Maths Past Year Paper SA-1(Set -2) - 2014, Class 10, CBSE Class 10 Notes | EduRev

Past Year Papers For Class 10

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Class 10 : Maths Past Year Paper SA-1(Set -2) - 2014, Class 10, CBSE Class 10 Notes | EduRev

 Page 1


 
 
 
 
Summative Assessment-1 Examination 2014-2015 
 Mathematics 
Class – X 
 
 Time allowed: 3:00 hours                                Maximum Marks: 90 
 
 General Instructions: 
a) All questions are compulsory. 
b) Question paper contains 31 questions divide into 4 sections A, B, C and D. 
c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 
10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry 
3 marks each. Question No. 21 to 31 carry 4 marks each. 
d) All questions in Section – A are very short answer questions. 
e) There are no overall choices in the question paper. 
f) Use of calculator is not permitted. 
g) If required Graph papers will be provided. 
 
 
Section A 
Question numbers 1 to 4 carry 1 mark each. 
1. If a graph y=p(x) does not cut x-axis at any point, then how many zeroes does a polynomial 
have? 
2. If the sides of two similar triangles are in ration 4:9, then find the ratio of their areas. 
3. If tan (30 ) Cot ? ? = + , then find the value of ? . 
4. The mean and mode of a frequency distribution are 28 and 16 respectively. Find the median. 
 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
5. Use Euclid’s division algorithm to find out the HCF of 135 and 225. 
6. Give the HCF (306,657)=9, find LCM (306,657). 
7. Find the quadratic Polynomial, the Sum and Product of whose zeroes are 4 and 1 
respectively. 
8. The cost of 2 kg of Apples and 1 kg of Grapes on a day was found to be Rs. 160. After a month, 
the cost of 4 kg of Apples and 2 kg of Grapes are Rs. 300. Represent the situation 
algebraically. 
9. Let ABC DEF ? ? ~ and their areas be respectively 64 sq.cm and 121 sq.cm. If EF=15.4 cm, 
find BC. 
10. The marks obtained by 30 students of class X of a certain school in a Mathematics paper 
consisting of 100 marks are presented in table below. Find the mean of the marks obtained 
by the students. 
Marks obtained 
1
( ) X 
Number of 
students 
1
( ) f 
Page 2


 
 
 
 
Summative Assessment-1 Examination 2014-2015 
 Mathematics 
Class – X 
 
 Time allowed: 3:00 hours                                Maximum Marks: 90 
 
 General Instructions: 
a) All questions are compulsory. 
b) Question paper contains 31 questions divide into 4 sections A, B, C and D. 
c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 
10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry 
3 marks each. Question No. 21 to 31 carry 4 marks each. 
d) All questions in Section – A are very short answer questions. 
e) There are no overall choices in the question paper. 
f) Use of calculator is not permitted. 
g) If required Graph papers will be provided. 
 
 
Section A 
Question numbers 1 to 4 carry 1 mark each. 
1. If a graph y=p(x) does not cut x-axis at any point, then how many zeroes does a polynomial 
have? 
2. If the sides of two similar triangles are in ration 4:9, then find the ratio of their areas. 
3. If tan (30 ) Cot ? ? = + , then find the value of ? . 
4. The mean and mode of a frequency distribution are 28 and 16 respectively. Find the median. 
 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
5. Use Euclid’s division algorithm to find out the HCF of 135 and 225. 
6. Give the HCF (306,657)=9, find LCM (306,657). 
7. Find the quadratic Polynomial, the Sum and Product of whose zeroes are 4 and 1 
respectively. 
8. The cost of 2 kg of Apples and 1 kg of Grapes on a day was found to be Rs. 160. After a month, 
the cost of 4 kg of Apples and 2 kg of Grapes are Rs. 300. Represent the situation 
algebraically. 
9. Let ABC DEF ? ? ~ and their areas be respectively 64 sq.cm and 121 sq.cm. If EF=15.4 cm, 
find BC. 
10. The marks obtained by 30 students of class X of a certain school in a Mathematics paper 
consisting of 100 marks are presented in table below. Find the mean of the marks obtained 
by the students. 
Marks obtained 
1
( ) X 
Number of 
students 
1
( ) f 
 
