Class 10 Mathematics (Standard): Answer Sheet for 2024 (Set 3) | Mathematics (Maths) Class 10 PDF Download

 Page 1


- 1 - 
 
 
MATHEMATICS (Standard)
 
CBSE Class-X (2024)
 
Answers & Solutions
GENERAL INSTRUCTIONS  
Read the following instructions carefully and 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 numbers 1 to 18 are multiple choice questions (MCQs) and question numbers  
19 and 20 are Assertion–Reason based questions of 1 mark each. 
(iv) In Section B, Question numbers 21 to 25 are very short answer (VSA) type questions, carrying 2 marks each. 
(v) In Section C, Question numbers 26 to 31 are short answer (SA) type questions, carrying 3 marks each. 
(vi) In Section D, Question numbers 32 to 35 are long answer (LA) type questions carrying 5 marks each. 
(vii) In Section E, Question numbers 36 to 38 are case-study based integrated questions carrying 4 marks 
each. Internal choice is provided in 2 marks question in each case-study. 
(viii) There is no overall choice. However, an internal choice has been provided in 2 questions in Section B,  
2 questions in Section C, 2 questions in Section D and 3 questions of 2 marks in Section E. 
(ix) Draw neat diagrams wherever required. Take ? = 22/7 wherever required, if not stated. 
(x) Use of calculators is NOT allowed.
 
Question Paper Code 
30/1/3 
SET-3 
Time: 3 Hrs. Max. Marks: 80 
Page 2


- 1 - 
 
 
MATHEMATICS (Standard)
 
CBSE Class-X (2024)
 
Answers & Solutions
GENERAL INSTRUCTIONS  
Read the following instructions carefully and 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 numbers 1 to 18 are multiple choice questions (MCQs) and question numbers  
19 and 20 are Assertion–Reason based questions of 1 mark each. 
(iv) In Section B, Question numbers 21 to 25 are very short answer (VSA) type questions, carrying 2 marks each. 
(v) In Section C, Question numbers 26 to 31 are short answer (SA) type questions, carrying 3 marks each. 
(vi) In Section D, Question numbers 32 to 35 are long answer (LA) type questions carrying 5 marks each. 
(vii) In Section E, Question numbers 36 to 38 are case-study based integrated questions carrying 4 marks 
each. Internal choice is provided in 2 marks question in each case-study. 
(viii) There is no overall choice. However, an internal choice has been provided in 2 questions in Section B,  
2 questions in Section C, 2 questions in Section D and 3 questions of 2 marks in Section E. 
(ix) Draw neat diagrams wherever required. Take ? = 22/7 wherever required, if not stated. 
(x) Use of calculators is NOT allowed.
 
Question Paper Code 
30/1/3 
SET-3 
Time: 3 Hrs. Max. Marks: 80 
 CBSE Board Exam-2024 (Class X) Mathematics (Standard) 
- 2 - 
SECTION-A 
This section consists of 20 questions of 1 mark each. 
1. If two positive integers p and q can be expressed as p = 18a
2
b
4
 and q = 20a
3
b
2
, where a and b are prime 
numbers, then LCM (p, q) is  [1] 
 (a) 2a
2
b
2
 (b) 180a
2
b
2
 
 (c) 12a
2
b
2
 (d) 180a
3
b
4
 
Answer (d)   [1] 
Sol. 180a
3
b
4
 
2. In an A.P., if the first term (a) = –16 and the common difference (d) = –2, then the sum of first 10 terms is [1] 
 (a) –200 (b) –70 
 (c) –250 (d) 250 
Answer (c)   [1] 
Sol. –250 
3. For some data x
1
, x
2
, ….. x
n
 with respective frequencies f
1
, f
2
, ….. f
n
, the value of ( ) -
?
1
n
ii
f x x is equal to [1] 
 (a) nx (b) 1 
 (c) 
? i
f (d) 0 
Answer (d)   [1] 
Sol. 0 
4. The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm is [1] 
 (a) 
? 4
cu cm
3
 (b) 
? 5
cu cm
3
 
