Class 10 Mathematics (Standard): CBSE (Official) Sample Question Paper (2024-25) | CBSE Sample Papers For Class 10 PDF Download

 Page 1


 
SAMPLE QUESTION PAPER  
Class X Session 2024-25  
MATHEMATICS STANDARD (Code No.041)  
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 Question of Section B, 2 
Questions of Section C and 2 Questions of Section D has been provided. An internal choice has 
been provided in all the 2 marks questions of Section E.  
9. Draw neat and clean figures wherever required.  
10. Take 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.  The graph of a quadratic polynomial p(x) passes through the points (-6,0), (0, -30),    
(4,-20) and (6,0). The zeroes of the polynomial are 
A) - 6,0                   B) 4, 6                     C) - 30,-20                        D) - 6,6 
 
1 
2. The value of k for which the system of equations 3x-ky= 7 and 6x+ 10y =3 is 
inconsistent, is 
A) -10                    B) -5                        C) 5                                  D) 7 
 
1 
3. Which of the following statements is not true? 
A) A number of secants can be drawn at any point on the circle. 
B) Only one tangent can be drawn at any point on a circle. 
C) A chord is a line segment joining two points on the circle 
D) From a point inside a circle only two tangents can be drawn. 
1 
4. If nth term of an A.P. is 7n-4 then the common difference of the A.P. is 
A) 7                         B) 7n                        C) - 4                               D) 4 
 
1 
Page 2


 
SAMPLE QUESTION PAPER  
Class X Session 2024-25  
MATHEMATICS STANDARD (Code No.041)  
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 Question of Section B, 2 
Questions of Section C and 2 Questions of Section D has been provided. An internal choice has 
been provided in all the 2 marks questions of Section E.  
9. Draw neat and clean figures wherever required.  
10. Take 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.  The graph of a quadratic polynomial p(x) passes through the points (-6,0), (0, -30),    
(4,-20) and (6,0). The zeroes of the polynomial are 
A) - 6,0                   B) 4, 6                     C) - 30,-20                        D) - 6,6 
 
1 
2. The value of k for which the system of equations 3x-ky= 7 and 6x+ 10y =3 is 
inconsistent, is 
A) -10                    B) -5                        C) 5                                  D) 7 
 
1 
3. Which of the following statements is not true? 
A) A number of secants can be drawn at any point on the circle. 
B) Only one tangent can be drawn at any point on a circle. 
C) A chord is a line segment joining two points on the circle 
D) From a point inside a circle only two tangents can be drawn. 
1 
4. If nth term of an A.P. is 7n-4 then the common difference of the A.P. is 
A) 7                         B) 7n                        C) - 4                               D) 4 
 
1 
 
5. The radius of the base of a right circular cone and the radius of a sphere are each 5 cm 
in length. If the volume of the cone is equal to the volume of the sphere then the height 
of the cone is  
A) 5 cm            B)    20 cm                       C)  10 cm                      D)    4 cm 
1 
6. 
If tan?? = 
5
2
 then 
4 ???????? + ????????
4 ????????  - ????????
 is equal to 
A) 
11
9
                  B) 
3
2
                         C) 
9
11
                             D) 4 
1 
7. In the given figure, a tangent has been drawn at a point P on the circle centred at O. 
 
 If ? TPQ= 110
?? then ?POQ is equal to 
A) 110
??                             B) 70
??                       C) 140
??                           D)55
?? 
1 
8. 
A quadratic polynomial having zeroes - 
v
5
2
   and  
v
5
2
  is 
A)  ?? 2
- 5v2 x +1           B) 8?? 2
 - 20      C) 15?? 2
- 6               D) ?? 2
 - 2v5  x -1  
 
1 
9. Consider the frequency distribution of 45 observations. 
 
Class 0-10 10-20 20-30 30-40 40-50 
Frequency 5 9 15 10 6 
The upper limit of median class is 
A) 20                           B) 10                          C) 30                                D) 40 
1 
10. O is the point of intersection of two chords AB and CD of a circle. 
  