 
 
 
10 1 
20 1 
36 3 
40 4 
50 3 
56 2 
60 4 
70 4 
72 1 
80 1 
88 2 
92 3 
95 1 
 
Section C 
Question number from 11 to 20 carry 3 marks each. 
11. Show that every positive odd integer is of the form 4q+1 or 4q+3, where q is some integer. 
12. Find the zeroes of the polynomial 
2
2 8 x x - - and verify the relationship between zeroes and 
the co-efficient. 
13. Solve 2x+3y=11 and 2x-4y=-24 and herice find the value of ‘m’ for which y=mx+3. 
14. In the given figure if LM CB  and , prove that 
AM AN
AB AD
= 
 
15. If the areas of two similar Triangles are equal, prove that they are congruent. 
16. In ABC ? , right angled at B, AB=24 cm, BC=7 cm. Determine  
a) Sin A. Cos A 
b) Sin C. Cos C 
17. If ( ) tan A B 3 + = and ( )
1
tan A-B
3
= , 0 90 A B ° < + = ° and A>B, find A and B. 
18. If A, B and C are interior angles of a triangle ABC, then show that sin cos
2 2
B C A + ? ? ? ?
=
? ? ? ?
? ? ? ?
 
19. The following data gives the information on the observed life times (in hours) of 225 electric 
components 
Life-time (in-hours) Frequency 
0-20 10 
20-40 35 
40-60 52 
Page 3


 
 
 
 
Summative Assessment-1 Examination 2014-2015 
 Mathematics 
Class – X 
 
 Time allowed: 3:00 hours                                Maximum Marks: 90 
 
 General Instructions: 
a) All questions are compulsory. 
b) Question paper contains 31 questions divide into 4 sections A, B, C and D. 
c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 
10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry 
3 marks each. Question No. 21 to 31 carry 4 marks each. 
d) All questions in Section – A are very short answer questions. 
e) There are no overall choices in the question paper. 
f) Use of calculator is not permitted. 
g) If required Graph papers will be provided. 
 
 
Section A 
Question numbers 1 to 4 carry 1 mark each. 
1. If a graph y=p(x) does not cut x-axis at any point, then how many zeroes does a polynomial 
have? 
2. If the sides of two similar triangles are in ration 4:9, then find the ratio of their areas. 
3. If tan (30 ) Cot ? ? = + , then find the value of ? . 
4. The mean and mode of a frequency distribution are 28 and 16 respectively. Find the median. 
 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
5. Use Euclid’s division algorithm to find out the HCF of 135 and 225. 
6. Give the HCF (306,657)=9, find LCM (306,657). 
7. Find the quadratic Polynomial, the Sum and Product of whose zeroes are 4 and 1 
respectively. 
8. The cost of 2 kg of Apples and 1 kg of Grapes on a day was found to be Rs. 160. After a month, 
the cost of 4 kg of Apples and 2 kg of Grapes are Rs. 300. Represent the situation 
algebraically. 
9. Let ABC DEF ? ? ~ and their areas be respectively 64 sq.cm and 121 sq.cm. If EF=15.4 cm, 
find BC. 
10. The marks obtained by 30 students of class X of a certain school in a Mathematics paper 
consisting of 100 marks are presented in table below. Find the mean of the marks obtained 
by the students. 
Marks obtained 
1
( ) X 
Number of 
students 
1
( ) f 
 
 
 