 (c) 
? 8
cu cm
3
 (d) 
? 2
cu cm
3
 
Answer (d)   [1] 
Sol. 
? 2
cu cm
3
 
5. A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres 
taken together, is [1] 
 (a) 1 : 1 (b) 1 : 4 
 (c) 2 : 3 (d) 3 : 2 
Answer (c)   [1] 
Sol. 2 : 3 
6. The centre of a circle is at (2, 0). If one end of a diameter is at (6, 0), then the other end is at [1] 
 (a) (0, 0) (b) (4, 0) 
 (c) (–2, 0) (d) (–6,0) 
Answer (c)   [1] 
Sol. (–2, 0) 
Page 3


- 1 - 
 
 
MATHEMATICS (Standard)
 
CBSE Class-X (2024)
 
Answers & Solutions
GENERAL INSTRUCTIONS  
Read the following instructions carefully and 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 numbers 1 to 18 are multiple choice questions (MCQs) and question numbers  
19 and 20 are Assertion–Reason based questions of 1 mark each. 
(iv) In Section B, Question numbers 21 to 25 are very short answer (VSA) type questions, carrying 2 marks each. 
(v) In Section C, Question numbers 26 to 31 are short answer (SA) type questions, carrying 3 marks each. 
(vi) In Section D, Question numbers 32 to 35 are long answer (LA) type questions carrying 5 marks each. 
(vii) In Section E, Question numbers 36 to 38 are case-study based integrated questions carrying 4 marks 
each. Internal choice is provided in 2 marks question in each case-study. 
(viii) There is no overall choice. However, an internal choice has been provided in 2 questions in Section B,  
2 questions in Section C, 2 questions in Section D and 3 questions of 2 marks in Section E. 
(ix) Draw neat diagrams wherever required. Take ? = 22/7 wherever required, if not stated. 
(x) Use of calculators is NOT allowed.
 
Question Paper Code 
30/1/3 
SET-3 
Time: 3 Hrs. Max. Marks: 80 
 CBSE Board Exam-2024 (Class X) Mathematics (Standard) 
- 2 - 
SECTION-A 
This section consists of 20 questions of 1 mark each. 
1. If two positive integers p and q can be expressed as p = 18a
2
b
4
 and q = 20a
3
b
2
, where a and b are prime 
numbers, then LCM (p, q) is  [1] 
 (a) 2a
2
b
2
 (b) 180a
2
b
2
 
 (c) 12a
2
b
2
 (d) 180a
3
b
4
 
Answer (d)   [1] 
Sol. 180a
3
b
4
 
2. In an A.P., if the first term (a) = –16 and the common difference (d) = –2, then the sum of first 10 terms is [1] 
 (a) –200 (b) –70 
 (c) –250 (d) 250 
Answer (c)   [1] 
Sol. –250 
3. For some data x
1
, x
2
, ….. x
n
 with respective frequencies f
1
, f
2
, ….. f
n
, the value of ( ) -
?
1
n
ii
f x x is equal to [1] 
 (a) nx (b) 1 
 (c) 
? i
f (d) 0 
Answer (d)   [1] 
Sol. 0 
4. The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm is [1] 
 (a) 
? 4
cu cm
3
 (b) 
? 5
cu cm
3
 
 (c) 
? 8
cu cm
3
 (d) 
? 2
cu cm
3
 
Answer (d)   [1] 
Sol. 
? 2
cu cm
3
 
5. A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres 
taken together, is [1] 
 (a) 1 : 1 (b) 1 : 4 
 (c) 2 : 3 (d) 3 : 2 
Answer (c)   [1] 
Sol. 2 : 3 
6. The centre of a circle is at (2, 0). If one end of a diameter is at (6, 0), then the other end is at [1] 
 (a) (0, 0) (b) (4, 0) 
 (c) (–2, 0) (d) (–6,0) 
Answer (c)   [1] 
Sol. (–2, 0) 
CBSE Board Exam-2024 (Class X) Mathematics (Standard) 
- 3 - 
7. One card is drawn at random from a well shuffled deck of 52 playing cards. The probability that it is a red ace 
card, is [1] 
 (a) 
1
13
 (b) 
1
26
 
