Class 10 Mathematics (Basic): Answer Sheet for 2023 (Set 2) | Mathematics (Maths) Class 10 PDF Download

 Page 1


- 1 -
 
Class-X
 
MATHEMATICS
 
(Basic)
 
(CBSE 2022-23)
 
Answers & Solution
GENERAL INSTRUCTIONS 
Read the following instructions very carefully and follow them : 
(i) This question paper contains 38 questions. All questions are compulsory.
(ii) Question paper is divided into FIVE sections – Section A, B, C, D and E.
(iii) In section A – question number 1 to 18 are multiple choice questions (MCQs) and question number
19 and 20 are Assertion-Reason based questions of 1 mark each.
(iv) In section B – question number 21 to 25 are Very Short Answer (VSA) type questions of 2 marks each.
(v) In section C – question number 26 to 31 are Short Answer (SA) type questions carrying 3 marks each.
(vi) In section D – question number 32 to 35 are Long Answer (LA) type questions carrying 5 marks each.
(vii) In section E – question number 36 to 38 are case based integrated units of assessment 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 in Section E.
(ix) Draw neat figures wherever required. Take ? = 22/7 wherever required if not stated.
(x) Use of calculators is NOT allowed.
 
Time: 3 Hrs. Max. Marks: 80 
Question Paper Code 
430/4/2 
SET-2 
Page 2


- 1 -
 
Class-X
 
MATHEMATICS
 
(Basic)
 
(CBSE 2022-23)
 
Answers & Solution
GENERAL INSTRUCTIONS 
Read the following instructions very carefully and follow them : 
(i) This question paper contains 38 questions. All questions are compulsory.
(ii) Question paper is divided into FIVE sections – Section A, B, C, D and E.
(iii) In section A – question number 1 to 18 are multiple choice questions (MCQs) and question number
19 and 20 are Assertion-Reason based questions of 1 mark each.
(iv) In section B – question number 21 to 25 are Very Short Answer (VSA) type questions of 2 marks each.
(v) In section C – question number 26 to 31 are Short Answer (SA) type questions carrying 3 marks each.
(vi) In section D – question number 32 to 35 are Long Answer (LA) type questions carrying 5 marks each.
(vii) In section E – question number 36 to 38 are case based integrated units of assessment 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 in Section E.
(ix) Draw neat figures wherever required. Take ? = 22/7 wherever required if not stated.
(x) Use of calculators is NOT allowed.
 
Time: 3 Hrs. Max. Marks: 80 
Question Paper Code 
430/4/2 
SET-2 
  Mathematics (Basic)_Class X 
- 2 - 
SECTION-A 
Section – A consists of Multiple Choice type questions of 1 mark each. [20×1=20] 
1. Let E be an event such that P(not E) = 
1
5
, then P(E) is equal to [1] 
 (a) 
1
5
 (b) 
2
5
 
 (c) 0 (d) 
4
5
 
Answer (d)   [1] 
Sol. 
1
()
5
PE = 
 
14
( ) 1–
55
PE== 
2. If p(x) = x
2
 + 5x + 6, then p(–2) is [1] 
 (a) 20 (b) 0 
 (c) –8 (d) 8 
Answer (b)   [1] 
Sol. p(x) = x
2
 + 5x + 6 
 p(–2) = (–2)
2
 + 5(–2) + 6 
          = 0 
3. The mode of the numbers 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7 is  [1] 
 (a) 2 (b) 3 
 (c) 4 (d) 5 
Answer (c)   [1] 
Sol. Numbers are 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7.  
 Most frequent number is 4, hence mode is 4. 
4. How many tangents can be drawn to a circle from a point on it? [1] 
 (a) One (b) Two 
 (c) Infinite (d) Zero 
Answer (a)   [1] 
Sol. One tangent can be drawn to a circle from a point on it. 
5. A quadratic equation whose one root is 2 and the sum of whose roots is zero, is [1] 
 (a) x
2
 + 4 = 0 (b) x
2
 – 2 = 0 
 (c) 4x
2
 – 1 = 0 (d) x
2
 – 4 = 0 
Answer (d)   [1] 
Sol. Let the roots be 2 and ?  
 2 + ? = 0 
 ? ? = –2 
 ? Product of roots = (2)(–2) = –4 
 ? Quadratic equation = x
2
 – 4 = 0 
Page 3