 
10 1 
20 1 
36 3 
40 4 
50 3 
56 2 
60 4 
70 4 
72 1 
80 1 
88 2 
92 3 
95 1 
 
Section C 
Question number from 11 to 20 carry 3 marks each. 
11. Show that every positive odd integer is of the form 4q+1 or 4q+3, where q is some integer. 
12. Find the zeroes of the polynomial 
2
2 8 x x - - and verify the relationship between zeroes and 
the co-efficient. 
13. Solve 2x+3y=11 and 2x-4y=-24 and herice find the value of ‘m’ for which y=mx+3. 
14. In the given figure if LM CB  and , prove that 
AM AN
AB AD
= 
 
15. If the areas of two similar Triangles are equal, prove that they are congruent. 
16. In ABC ? , right angled at B, AB=24 cm, BC=7 cm. Determine  
a) Sin A. Cos A 
b) Sin C. Cos C 
17. If ( ) tan A B 3 + = and ( )
1
tan A-B
3
= , 0 90 A B ° < + = ° and A>B, find A and B. 
18. If A, B and C are interior angles of a triangle ABC, then show that sin cos
2 2
B C A + ? ? ? ?
=
? ? ? ?
? ? ? ?
 
19. The following data gives the information on the observed life times (in hours) of 225 electric 
components 
Life-time (in-hours) Frequency 
0-20 10 
20-40 35 
40-60 52 
 
 
 
 
60-80 61 
80-100 38 
100-120 29 
Determine the modal life time of the components. 
20. The distribution below gives the weight of 30 students of a class. Find the median weight of 
students. 
Weight (in kg) Number of students 
40-45 2 
45-50 3 
50-55 8 
55-60 6 
60-65 6 
65-70 3 
70-75 2 
 
Section D 
Questions 21 to 31 carry 4 marks each. 
21. Prove that 3 2 5 + is irrational. 
22. On dividing 
3 2
3 2 x x x - + + by a polynomial g(x), the quotient and the remainder were (x-2) 
and (-2x+4) respectively. Find g(x). 
Or 
Find all the zeroes of 
4 3 2
2 3 3 6 2 x x x x - - + - if you know that two of its zeroes are 2 and 
2 - 
23. Form the pair of linear equations in the following problem and find their Solution 
graphically. 
10 students of class X took part in Mathematics Quiz. If the number of girls is 4 more than the 
number of boys. Find the number of boys and girls who took part in the Quiz. 
24. Places A and B are 100 km apart on a highway. One can start from A and another from B at 
the same time if the cars travel in the same direction at different speeds, they meet in 5 
hours. If they travel towards each other, they meet in 1 hour. What are the speeds of two 
cars. 
Or 
Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she 
travels 60 km by train and the remaining by bus. If she travels 100 km by train and the 
remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus 
separately. 
25. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares 
of the diagonals. 
26. Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ 
and QR and median PM of another triangle PQR. Show that ABC PQR ? ? ~ . 
Or 
Page 4


 
 
 
 
Summative Assessment-1 Examination 2014-2015 
 Mathematics 
Class – X 
 
 Time allowed: 3:00 hours                                Maximum Marks: 90 
 
 General Instructions: 
a) All questions are compulsory. 
b) Question paper contains 31 questions divide into 4 sections A, B, C and D. 
c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 
10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry 
3 marks each. Question No. 21 to 31 carry 4 marks each. 
d) All questions in Section – A are very short answer questions. 
e) There are no overall choices in the question paper. 
f) Use of calculator is not permitted. 
g) If required Graph papers will be provided. 
 