 (c) 
1
52
 (d) 
1
2
 
Answer (b)   [1] 
Sol. 
1
26
 
8. The middle most observation of every data arranged in order is called [1] 
 (a) mode (b) median 
 (c) mean (d) deviation 
Answer (b)   [1] 
Sol. Median 
9. For ? = 30°, the value of (2 sin ? cos ?) is [1] 
 (a) 1 (b) 
3
2
 
 (c) 
3
4
 (d) 
3
2
 
Answer (b)   [1] 
Sol. 
3
2 sin30 cos30
2
? ? = 
10. If the roots of equation ax
2
 + bx + c = 0, a ? 0 are real and equal, then which of the following relation is true? [1] 
 (a) 
2
=
b
a
c
 (b) b
2
 = ac 
 (c) 
2
4
=
b
ac (d) 
2
=
b
c
a
 
Answer (c)   [1] 
Sol. b
2
 = 4ac 
11. From the data 1, 4, 7, 9, 16, 21, 25, if all the even numbers are removed, then the probability of getting at random 
a prime number from the remaining is [1] 
 (a) 
2
5
 (b) 
1
5
 
 (c) 
1
7
 (d) 
2
7
 
Answer (b)   [1] 
Sol. 
1
5
 
Page 4


- 1 - 
 
 
MATHEMATICS (Standard)
 
CBSE Class-X (2024)
 
Answers & Solutions
GENERAL INSTRUCTIONS  
Read the following instructions carefully and 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 numbers 1 to 18 are multiple choice questions (MCQs) and question numbers  
19 and 20 are Assertion–Reason based questions of 1 mark each. 
(iv) In Section B, Question numbers 21 to 25 are very short answer (VSA) type questions, carrying 2 marks each. 
(v) In Section C, Question numbers 26 to 31 are short answer (SA) type questions, carrying 3 marks each. 
(vi) In Section D, Question numbers 32 to 35 are long answer (LA) type questions carrying 5 marks each. 
(vii) In Section E, Question numbers 36 to 38 are case-study based integrated questions carrying 4 marks 
each. Internal choice is provided in 2 marks question in each case-study. 
(viii) There is no overall choice. However, an internal choice has been provided in 2 questions in Section B,  
2 questions in Section C, 2 questions in Section D and 3 questions of 2 marks in Section E. 
(ix) Draw neat diagrams wherever required. Take ? = 22/7 wherever required, if not stated. 
(x) Use of calculators is NOT allowed.
 
Question Paper Code 
30/1/3 
SET-3 
Time: 3 Hrs. Max. Marks: 80 
 CBSE Board Exam-2024 (Class X) Mathematics (Standard) 
- 2 - 
SECTION-A 
This section consists of 20 questions of 1 mark each. 
1. If two positive integers p and q can be expressed as p = 18a
2
b
4
 and q = 20a
3
b
2
, where a and b are prime 
numbers, then LCM (p, q) is  [1] 
 (a) 2a
2
b
2
 (b) 180a
2
b
2
 
 (c) 12a
2
b
2
 (d) 180a
3
b
4
 
Answer (d)   [1] 
Sol. 180a
3
b
4
 
2. In an A.P., if the first term (a) = –16 and the common difference (d) = –2, then the sum of first 10 terms is [1] 
 (a) –200 (b) –70 
 (c) –250 (d) 250 
Answer (c)   [1] 
Sol. –250 
3. For some data x
1
, x
2
, ….. x
n
 with respective frequencies f
1
, f
2
, ….. f
n
, the value of ( ) -
?
1
n
ii
f x x is equal to [1] 
 (a) nx (b) 1 
 (c) 
? i
f (d) 0 
Answer (d)   [1] 
Sol. 0 
4. The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm is [1] 
 (a) 
? 4
cu cm
3
 (b) 
? 5
cu cm
3
 