- 1 -
 
Class-X
 
MATHEMATICS
 
(Basic)
 
(CBSE 2022-23)
 
Answers & Solution
GENERAL INSTRUCTIONS 
Read the following instructions very carefully and follow them : 
(i) This question paper contains 38 questions. All questions are compulsory.
(ii) Question paper is divided into FIVE sections – Section A, B, C, D and E.
(iii) In section A – question number 1 to 18 are multiple choice questions (MCQs) and question number
19 and 20 are Assertion-Reason based questions of 1 mark each.
(iv) In section B – question number 21 to 25 are Very Short Answer (VSA) type questions of 2 marks each.
(v) In section C – question number 26 to 31 are Short Answer (SA) type questions carrying 3 marks each.
(vi) In section D – question number 32 to 35 are Long Answer (LA) type questions carrying 5 marks each.
(vii) In section E – question number 36 to 38 are case based integrated units of assessment 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 in Section E.
(ix) Draw neat figures wherever required. Take ? = 22/7 wherever required if not stated.
(x) Use of calculators is NOT allowed.
 
Time: 3 Hrs. Max. Marks: 80 
Question Paper Code 
430/4/2 
SET-2 
  Mathematics (Basic)_Class X 
- 2 - 
SECTION-A 
Section – A consists of Multiple Choice type questions of 1 mark each. [20×1=20] 
1. Let E be an event such that P(not E) = 
1
5
, then P(E) is equal to [1] 
 (a) 
1
5
 (b) 
2
5
 
 (c) 0 (d) 
4
5
 
Answer (d)   [1] 
Sol. 
1
()
5
PE = 
 
14
( ) 1–
55
PE== 
2. If p(x) = x
2
 + 5x + 6, then p(–2) is [1] 
 (a) 20 (b) 0 
 (c) –8 (d) 8 
Answer (b)   [1] 
Sol. p(x) = x
2
 + 5x + 6 
 p(–2) = (–2)
2
 + 5(–2) + 6 
          = 0 
3. The mode of the numbers 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7 is  [1] 
 (a) 2 (b) 3 
 (c) 4 (d) 5 
Answer (c)   [1] 
Sol. Numbers are 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7.  
 Most frequent number is 4, hence mode is 4. 
4. How many tangents can be drawn to a circle from a point on it? [1] 
 (a) One (b) Two 
 (c) Infinite (d) Zero 
Answer (a)   [1] 
Sol. One tangent can be drawn to a circle from a point on it. 
5. A quadratic equation whose one root is 2 and the sum of whose roots is zero, is [1] 
 (a) x
2
 + 4 = 0 (b) x
2
 – 2 = 0 
 (c) 4x
2
 – 1 = 0 (d) x
2
 – 4 = 0 
Answer (d)   [1] 
Sol. Let the roots be 2 and ?  
 2 + ? = 0 
 ? ? = –2 
 ? Product of roots = (2)(–2) = –4 
 ? Quadratic equation = x
2
 – 4 = 0 
Mathematics (Basic)_Class X   
- 3 - 
6. Which of the following is not a quadratic equation? [1] 
 (a) 2(x – 1)
2
 = 4x
2
 – 2x + 1 (b) 2x – x
2
 = x
2
 + 5 
 (c) 
( )
2
22
2 3 3 5 x x x x + + = - (d) (x
2
 + 2x)
2
 = x
4
 + 3 + 4x
3 
Answer (c)   [1] 
Sol. 
 