 
Section A 
Question numbers 1 to 4 carry 1 mark each. 
1. If a graph y=p(x) does not cut x-axis at any point, then how many zeroes does a polynomial 
have? 
2. If the sides of two similar triangles are in ration 4:9, then find the ratio of their areas. 
3. If tan (30 ) Cot ? ? = + , then find the value of ? . 
4. The mean and mode of a frequency distribution are 28 and 16 respectively. Find the median. 
 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
5. Use Euclid’s division algorithm to find out the HCF of 135 and 225. 
6. Give the HCF (306,657)=9, find LCM (306,657). 
7. Find the quadratic Polynomial, the Sum and Product of whose zeroes are 4 and 1 
respectively. 
8. The cost of 2 kg of Apples and 1 kg of Grapes on a day was found to be Rs. 160. After a month, 
the cost of 4 kg of Apples and 2 kg of Grapes are Rs. 300. Represent the situation 
algebraically. 
9. Let ABC DEF ? ? ~ and their areas be respectively 64 sq.cm and 121 sq.cm. If EF=15.4 cm, 
find BC. 
10. The marks obtained by 30 students of class X of a certain school in a Mathematics paper 
consisting of 100 marks are presented in table below. Find the mean of the marks obtained 
by the students. 
Marks obtained 
1
( ) X 
Number of 
students 
1
( ) f 
 
 
 
 
10 1 
20 1 
36 3 
40 4 
50 3 
56 2 
60 4 
70 4 
72 1 
80 1 
88 2 
92 3 
95 1 
 
Section C 
Question number from 11 to 20 carry 3 marks each. 
11. Show that every positive odd integer is of the form 4q+1 or 4q+3, where q is some integer. 
12. Find the zeroes of the polynomial 
2
2 8 x x - - and verify the relationship between zeroes and 
the co-efficient. 
13. Solve 2x+3y=11 and 2x-4y=-24 and herice find the value of ‘m’ for which y=mx+3. 
14. In the given figure if LM CB  and , prove that 
AM AN
AB AD
= 
 
15. If the areas of two similar Triangles are equal, prove that they are congruent. 
16. In ABC ? , right angled at B, AB=24 cm, BC=7 cm. Determine  
a) Sin A. Cos A 
b) Sin C. Cos C 
17. If ( ) tan A B 3 + = and ( )
1
tan A-B
3
= , 0 90 A B ° < + = ° and A>B, find A and B. 
18. If A, B and C are interior angles of a triangle ABC, then show that sin cos
2 2
B C A + ? ? ? ?
=
? ? ? ?
? ? ? ?
 
19. The following data gives the information on the observed life times (in hours) of 225 electric 
components 
Life-time (in-hours) Frequency 
0-20 10 
20-40 35 
40-60 52 
 
 
 
 
60-80 61 
80-100 38 
100-120 29 
Determine the modal life time of the components. 
20. The distribution below gives the weight of 30 students of a class. Find the median weight of 
students. 
Weight (in kg) Number of students 
40-45 2 
45-50 3 
50-55 8 
55-60 6 
60-65 6 
65-70 3 
70-75 2 
 
Section D 
Questions 21 to 31 carry 4 marks each. 
21. Prove that 3 2 5 + is irrational. 
22. On dividing 
3 2
3 2 x x x - + + by a polynomial g(x), the quotient and the remainder were (x-2) 
and (-2x+4) respectively. Find g(x). 
Or 
Find all the zeroes of 
4 3 2
2 3 3 6 2 x x x x - - + - if you know that two of its zeroes are 2 and 
2 - 
23. Form the pair of linear equations in the following problem and find their Solution 
graphically. 
10 students of class X took part in Mathematics Quiz. If the number of girls is 4 more than the 
number of boys. Find the number of boys and girls who took part in the Quiz. 
24. Places A and B are 100 km apart on a highway. One can start from A and another from B at 
the same time if the cars travel in the same direction at different speeds, they meet in 5 
hours. If they travel towards each other, they meet in 1 hour. What are the speeds of two 
cars. 
Or 
Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she 
travels 60 km by train and the remaining by bus. If she travels 100 km by train and the 
remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus 
separately. 
25. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares 
of the diagonals. 
26. Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ 
and QR and median PM of another triangle PQR. Show that ABC PQR ? ? ~ . 
Or 
 
 
 