 (c) 
? 8
cu cm
3
 (d) 
? 2
cu cm
3
 
Answer (d)   [1] 
Sol. 
? 2
cu cm
3
 
5. A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres 
taken together, is [1] 
 (a) 1 : 1 (b) 1 : 4 
 (c) 2 : 3 (d) 3 : 2 
Answer (c)   [1] 
Sol. 2 : 3 
6. The centre of a circle is at (2, 0). If one end of a diameter is at (6, 0), then the other end is at [1] 
 (a) (0, 0) (b) (4, 0) 
 (c) (–2, 0) (d) (–6,0) 
Answer (c)   [1] 
Sol. (–2, 0) 
CBSE Board Exam-2024 (Class X) Mathematics (Standard) 
- 3 - 
7. One card is drawn at random from a well shuffled deck of 52 playing cards. The probability that it is a red ace 
card, is [1] 
 (a) 
1
13
 (b) 
1
26
 
 (c) 
1
52
 (d) 
1
2
 
Answer (b)   [1] 
Sol. 
1
26
 
8. The middle most observation of every data arranged in order is called [1] 
 (a) mode (b) median 
 (c) mean (d) deviation 
Answer (b)   [1] 
Sol. Median 
9. For ? = 30°, the value of (2 sin ? cos ?) is [1] 
 (a) 1 (b) 
3
2
 
 (c) 
3
4
 (d) 
3
2
 
Answer (b)   [1] 
Sol. 
3
2 sin30 cos30
2
? ? = 
10. If the roots of equation ax
2
 + bx + c = 0, a ? 0 are real and equal, then which of the following relation is true? [1] 
 (a) 
2
=
b
a
c
 (b) b
2
 = ac 
 (c) 
2
4
=
b
ac (d) 
2
=
b
c
a
 
Answer (c)   [1] 
Sol. b
2
 = 4ac 
11. From the data 1, 4, 7, 9, 16, 21, 25, if all the even numbers are removed, then the probability of getting at random 
a prime number from the remaining is [1] 
 (a) 
2
5
 (b) 
1
5
 
 (c) 
1
7
 (d) 
2
7
 
Answer (b)   [1] 
Sol. 
1
5
 
 CBSE Board Exam-2024 (Class X) Mathematics (Standard) 
- 4 - 
12. AD is a median of ?ABC with vertices A(5, –6), B(6, 4) and C(0, 0). Length AD is equal to : [1] 
 (a) 68 units (b) 2 15 units 
 (c) 101 units (d) 10 units 
Answer (a)   [1] 
Sol. 68 units 
13. Two dice are rolled together. The probability of getting sum of numbers on the two dice as 2, 3 or 5, is: [1] 
 (a) 
7
36
 (b) 
11
36
 
 (c) 
5
36
 (d) 
4
9
 
Answer (a)   [1] 
Sol. 
7
36
 
14. If the distance between the points (3, –5) and (x, –5) is 15 units, then the values of x are:  [1] 
 (a) 12, –18 (b) –12, 18 
 (c) 18, 5 (d) –9, –12 
Answer (b)   [1] 
Sol. –12, 18 
15. In the given figure, graphs of two linear equations are shown. The pair of these linear equations is: [1] 
 
 (a) consistent with unique solution. 
 (b) consistent with infinitely many solutions. 
 (c) inconsistent. 
 (d) inconsistent but can be made consistent by extending these lines. 
Answer (a)   [1] 
Sol. consistent with unique solution. 
16. If ?, ? are the zeroes of the polynomial 6x
2
 – 5x – 4, then +
??
11
 is equal to [1] 
 (a) 
5
4
 (b) 
5
–
4
 
 (c) 
4
5
 (d) 
5
24
 
Answer (b)   [1] 
Sol. 
5
–
4
 
Page 5


- 1 - 
 
 
MATHEMATICS (Standard)
 