( )
2
22
2 3 3 5 x x x x + + = - 
 ? 2x
2
 + 3 + 26x + x
2
 = 3x
2
 – 5x 
 ? 2 6 5 3 0 xx + + = 
 ? Not a quadratic equation
 
7. A quadratic polynomial whose sum and product of zeroes are 2 and –1 respectively is [1] 
 (a) x
2
 + 2x + 1 (b) x
2
 – 2x – 1 
 (c) x
2
 + 2x – 1 (d) x
2
 – 2x + 1 
Answer (b)   [1] 
Sol. x
2
 – 2x – 1 is the required polynomial. 
8. (HCF × LCM) for the numbers 30 and 70 is [1] 
 (a) 2100 (b) 21 
 (c) 210 (d) 70 
Answer (a)   [1] 
Sol. HCF × LCM = 30 × 70 
   = 2100 
9. The length of the arc of a circle of radius 14 cm which subtends an angle of 60° at the centre of the circle is [1] 
 (a) 
44
3
 cm (b) 
88
3
 cm 
 (c) 
308
3
 cm (d) 
616
3
 cm 
Answer (a)   [1] 
Sol. length of arc = 
2 14
6
??
 
   = 
44
3
 cm  
10. If the radius of a semi-circular protractor is 7 cm, then its perimeter is  [1] 
 (a) 11 cm (b) 14 cm 
 (c) 22 cm (d) 36 cm 
Answer (d)   [1] 
Sol. Perimeter of protractor = ?r + 2r 
    = 22 + 14 
    = 36 cm 
Page 4


- 1 -
 
Class-X
 
MATHEMATICS
 
(Basic)
 
(CBSE 2022-23)
 
Answers & Solution
GENERAL INSTRUCTIONS 
Read the following instructions very carefully and follow them : 
(i) This question paper contains 38 questions. All questions are compulsory.
(ii) Question paper is divided into FIVE sections – Section A, B, C, D and E.
(iii) In section A – question number 1 to 18 are multiple choice questions (MCQs) and question number
19 and 20 are Assertion-Reason based questions of 1 mark each.
(iv) In section B – question number 21 to 25 are Very Short Answer (VSA) type questions of 2 marks each.
(v) In section C – question number 26 to 31 are Short Answer (SA) type questions carrying 3 marks each.
(vi) In section D – question number 32 to 35 are Long Answer (LA) type questions carrying 5 marks each.
(vii) In section E – question number 36 to 38 are case based integrated units of assessment 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 in Section E.
(ix) Draw neat figures wherever required. Take ? = 22/7 wherever required if not stated.
(x) Use of calculators is NOT allowed.
 
Time: 3 Hrs. Max. Marks: 80 
Question Paper Code 
430/4/2 
SET-2 
  Mathematics (Basic)_Class X 
- 2 - 
SECTION-A 
Section – A consists of Multiple Choice type questions of 1 mark each. [20×1=20] 
1. Let E be an event such that P(not E) = 
1
5
, then P(E) is equal to [1] 
 (a) 
1
5
 (b) 
2
5
 