If  ??????? = 80
?? and OA = OD then ???????? ??????  ???????? are 
A) equilateral and similar                       B) isosceles and similar                                       
C) isosceles but not similar                    D) not similar 
 
 
1 
 
Q 
O 
P T 
 
 
 
A 
D 
B 
C 
O 
 
 
Page 3


 
SAMPLE QUESTION PAPER  
Class X Session 2024-25  
MATHEMATICS STANDARD (Code No.041)  
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 Question of Section B, 2 
Questions of Section C and 2 Questions of Section D has been provided. An internal choice has 
been provided in all the 2 marks questions of Section E.  
9. Draw neat and clean figures wherever required.  
10. Take 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.  The graph of a quadratic polynomial p(x) passes through the points (-6,0), (0, -30),    
(4,-20) and (6,0). The zeroes of the polynomial are 
A) - 6,0                   B) 4, 6                     C) - 30,-20                        D) - 6,6 
 
1 
2. The value of k for which the system of equations 3x-ky= 7 and 6x+ 10y =3 is 
inconsistent, is 
A) -10                    B) -5                        C) 5                                  D) 7 
 
1 
3. Which of the following statements is not true? 
A) A number of secants can be drawn at any point on the circle. 
B) Only one tangent can be drawn at any point on a circle. 
C) A chord is a line segment joining two points on the circle 
D) From a point inside a circle only two tangents can be drawn. 
1 
4. If nth term of an A.P. is 7n-4 then the common difference of the A.P. is 
A) 7                         B) 7n                        C) - 4                               D) 4 
 
1 
 
5. The radius of the base of a right circular cone and the radius of a sphere are each 5 cm 
in length. If the volume of the cone is equal to the volume of the sphere then the height 
of the cone is  
A) 5 cm            B)    20 cm                       C)  10 cm                      D)    4 cm 
1 
6. 
If tan?? = 
5
2
 then 
4 ???????? + ????????
4 ????????  - ????????
 is equal to 
A) 
11
9
                  B) 
3
2
                         C) 
9
11
                             D) 4 
1 
7. In the given figure, a tangent has been drawn at a point P on the circle centred at O. 
 
 If ? TPQ= 110
?? then ?POQ is equal to 
A) 110
??                             B) 70
??                       C) 140
??                           D)55
?? 
1 
8. 
A quadratic polynomial having zeroes - 
v
5
2
   and  
v
5
2
  is 
A)  ?? 2
- 5v2 x +1           B) 8?? 2
 - 20      C) 15?? 2
- 6               D) ?? 2
 - 2v5  x -1  
 
1 
9. Consider the frequency distribution of 45 observations. 
 
Class 0-10 10-20 20-30 30-40 40-50 
Frequency 5 9 15 10 6 
The upper limit of median class is 
A) 20                           B) 10                          C) 30                                D) 40 
1 
10. O is the point of intersection of two chords AB and CD of a circle. 
  
If  ??????? = 80
?? and OA = OD then ???????? ??????  ???????? are 
A) equilateral and similar                       B) isosceles and similar                                       
C) isosceles but not similar                    D) not similar 
 
 
1 
 
Q 
O 
P T 
 
 
 
A 
D 
B 
C 
O 
 
 
 
11. The roots of the quadratic equation ?? 2
+x-1 = 0 are 
A) Irrational and distinct                               B) not real      
      C ) rational and distinct                                D) real and equal 
1 
12. If ?? = 30
?? 
  then the value of 3tan??   is 
A)1                        B) 
1
v3
                     C ) 
3
v3
               (D) not defined 
1 
13. 
The  volume of a solid hemisphere is 
396
7
 ????
3
.The total surface area of the solid 
hemisphere (in sq.cm) is 
       A) 
396
7
                   B)  
594
7
                       C)  
549
7
                     D)  
604
7
 