CBSE Class-X (2024)
 
Answers & Solutions
GENERAL INSTRUCTIONS  
Read the following instructions carefully and 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 numbers 1 to 18 are multiple choice questions (MCQs) and question numbers  
19 and 20 are Assertion–Reason based questions of 1 mark each. 
(iv) In Section B, Question numbers 21 to 25 are very short answer (VSA) type questions, carrying 2 marks each. 
(v) In Section C, Question numbers 26 to 31 are short answer (SA) type questions, carrying 3 marks each. 
(vi) In Section D, Question numbers 32 to 35 are long answer (LA) type questions carrying 5 marks each. 
(vii) In Section E, Question numbers 36 to 38 are case-study based integrated questions carrying 4 marks 
each. Internal choice is provided in 2 marks question in each case-study. 
(viii) There is no overall choice. However, an internal choice has been provided in 2 questions in Section B,  
2 questions in Section C, 2 questions in Section D and 3 questions of 2 marks in Section E. 
(ix) Draw neat diagrams wherever required. Take ? = 22/7 wherever required, if not stated. 
(x) Use of calculators is NOT allowed.
 
Question Paper Code 
30/1/3 
SET-3 
Time: 3 Hrs. Max. Marks: 80 
 CBSE Board Exam-2024 (Class X) Mathematics (Standard) 
- 2 - 
SECTION-A 
This section consists of 20 questions of 1 mark each. 
1. If two positive integers p and q can be expressed as p = 18a
2
b
4
 and q = 20a
3
b
2
, where a and b are prime 
numbers, then LCM (p, q) is  [1] 
 (a) 2a
2
b
2
 (b) 180a
2
b
2
 
 (c) 12a
2
b
2
 (d) 180a
3
b
4
 
Answer (d)   [1] 
Sol. 180a
3
b
4
 
2. In an A.P., if the first term (a) = –16 and the common difference (d) = –2, then the sum of first 10 terms is [1] 
 (a) –200 (b) –70 
 (c) –250 (d) 250 
Answer (c)   [1] 
Sol. –250 
3. For some data x
1
, x
2
, ….. x
n
 with respective frequencies f
1
, f
2
, ….. f
n
, the value of ( ) -
?
1
n
ii
f x x is equal to [1] 
 (a) nx (b) 1 
 (c) 
? i
f (d) 0 
Answer (d)   [1] 
Sol. 0 
4. The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm is [1] 
 (a) 
? 4
cu cm
3
 (b) 
? 5
cu cm
3
 
 (c) 
? 8
cu cm
3
 (d) 
? 2
cu cm
3
 
Answer (d)   [1] 
Sol. 
? 2
cu cm
3
 
5. A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres 
taken together, is [1] 
 (a) 1 : 1 (b) 1 : 4 
 (c) 2 : 3 (d) 3 : 2 
Answer (c)   [1] 
Sol. 2 : 3 
6. The centre of a circle is at (2, 0). If one end of a diameter is at (6, 0), then the other end is at [1] 
 (a) (0, 0) (b) (4, 0) 
 (c) (–2, 0) (d) (–6,0) 
Answer (c)   [1] 
Sol. (–2, 0) 
CBSE Board Exam-2024 (Class X) Mathematics (Standard) 
- 3 - 
7. One card is drawn at random from a well shuffled deck of 52 playing cards. The probability that it is a red ace 
card, is [1] 
 (a) 
1
13
 (b) 
1
26
 
 (c) 
1
52
 (d) 
1
2
 
Answer (b)   [1] 
Sol. 
1
26
 
8. The middle most observation of every data arranged in order is called [1] 
 (a) mode (b) median 
 (c) mean (d) deviation 
Answer (b)   [1] 
Sol. Median 
9. For ? = 30°, the value of (2 sin ? cos ?) is [1] 
 (a) 1 (b) 
3
2
 