 (c) 0 (d) 
4
5
 
Answer (d)   [1] 
Sol. 
1
()
5
PE = 
 
14
( ) 1–
55
PE== 
2. If p(x) = x
2
 + 5x + 6, then p(–2) is [1] 
 (a) 20 (b) 0 
 (c) –8 (d) 8 
Answer (b)   [1] 
Sol. p(x) = x
2
 + 5x + 6 
 p(–2) = (–2)
2
 + 5(–2) + 6 
          = 0 
3. The mode of the numbers 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7 is  [1] 
 (a) 2 (b) 3 
 (c) 4 (d) 5 
Answer (c)   [1] 
Sol. Numbers are 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7.  
 Most frequent number is 4, hence mode is 4. 
4. How many tangents can be drawn to a circle from a point on it? [1] 
 (a) One (b) Two 
 (c) Infinite (d) Zero 
Answer (a)   [1] 
Sol. One tangent can be drawn to a circle from a point on it. 
5. A quadratic equation whose one root is 2 and the sum of whose roots is zero, is [1] 
 (a) x
2
 + 4 = 0 (b) x
2
 – 2 = 0 
 (c) 4x
2
 – 1 = 0 (d) x
2
 – 4 = 0 
Answer (d)   [1] 
Sol. Let the roots be 2 and ?  
 2 + ? = 0 
 ? ? = –2 
 ? Product of roots = (2)(–2) = –4 
 ? Quadratic equation = x
2
 – 4 = 0 
Mathematics (Basic)_Class X   
- 3 - 
6. Which of the following is not a quadratic equation? [1] 
 (a) 2(x – 1)
2
 = 4x
2
 – 2x + 1 (b) 2x – x
2
 = x
2
 + 5 
 (c) 
( )
2
22
2 3 3 5 x x x x + + = - (d) (x
2
 + 2x)
2
 = x
4
 + 3 + 4x
3 
Answer (c)   [1] 
Sol. 
 
( )
2
22
2 3 3 5 x x x x + + = - 
 ? 2x
2
 + 3 + 26x + x
2
 = 3x
2
 – 5x 
 ? 2 6 5 3 0 xx + + = 
 ? Not a quadratic equation
 
7. A quadratic polynomial whose sum and product of zeroes are 2 and –1 respectively is [1] 
 (a) x
2
 + 2x + 1 (b) x
2
 – 2x – 1 
 (c) x
2
 + 2x – 1 (d) x
2
 – 2x + 1 
Answer (b)   [1] 
Sol. x
2
 – 2x – 1 is the required polynomial. 
8. (HCF × LCM) for the numbers 30 and 70 is [1] 
 (a) 2100 (b) 21 
 (c) 210 (d) 70 
Answer (a)   [1] 
Sol. HCF × LCM = 30 × 70 
   = 2100 
9. The length of the arc of a circle of radius 14 cm which subtends an angle of 60° at the centre of the circle is [1] 
 (a) 
44
3
 cm (b) 
88
3
 cm 
 (c) 
308
3
 cm (d) 
616
3
 cm 
Answer (a)   [1] 
Sol. length of arc = 
2 14
6
??
 
   = 
44
3
 cm  
10. If the radius of a semi-circular protractor is 7 cm, then its perimeter is  [1] 
 (a) 11 cm (b) 14 cm 
 (c) 22 cm (d) 36 cm 
Answer (d)   [1] 
Sol. Perimeter of protractor = ?r + 2r 
    = 22 + 14 
    = 36 cm 
  Mathematics (Basic)_Class X 
- 4 - 
11. The angle of elevation of the top of a 15 m high tower at a point 15 3 m away from the base of the tower is: [1] 
 (a) 30º (b) 45º 
 (c) 60º (d) 90º 
Answer (a)   [1] 
Sol. 
 
 
15 1
tan
15 3 3
? = = 
 ? ? = 30º 
12. 
24
sin0º cos0º
35
??
-
??
??
 is equal to [1] 
 (a) 
2
3
 (b) 
4
5
-
 
 (c) 0 (d) 
2
15
-
 
Answer (b)   [1] 
Sol. 
24
0 – 1
35
?? = 
–4
5
 
13. From a well-shuffled deck of 52 cards, a card is drawn at random. What is the probability of getting king of 
hearts?  [1] 
 (a) 
1
52
 (b) 
1
26
 
 (c) 
1
13
 (d) 
12
13
 
Answer (a)   [1] 
Sol. There is only 1 king of hearts in a deck of 52 cards.  
 ? Required probability = 
1
52
 
14. The number (5 3 5 5) -+ is [1] 
 (a) an integer (b) a rational number 
 (c) an irrational number (d) a whole number 
Answer (c)   [1] 
Sol. 5 – 3 5 5 + 
 = 5 – 2 5 (An irrational number) 
Page 5