   
1 
14. In a bag containing 24 balls, 4 are blue, 11 are green and the rest are white. One ball is 
drawn at random. The probability that drawn ball is white in colour is 
?? )
1
6
               B) 
3
8
                  C ) 
11
24
                    D) 
5
8
  
1 
15. The point on the x- axis nearest to the point (-4,-5) is 
A) (0, 0)             B) (-4, 0)                     C ) (-5, 0)               D) (v 41, 0) 
1 
16. Which of the following gives the middle most observation of the data? 
A) Median          B) Mean                       C) Range              D) Mode 
1 
17. A point on the x-axis divides the line segment joining the points A(2, -3) and B(5, 6) in 
the ratio 1:2. The point is 
A) (4, 0)             B) (
7
2
 , 
3
2
 )                C) (3, 0)                   D) (0,3) 
1 
18. A card is drawn from a well shuffled deck of playing cards. The probability of getting red 
face card is 
?? ) 
3
13
                B) 
1
2
                      C) 
3
52
                           D) 
3
26
  
1 
 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): HCF of any two consecutive even natural numbers is always 2. 
Reason (R): Even natural numbers are divisible by 2. 
1 
20. Assertion (A): If the radius of sector of a circle is reduced to its half and angle is 
doubled then the perimeter of the sector remains the same. 
1 
Page 4


 
SAMPLE QUESTION PAPER  
Class X Session 2024-25  
MATHEMATICS STANDARD (Code No.041)  
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 Question of Section B, 2 
Questions of Section C and 2 Questions of Section D has been provided. An internal choice has 
been provided in all the 2 marks questions of Section E.  
9. Draw neat and clean figures wherever required.  
10. Take 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.  The graph of a quadratic polynomial p(x) passes through the points (-6,0), (0, -30),    
(4,-20) and (6,0). The zeroes of the polynomial are 
A) - 6,0                   B) 4, 6                     C) - 30,-20                        D) - 6,6 
 
1 
2. The value of k for which the system of equations 3x-ky= 7 and 6x+ 10y =3 is 
inconsistent, is 
A) -10                    B) -5                        C) 5                                  D) 7 
 
1 
3. Which of the following statements is not true? 
A) A number of secants can be drawn at any point on the circle. 
B) Only one tangent can be drawn at any point on a circle. 
C) A chord is a line segment joining two points on the circle 
D) From a point inside a circle only two tangents can be drawn. 
1 
4. If nth term of an A.P. is 7n-4 then the common difference of the A.P. is 
A) 7                         B) 7n                        C) - 4                               D) 4 
 
1 
 
5. The radius of the base of a right circular cone and the radius of a sphere are each 5 cm 
in length. If the volume of the cone is equal to the volume of the sphere then the height 
of the cone is  
A) 5 cm            B)    20 cm                       C)  10 cm                      D)    4 cm 
1 
6. 
If tan?? = 
5
2
 then 
4 ???????? + ????????
4 ????????  - ????????
 is equal to 
A) 
11
9
                  B) 
3
2
                         C) 
9
11
                             D) 4 
1 
7. In the given figure, a tangent has been drawn at a point P on the circle centred at O. 
 
 If ? TPQ= 110
?? then ?POQ is equal to 
A) 110
??                             B) 70
??                       C) 140
??                           D)55
?? 
1 
8. 
A quadratic polynomial having zeroes - 
v
5
2
   and  
v
5
2
  is 
A)  ?? 2
- 5v2 x +1           B) 8?? 2
 - 20      C) 15?? 2
- 6               D) ?? 2
 - 2v5  x -1  
 
1 
9. Consider the frequency distribution of 45 observations. 
 
Class 0-10 10-20 20-30 30-40 40-50 
Frequency 5 9 15 10 6 
The upper limit of median class is 
A) 20                           B) 10                          C) 30                                D) 40 
1 
10. O is the point of intersection of two chords AB and CD of a circle. 
  