 
The ratio of areas of two similar triangles is equal to the square of the ratios of their 
corresponding sides. 
27. In PQR ? , right angled at Q, PR+QR=25 cm and PQ=5cm. determine the values of sin P, cos P 
and tan P. 
28. Prove that 
sin cos 1 1
sin cos 1 sec tan
A A
A A A A
- +
=
+ - - 
Using the identity 
2 2
sec 1 tan A A = + 
29. Show that 
2
1 sec sin
sec 1 cos
A A
A A
+
=
- 
Or 
Prove that  
1 sin
sec tan
1 sin
A
A A
A
+
= +
- 
30. The following table gives production yield per hectare of wheat of 100 farms of a village 
Production yield Number of farms 
50-55 2 
55-60 8 
60-65 12 
65-70 24 
70-75 38 
75-80 16 
Change the distribution to a more than type distribution and draw its ogive. What conclusion 
do you draw from this table. 
31. If the median of the distribution given below is 28.5, find the values of x and y. 
Class-interval Frequency 
0-10 5 
10-20 x 
20-30 20 
30-40 15 
40-50 y 
50-60 5 
Total 60 
   Or 
The following frequency distribution gives the monthly consumption of electricity of 68 
consumers of a locality. Mr Sharma always saves electricity by switching off all electrical 
equipments immediately after their usage so his family belongs to the group 65-85. 
Monthly 
consumption of 
electricity (in units) 
Number of 
consumers 
65-85 4 
85-105 5 
105-125 13 
Page 5


 
 
 
 
Summative Assessment-1 Examination 2014-2015 
 Mathematics 
Class – X 
 
 Time allowed: 3:00 hours                                Maximum Marks: 90 
 
 General Instructions: 
a) All questions are compulsory. 
b) Question paper contains 31 questions divide into 4 sections A, B, C and D. 
c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 
10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry 
3 marks each. Question No. 21 to 31 carry 4 marks each. 
d) All questions in Section – A are very short answer questions. 
e) There are no overall choices in the question paper. 
f) Use of calculator is not permitted. 
g) If required Graph papers will be provided. 
 
 
Section A 
Question numbers 1 to 4 carry 1 mark each. 
1. If a graph y=p(x) does not cut x-axis at any point, then how many zeroes does a polynomial 
have? 
2. If the sides of two similar triangles are in ration 4:9, then find the ratio of their areas. 
3. If tan (30 ) Cot ? ? = + , then find the value of ? . 
4. The mean and mode of a frequency distribution are 28 and 16 respectively. Find the median. 
 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
5. Use Euclid’s division algorithm to find out the HCF of 135 and 225. 
6. Give the HCF (306,657)=9, find LCM (306,657). 
7. Find the quadratic Polynomial, the Sum and Product of whose zeroes are 4 and 1 
respectively. 
8. The cost of 2 kg of Apples and 1 kg of Grapes on a day was found to be Rs. 160. After a month, 
the cost of 4 kg of Apples and 2 kg of Grapes are Rs. 300. Represent the situation 
algebraically. 
9. Let ABC DEF ? ? ~ and their areas be respectively 64 sq.cm and 121 sq.cm. If EF=15.4 cm, 
find BC. 
10. The marks obtained by 30 students of class X of a certain school in a Mathematics paper 
consisting of 100 marks are presented in table below. Find the mean of the marks obtained 
by the students. 
Marks obtained 
1
( ) X 
Number of 
students 
1
( ) f 
 
 
 
 
10 1 
20 1 
36 3 
40 4 
50 3 
56 2 
60 4 
70 4 
72 1 
80 1 
88 2 
92 3 
95 1 
 
Section C 
Question number from 11 to 20 carry 3 marks each. 
11. Show that every positive odd integer is of the form 4q+1 or 4q+3, where q is some integer. 
12. Find the zeroes of the polynomial 
2
2 8 x x - - and verify the relationship between zeroes and 
the co-efficient. 
13. Solve 2x+3y=11 and 2x-4y=-24 and herice find the value of ‘m’ for which y=mx+3. 
14. In the given figure if LM CB  and , prove that 
AM AN
AB AD
= 
 
15. If the areas of two similar Triangles are equal, prove that they are congruent. 
16. In ABC ? , right angled at B, AB=24 cm, BC=7 cm. Determine  
a) Sin A. Cos A 
b) Sin C. Cos C 
17. If ( ) tan A B 3 + = and ( )
1
tan A-B
3
= , 0 90 A B ° < + = ° and A>B, find A and B. 
18. If A, B and C are interior angles of a triangle ABC, then show that sin cos
2 2
B C A + ? ? ? ?
=
? ? ? ?
? ? ? ?
 