- 1 -
 
Class-X
 
MATHEMATICS
 
(Basic)
 
(CBSE 2022-23)
 
Answers & Solution
GENERAL INSTRUCTIONS 
Read the following instructions very carefully and follow them : 
(i) This question paper contains 38 questions. All questions are compulsory.
(ii) Question paper is divided into FIVE sections – Section A, B, C, D and E.
(iii) In section A – question number 1 to 18 are multiple choice questions (MCQs) and question number
19 and 20 are Assertion-Reason based questions of 1 mark each.
(iv) In section B – question number 21 to 25 are Very Short Answer (VSA) type questions of 2 marks each.
(v) In section C – question number 26 to 31 are Short Answer (SA) type questions carrying 3 marks each.
(vi) In section D – question number 32 to 35 are Long Answer (LA) type questions carrying 5 marks each.
(vii) In section E – question number 36 to 38 are case based integrated units of assessment 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 in Section E.
(ix) Draw neat figures wherever required. Take ? = 22/7 wherever required if not stated.
(x) Use of calculators is NOT allowed.
 
Time: 3 Hrs. Max. Marks: 80 
Question Paper Code 
430/4/2 
SET-2 
  Mathematics (Basic)_Class X 
- 2 - 
SECTION-A 
Section – A consists of Multiple Choice type questions of 1 mark each. [20×1=20] 
1. Let E be an event such that P(not E) = 
1
5
, then P(E) is equal to [1] 
 (a) 
1
5
 (b) 
2
5
 
 (c) 0 (d) 
4
5
 
Answer (d)   [1] 
Sol. 
1
()
5
PE = 
 
14
( ) 1–
55
PE== 
2. If p(x) = x
2
 + 5x + 6, then p(–2) is [1] 
 (a) 20 (b) 0 
 (c) –8 (d) 8 
Answer (b)   [1] 
Sol. p(x) = x
2
 + 5x + 6 
 p(–2) = (–2)
2
 + 5(–2) + 6 
          = 0 
3. The mode of the numbers 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7 is  [1] 
 (a) 2 (b) 3 
 (c) 4 (d) 5 
Answer (c)   [1] 
Sol. Numbers are 2, 3, 3, 4, 5, 4, 4, 5, 3, 4, 2, 6, 7.  
 Most frequent number is 4, hence mode is 4. 
4. How many tangents can be drawn to a circle from a point on it? [1] 
 (a) One (b) Two 
 (c) Infinite (d) Zero 
Answer (a)   [1] 
Sol. One tangent can be drawn to a circle from a point on it. 
5. A quadratic equation whose one root is 2 and the sum of whose roots is zero, is [1] 
 (a) x
2
 + 4 = 0 (b) x
2
 – 2 = 0 
 (c) 4x
2
 – 1 = 0 (d) x
2
 – 4 = 0 
Answer (d)   [1] 
Sol. Let the roots be 2 and ?  
 2 + ? = 0 
 ? ? = –2 
 ? Product of roots = (2)(–2) = –4 
 ? Quadratic equation = x
2
 – 4 = 0 
Mathematics (Basic)_Class X   
- 3 - 
6. Which of the following is not a quadratic equation? [1] 
 (a) 2(x – 1)
2
 = 4x
2
 – 2x + 1 (b) 2x – x
2
 = x
2
 + 5 
 (c) 
( )
2
22
2 3 3 5 x x x x + + = - (d) (x
2
 + 2x)
2
 = x
4
 + 3 + 4x
3 
Answer (c)   [1] 
Sol. 
 