If  ??????? = 80
?? and OA = OD then ???????? ??????  ???????? are 
A) equilateral and similar                       B) isosceles and similar                                       
C) isosceles but not similar                    D) not similar 
 
 
1 
 
Q 
O 
P T 
 
 
 
A 
D 
B 
C 
O 
 
 
 
11. The roots of the quadratic equation ?? 2
+x-1 = 0 are 
A) Irrational and distinct                               B) not real      
      C ) rational and distinct                                D) real and equal 
1 
12. If ?? = 30
?? 
  then the value of 3tan??   is 
A)1                        B) 
1
v3
                     C ) 
3
v3
               (D) not defined 
1 
13. 
The  volume of a solid hemisphere is 
396
7
 ????
3
.The total surface area of the solid 
hemisphere (in sq.cm) is 
       A) 
396
7
                   B)  
594
7
                       C)  
549
7
                     D)  
604
7
 
   
1 
14. In a bag containing 24 balls, 4 are blue, 11 are green and the rest are white. One ball is 
drawn at random. The probability that drawn ball is white in colour is 
?? )
1
6
               B) 
3
8
                  C ) 
11
24
                    D) 
5
8
  
1 
15. The point on the x- axis nearest to the point (-4,-5) is 
A) (0, 0)             B) (-4, 0)                     C ) (-5, 0)               D) (v 41, 0) 
1 
16. Which of the following gives the middle most observation of the data? 
A) Median          B) Mean                       C) Range              D) Mode 
1 
17. A point on the x-axis divides the line segment joining the points A(2, -3) and B(5, 6) in 
the ratio 1:2. The point is 
A) (4, 0)             B) (
7
2
 , 
3
2
 )                C) (3, 0)                   D) (0,3) 
1 
18. A card is drawn from a well shuffled deck of playing cards. The probability of getting red 
face card is 
?? ) 
3
13
                B) 
1
2
                      C) 
3
52
                           D) 
3
26
  
1 
 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): HCF of any two consecutive even natural numbers is always 2. 
Reason (R): Even natural numbers are divisible by 2. 
1 
20. Assertion (A): If the radius of sector of a circle is reduced to its half and angle is 
doubled then the perimeter of the sector remains the same. 
1 
 
Reason (R): The length of the arc subtending angle ? at the centre of a circle of radius r 
= 
?????? 180
. 
                                                                 Section B  
 
Section B consists of 5 questions of 2 marks each.  
 
 
21. 
 
      
 
      (A)Find the H.C.F and L.C.M of 480 and 720 using the Prime factorisation method. 
                                                               OR 
(A) The H.C.F of 85 and 238 is expressible in the form 85m -238. Find the value of 
m. 
2 
22. 
 
 
 
     
(A) Two dice are rolled together bearing numbers 4, 6, 7, 9, 11, 12. Find the 
probability that the product of numbers obtained is an odd number 
                                                                OR 
(B) How many positive three digit integers have the hundredths digit 8 and unit’s 
digit 5? Find the probability of selecting one such number out of all three digit 
numbers. 
2 
23. 
Evaluate:  
2?????? 
2
60
??  
 - ?????? 2
30
?? ?????? 2 
45
?? 
2 
24. 
Find the point(s) on the x-axis which is at a distance of v 41   units from the point (8, -5). 
2 
25.  
 
       
Show that the points A(-5,6), B(3, 0) and C( 9, 8) are the vertices of an isosceles 
triangle.                        
2 
 Section C  
 
Section C consists of 6 questions of 3 marks each. 
 