 (c) 
3
4
 (d) 
3
2
 
Answer (b)   [1] 
Sol. 
3
2 sin30 cos30
2
? ? = 
10. If the roots of equation ax
2
 + bx + c = 0, a ? 0 are real and equal, then which of the following relation is true? [1] 
 (a) 
2
=
b
a
c
 (b) b
2
 = ac 
 (c) 
2
4
=
b
ac (d) 
2
=
b
c
a
 
Answer (c)   [1] 
Sol. b
2
 = 4ac 
11. From the data 1, 4, 7, 9, 16, 21, 25, if all the even numbers are removed, then the probability of getting at random 
a prime number from the remaining is [1] 
 (a) 
2
5
 (b) 
1
5
 
 (c) 
1
7
 (d) 
2
7
 
Answer (b)   [1] 
Sol. 
1
5
 
 CBSE Board Exam-2024 (Class X) Mathematics (Standard) 
- 4 - 
12. AD is a median of ?ABC with vertices A(5, –6), B(6, 4) and C(0, 0). Length AD is equal to : [1] 
 (a) 68 units (b) 2 15 units 
 (c) 101 units (d) 10 units 
Answer (a)   [1] 
Sol. 68 units 
13. Two dice are rolled together. The probability of getting sum of numbers on the two dice as 2, 3 or 5, is: [1] 
 (a) 
7
36
 (b) 
11
36
 
 (c) 
5
36
 (d) 
4
9
 
Answer (a)   [1] 
Sol. 
7
36
 
14. If the distance between the points (3, –5) and (x, –5) is 15 units, then the values of x are:  [1] 
 (a) 12, –18 (b) –12, 18 
 (c) 18, 5 (d) –9, –12 
Answer (b)   [1] 
Sol. –12, 18 
15. In the given figure, graphs of two linear equations are shown. The pair of these linear equations is: [1] 
 
 (a) consistent with unique solution. 
 (b) consistent with infinitely many solutions. 
 (c) inconsistent. 
 (d) inconsistent but can be made consistent by extending these lines. 
Answer (a)   [1] 
Sol. consistent with unique solution. 
16. If ?, ? are the zeroes of the polynomial 6x
2
 – 5x – 4, then +
??
11
 is equal to [1] 
 (a) 
5
4
 (b) 
5
–
4
 
 (c) 
4
5
 (d) 
5
24
 
Answer (b)   [1] 
Sol. 
5
–
4
 
CBSE Board Exam-2024 (Class X) Mathematics (Standard) 
- 5 - 
17. If sec ? – tan ? = m, then the value of sec ? + tan ? is [1] 
 (a) -
1
1
m
 (b) m
2
 – 1 
 (c) 
1
m
 (d) –m 
Answer (c)   [1] 
Sol. 
1
m
 
18. The zeroes of a polynomial x
2
 + px + q are twice the zeroes of the polynomial 4x
2
 – 5x – 6. The value of p is [1] 
 (a) 
5
–
2
 (b) 
5
2
 
 (c) –5 (d) 10 
Answer (a)   [1] 
Sol. 
5
–
2
 
Directions : 
In Q. No. 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 correct explanation of Assertion (A) 
 (b) Both, Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation for 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 tangents drawn at the end points of a diameter of a circle, are parallel. 
 Reason (R): Diameter of a circle is the longest chord. [1] 
Answer (b)  [1] 
20. Assertion (A): If the graph of a polynomial touches x-axis at only one point, then the polynomial cannot be a 
quadratic polynomial. 
 Reason (R): A polynomial of degree n(n > 1) can have at most n zeroes. [1] 
Answer (d) [1] 
SECTION-B
 
This section consists of 5 questions of 2 marks each. 
21. In a pack of 52 playing cards one card is lost. From the remaining cards, a card is drawn at random. Find the 
probability that the drawn card is queen of heart, if the lost card is a black card.  [2] 
Sol. One card lost is a black card 
 Total number of outcomes = 51   [½] 
 Number of favourable outcome = 1   [½] 
 Required probability = 
Number of favourable outcomes 1
Total number of outcomes 51
= [1]