( )
2
22
2 3 3 5 x x x x + + = - 
 ? 2x
2
 + 3 + 26x + x
2
 = 3x
2
 – 5x 
 ? 2 6 5 3 0 xx + + = 
 ? Not a quadratic equation
 
7. A quadratic polynomial whose sum and product of zeroes are 2 and –1 respectively is [1] 
 (a) x
2
 + 2x + 1 (b) x
2
 – 2x – 1 
 (c) x
2
 + 2x – 1 (d) x
2
 – 2x + 1 
Answer (b)   [1] 
Sol. x
2
 – 2x – 1 is the required polynomial. 
8. (HCF × LCM) for the numbers 30 and 70 is [1] 
 (a) 2100 (b) 21 
 (c) 210 (d) 70 
Answer (a)   [1] 
Sol. HCF × LCM = 30 × 70 
   = 2100 
9. The length of the arc of a circle of radius 14 cm which subtends an angle of 60° at the centre of the circle is [1] 
 (a) 
44
3
 cm (b) 
88
3
 cm 
 (c) 
308
3
 cm (d) 
616
3
 cm 
Answer (a)   [1] 
Sol. length of arc = 
2 14
6
??
 
   = 
44
3
 cm  
10. If the radius of a semi-circular protractor is 7 cm, then its perimeter is  [1] 
 (a) 11 cm (b) 14 cm 
 (c) 22 cm (d) 36 cm 
Answer (d)   [1] 
Sol. Perimeter of protractor = ?r + 2r 
    = 22 + 14 
    = 36 cm 
  Mathematics (Basic)_Class X 
- 4 - 
11. The angle of elevation of the top of a 15 m high tower at a point 15 3 m away from the base of the tower is: [1] 
 (a) 30º (b) 45º 
 (c) 60º (d) 90º 
Answer (a)   [1] 
Sol. 
 
 
15 1
tan
15 3 3
? = = 
 ? ? = 30º 
12. 
24
sin0º cos0º
35
??
-
??
??
 is equal to [1] 
 (a) 
2
3
 (b) 
4
5
-
 
 (c) 0 (d) 
2
15
-
 
Answer (b)   [1] 
Sol. 
24
0 – 1
35
?? = 
–4
5
 
13. From a well-shuffled deck of 52 cards, a card is drawn at random. What is the probability of getting king of 
hearts?  [1] 
 (a) 
1
52
 (b) 
1
26
 
 (c) 
1
13
 (d) 
12
13
 
Answer (a)   [1] 
Sol. There is only 1 king of hearts in a deck of 52 cards.  
 ? Required probability = 
1
52
 
14. The number (5 3 5 5) -+ is [1] 
 (a) an integer (b) a rational number 
 (c) an irrational number (d) a whole number 
Answer (c)   [1] 
Sol. 5 – 3 5 5 + 
 = 5 – 2 5 (An irrational number) 
Mathematics (Basic)_Class X   
- 5 - 
15. If the pair of linear equations x – y = 1, x + ky = 5 has a unique solution x = 2, y = 1, then the value of k is [1] 
 (a) –2 (b) –3 
 (c) 3 (d) 4 
Answer (c)   [1] 
Sol. x + ky = 5 
 At x = 2, y = 1      
 2 + k.1 = 5 
 ? k = 3     
16. If ?ABC ~ ?DEF and ?A = 47°, ?E = 83°, then ?C is equal: [1] 
 (a) 47° (b) 50° 
 (c) 83° (d) 130° 
Answer (b)   [1] 
Sol. ?E = ?B = 83° 
  ?A + ?B + ?C = 180° 
  ? ?C = 50° 
17. The length of the tangent from an external point A to a circle, of radius 3 cm, is 4 cm. The distance of A from the 
centre of the circle is: [1] 
 (a) 7 cm (b) 5 cm 
 (c) 7 cm (d) 25 cm 
Answer (b)   [1] 
Sol. ?OPA = 90° 
 ? OA
2
 = 3
2
 + 4
2
 
 ? OA = 5 cm 
  
18. The pair of linear equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 has: [1] 
 (a) a unique solution (b) exactly two solutions  
 (c) infinitely many solutions (d) no solution 
Answer (d)   [1] 
Sol. 
1 2 5
3 6 1
=?
--
 
 
1 1 1
2 2 2
=?
a b c
a b c