26.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
      
(A) In ?? ABC, D, E and F are midpoints of BC,CA and AB respectively. Prove that  
? ?????? ~ ? DEF and   ? DEF ~ ? ABC 
 
                                                              OR 
 
(B) In ?? ABC, P and Q are points on AB and AC respectively such that PQ is parallel 
to BC. 
3 
Page 5


 
SAMPLE QUESTION PAPER  
Class X Session 2024-25  
MATHEMATICS STANDARD (Code No.041)  
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 Question of Section B, 2 
Questions of Section C and 2 Questions of Section D has been provided. An internal choice has 
been provided in all the 2 marks questions of Section E.  
9. Draw neat and clean figures wherever required.  
10. Take 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.  The graph of a quadratic polynomial p(x) passes through the points (-6,0), (0, -30),    
(4,-20) and (6,0). The zeroes of the polynomial are 
A) - 6,0                   B) 4, 6                     C) - 30,-20                        D) - 6,6 
 
1 
2. The value of k for which the system of equations 3x-ky= 7 and 6x+ 10y =3 is 
inconsistent, is 
A) -10                    B) -5                        C) 5                                  D) 7 
 
1 
3. Which of the following statements is not true? 
A) A number of secants can be drawn at any point on the circle. 
B) Only one tangent can be drawn at any point on a circle. 
C) A chord is a line segment joining two points on the circle 
D) From a point inside a circle only two tangents can be drawn. 
1 
4. If nth term of an A.P. is 7n-4 then the common difference of the A.P. is 
A) 7                         B) 7n                        C) - 4                               D) 4 
 
1 
 
5. The radius of the base of a right circular cone and the radius of a sphere are each 5 cm 
in length. If the volume of the cone is equal to the volume of the sphere then the height 
of the cone is  
A) 5 cm            B)    20 cm                       C)  10 cm                      D)    4 cm 
1 
6. 
If tan?? = 
5
2
 then 
4 ???????? + ????????
4 ????????  - ????????
 is equal to 
A) 
11
9
                  B) 
3
2
                         C) 
9
11
                             D) 4 
1 
7. In the given figure, a tangent has been drawn at a point P on the circle centred at O. 
 
 If ? TPQ= 110
?? then ?POQ is equal to 
A) 110
??                             B) 70
??                       C) 140
??                           D)55
?? 
1 
8. 
A quadratic polynomial having zeroes - 
v
5
2
   and  
v
5
2
  is 
A)  ?? 2
- 5v2 x +1           B) 8?? 2
 - 20      C) 15?? 2
- 6               D) ?? 2
 - 2v5  x -1  
 
1 
9. Consider the frequency distribution of 45 observations. 
 
Class 0-10 10-20 20-30 30-40 40-50 
Frequency 5 9 15 10 6 
The upper limit of median class is 
A) 20                           B) 10                          C) 30                                D) 40 
1 
10. O is the point of intersection of two chords AB and CD of a circle. 
  
If  ??????? = 80
?? and OA = OD then ???????? ??????  ???????? are 
A) equilateral and similar                       B) isosceles and similar                                       
C) isosceles but not similar                    D) not similar 
 
 
1 
 
Q 
O 
P T 
 
 
 
A 
D 
B 
C 
O 
 
 
 
11. The roots of the quadratic equation ?? 2
+x-1 = 0 are 
A) Irrational and distinct                               B) not real      
      C ) rational and distinct                                D) real and equal 
1 
12. If ?? = 30
?? 
  then the value of 3tan??   is 
A)1                        B) 
1
v3
                     C ) 
3
v3
               (D) not defined 
1 
13. 
The  volume of a solid hemisphere is 
396
7
 ????
3
.The total surface area of the solid 
hemisphere (in sq.cm) is 
       A) 
396
7
                   B)  
594
7
                       C)  
549
7
                     D)  
604
7
 
   
1 
14. In a bag containing 24 balls, 4 are blue, 11 are green and the rest are white. One ball is 
drawn at random. The probability that drawn ball is white in colour is 
?? )
1
6
               B) 
3
8
                  C ) 
11
24
                    D) 
5
8
  
