Basic) exam offers several benefits, including familiarization with the exam pattern, improved time management skills, and identification of strengths and weaknesses in various topics. Regular practice helps students enhance their problem-solving speed and accuracy, ultimately boosting their confidence before the actual exam.
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