19. The following data gives the information on the observed life times (in hours) of 225 electric 
components 
Life-time (in-hours) Frequency 
0-20 10 
20-40 35 
40-60 52 
 
 
 
 
60-80 61 
80-100 38 
100-120 29 
Determine the modal life time of the components. 
20. The distribution below gives the weight of 30 students of a class. Find the median weight of 
students. 
Weight (in kg) Number of students 
40-45 2 
45-50 3 
50-55 8 
55-60 6 
60-65 6 
65-70 3 
70-75 2 
 
Section D 
Questions 21 to 31 carry 4 marks each. 
21. Prove that 3 2 5 + is irrational. 
22. On dividing 
3 2
3 2 x x x - + + by a polynomial g(x), the quotient and the remainder were (x-2) 
and (-2x+4) respectively. Find g(x). 
Or 
Find all the zeroes of 
4 3 2
2 3 3 6 2 x x x x - - + - if you know that two of its zeroes are 2 and 
2 - 
23. Form the pair of linear equations in the following problem and find their Solution 
graphically. 
10 students of class X took part in Mathematics Quiz. If the number of girls is 4 more than the 
number of boys. Find the number of boys and girls who took part in the Quiz. 
24. Places A and B are 100 km apart on a highway. One can start from A and another from B at 
the same time if the cars travel in the same direction at different speeds, they meet in 5 
hours. If they travel towards each other, they meet in 1 hour. What are the speeds of two 
cars. 
Or 
Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she 
travels 60 km by train and the remaining by bus. If she travels 100 km by train and the 
remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus 
separately. 
25. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares 
of the diagonals. 
26. Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ 
and QR and median PM of another triangle PQR. Show that ABC PQR ? ? ~ . 
Or 
 
 
 
 
The ratio of areas of two similar triangles is equal to the square of the ratios of their 
corresponding sides. 
27. In PQR ? , right angled at Q, PR+QR=25 cm and PQ=5cm. determine the values of sin P, cos P 
and tan P. 
28. Prove that 
sin cos 1 1
sin cos 1 sec tan
A A
A A A A
- +
=
+ - - 
Using the identity 
2 2
sec 1 tan A A = + 
29. Show that 
2
1 sec sin
sec 1 cos
A A
A A
+
=
- 
Or 
Prove that  
1 sin
sec tan
1 sin
A
A A
A
+
= +
- 
30. The following table gives production yield per hectare of wheat of 100 farms of a village 
Production yield Number of farms 
50-55 2 
55-60 8 
60-65 12 
65-70 24 
70-75 38 
75-80 16 
Change the distribution to a more than type distribution and draw its ogive. What conclusion 
do you draw from this table. 
31. If the median of the distribution given below is 28.5, find the values of x and y. 
Class-interval Frequency 
0-10 5 
10-20 x 
20-30 20 
30-40 15 
40-50 y 
50-60 5 
Total 60 
   Or 
The following frequency distribution gives the monthly consumption of electricity of 68 
consumers of a locality. Mr Sharma always saves electricity by switching off all electrical 
equipments immediately after their usage so his family belongs to the group 65-85. 
Monthly 
consumption of 
electricity (in units) 
Number of 
consumers 
65-85 4 
85-105 5 
105-125 13 
 
 
 
 
125-145 20 
145-165 14 
165-185 8 
185-205 4 
Find the mean and mode of the data. What moral values of Mr. Sharma have been depicted in 
his situation? 
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