1 
15. The point on the x- axis nearest to the point (-4,-5) is 
A) (0, 0)             B) (-4, 0)                     C ) (-5, 0)               D) (v 41, 0) 
1 
16. Which of the following gives the middle most observation of the data? 
A) Median          B) Mean                       C) Range              D) Mode 
1 
17. A point on the x-axis divides the line segment joining the points A(2, -3) and B(5, 6) in 
the ratio 1:2. The point is 
A) (4, 0)             B) (
7
2
 , 
3
2
 )                C) (3, 0)                   D) (0,3) 
1 
18. A card is drawn from a well shuffled deck of playing cards. The probability of getting red 
face card is 
?? ) 
3
13
                B) 
1
2
                      C) 
3
52
                           D) 
3
26
  
1 
 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): HCF of any two consecutive even natural numbers is always 2. 
Reason (R): Even natural numbers are divisible by 2. 
1 
20. Assertion (A): If the radius of sector of a circle is reduced to its half and angle is 
doubled then the perimeter of the sector remains the same. 
1 
 
Reason (R): The length of the arc subtending angle ? at the centre of a circle of radius r 
= 
?????? 180
. 
                                                                 Section B  
 
Section B consists of 5 questions of 2 marks each.  
 
 
21. 
 
      
 
      (A)Find the H.C.F and L.C.M of 480 and 720 using the Prime factorisation method. 
                                                               OR 
(A) The H.C.F of 85 and 238 is expressible in the form 85m -238. Find the value of 
m. 
2 
22. 
 
 
 
     
(A) Two dice are rolled together bearing numbers 4, 6, 7, 9, 11, 12. Find the 
probability that the product of numbers obtained is an odd number 
                                                                OR 
(B) How many positive three digit integers have the hundredths digit 8 and unit’s 
digit 5? Find the probability of selecting one such number out of all three digit 
numbers. 
2 
23. 
Evaluate:  
2?????? 
2
60
??  
 - ?????? 2
30
?? ?????? 2 
45
?? 
2 
24. 
Find the point(s) on the x-axis which is at a distance of v 41   units from the point (8, -5). 
2 
25.  
 
       
Show that the points A(-5,6), B(3, 0) and C( 9, 8) are the vertices of an isosceles 
triangle.                        
2 
 Section C  
 
Section C consists of 6 questions of 3 marks each. 
 
26.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
      
(A) In ?? ABC, D, E and F are midpoints of BC,CA and AB respectively. Prove that  
? ?????? ~ ? DEF and   ? DEF ~ ? ABC 
 
                                                              OR 
 
(B) In ?? ABC, P and Q are points on AB and AC respectively such that PQ is parallel 
to BC. 
3 
 
 Prove that the median AD drawn from A on BC bisects PQ.  
 
 
27. The sum of two numbers is 18 and the sum of their reciprocals is 9/40. Find the 
numbers. 
3 
28. 
If ??  and ?? are zeroes of a polynomial 6?? 2 
-5x+1 then form a quadratic 
polynomial whose zeroes are ?? 2
 and ?? 2
.                                             
3 
29. If cos? + sin? = 1 , then prove that cos? - sin? = ±1 3 
30. (A) The minute hand of a wall clock is 18 cm long. Find the area of the face 
of the clock described by the minute hand in 35 minutes.  
                                                           OR 
(B) AB is a chord of a circle centred at O such that ?AOB=60°.  If OA = 14 cm 
then find the area of the minor segment. (take v3 =1.73) 
 
 
3 
31. 
Prove that v3 is an irrational number. 
3 
                                                              Section D  
 
Section D consists of 4 questions of 5 marks each  
 
32. (A) Solve the following system of linear equations graphically: 
 x+2y = 3, 2x-3y+8 = 0 
                                                              OR 
(B) Places A and B are 180 km apart on a highway. One car starts from A and 
another from B at the same time. If the car travels in the same direction at 
5 
 
A 
P 
R 
Q 
B 
D 
C 
 
O 
A 
B