Maths Past Year Paper SA-1(Set -6) - 2016, Class 10, CBSE Class 10 Notes | EduRev

Past Year Papers For Class 10

Class 10 : Maths Past Year Paper SA-1(Set -6) - 2016, Class 10, CBSE Class 10 Notes | EduRev

 Page 1


 
 
 
 
1JD39IH 
?????? ???
? – I, 2016-17 
SUMMATIVE ASSESSMENT – I, 2016 – 17 
???? / MATHEMATICS  
?
? – X / CLASS – X 
?????? ???:3 ??             ?????? ???:90 
Time Allowed : 3 hours               Maximum Marks: 90 
 
???? ???? : 
1. ???  ?????? ? | 
2. ??  ?
 ? 31  ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?-
? ? 4  ? ???? ?? 1 ??? ?? ??; ?-? ? 6  ? ???? ?? ?? 2 ??? 
??; ?-? ? 10  ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11  ? ???? 
?? ?? 4 ??? ? | 
3. ??  ?
 ? ??? ???  ???? ?? | 
4. ????????? ?? ??? ???$? ?? | 
 
General Instructions: 
1. All questions are compulsory. 
2. The question paper consists of 31 questions divided into four sections A, B, C and D. 
Section–A comprises of 4 questions of 1 mark each; Section- B comprises of 6 questions of 
2 marks each; Section–C comprises of 10 questions of 3 marks each and Section–D 
comprise of 11 questions of 4 marks each. 
3. There is no overall choice in this question paper. 
4. Use of calculator is not permitted. 
 
? - ? / SECTION – A 
 
 ??%? 1 ?? 4 ? ?? 1 ??? ?? | 
Question numbers 1 to 4 carry one mark each. 
 
1. ?
??? PQR ?, ?????? PQ ??? PR ?? (??? ??+?? S ??? T ?? ??? -.?? ? ?? 
ST||OR ? | ??? PS=4 cm, PQ=9 cm ??? PR=4.5 cm ??, ?? PT /?? ????? | 
In PQR, ? S and T are points on the sides PQ and PR respectively such that ST||QR. If PS = 
4cm, PQ = 9cm and PR = 4.5cm, then find PT. 
 
2. cosec48
o
 + tan88
o
 ?? 0
o
 ?? 45
o
 ?? ??? ?? ????? ?? t–???????? ?? ???? ? 34 ????? 
| 
Express cosec48
o
 + tan88
o
 in terms of t – ratios of angles between 0
o
 and 45
o
. 
 
3. ??? ? ?? ??? 0
o
 ?? 90
o
 ?? ???? ??, ?? sin? ?? ??? ?? 6? ???? ??? 
Page 2


 
 
 
 
1JD39IH 
?????? ???
? – I, 2016-17 
SUMMATIVE ASSESSMENT – I, 2016 – 17 
???? / MATHEMATICS  
?
? – X / CLASS – X 
?????? ???:3 ??             ?????? ???:90 
Time Allowed : 3 hours               Maximum Marks: 90 
 
???? ???? : 
1. ???  ?????? ? | 
2. ??  ?
 ? 31  ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?-
? ? 4  ? ???? ?? 1 ??? ?? ??; ?-? ? 6  ? ???? ?? ?? 2 ??? 
??; ?-? ? 10  ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11  ? ???? 
?? ?? 4 ??? ? | 
3. ??  ?
 ? ??? ???  ???? ?? | 
4. ????????? ?? ??? ???$? ?? | 
 
General Instructions: 
1. All questions are compulsory. 
2. The question paper consists of 31 questions divided into four sections A, B, C and D. 
Section–A comprises of 4 questions of 1 mark each; Section- B comprises of 6 questions of 
2 marks each; Section–C comprises of 10 questions of 3 marks each and Section–D 
comprise of 11 questions of 4 marks each. 
3. There is no overall choice in this question paper. 
4. Use of calculator is not permitted. 
 
? - ? / SECTION – A 
 
 ??%? 1 ?? 4 ? ?? 1 ??? ?? | 
Question numbers 1 to 4 carry one mark each. 
 
1. ?
??? PQR ?, ?????? PQ ??? PR ?? (??? ??+?? S ??? T ?? ??? -.?? ? ?? 
ST||OR ? | ??? PS=4 cm, PQ=9 cm ??? PR=4.5 cm ??, ?? PT /?? ????? | 
In PQR, ? S and T are points on the sides PQ and PR respectively such that ST||QR. If PS = 
4cm, PQ = 9cm and PR = 4.5cm, then find PT. 
 
2. cosec48
o
 + tan88
o
 ?? 0
o
 ?? 45
o
 ?? ??? ?? ????? ?? t–???????? ?? ???? ? 34 ????? 
| 
Express cosec48
o
 + tan88
o
 in terms of t – ratios of angles between 0
o
 and 45
o
. 
 
3. ??? ? ?? ??? 0
o
 ?? 90
o
 ?? ???? ??, ?? sin? ?? ??? ?? 6? ???? ??? 
 
 
 
 
What happens to value of sin? when ? increase from 0
o
 top 90
o
. 
 
4. ?? ??????? ????? ?? ??? ???? 9?, ?????? ?? ??<? /?? ????? ???? ?9?? 
= 12.4 ?? ??< = 10.5 ???? ?? | 
Find median of the data, using an empirical relation when it is given that mode = 12.4 and 
mean = 10.5. 
 
? – ? / SECTION B 
 
 ??%? 5 ?? 10 ? ?? ?? 2 ??? ? | 
Question numbers 5 to 10 carry two marks each. 
 
5. ???$?? ?? ??? ???=? ???? ????A? ?? B? 4q+1 ?? 4q+3 ?? B? ?? ???? ??, 
???? q ??? ???=? ????A? ?? | 
Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some positive 
integer. 
 
6. ??C ????? ?? 
3 2
4
 ?? ??D???? ??%? ?? | 
Prove that 
3 2
4
 is an irrational number. 
 
7. /?? ????? ?? ??E ????? ?????? ??G ?? ??H??? ???????? ??? ?????? ?? ??+?? 
?? ??I?? ???? ?, ?????? ? ???? ?????? ?: 
2x – 3y + 6 = 0 
4x – 5y + 2 = 0 
Find whether the lines representing the following pair of linear equations intersect at a 
point are parallel or coincident: 
2x – 3y + 6 = 0 
4x – 5y + 2 = 0 
 
8. ????? ?, AD /?? ?????, AB = BC = 1cm ??? CD = 2cm ?? |  
 
In the figure, find AD if AB = BC = 1cm CD = 2cm.  
Page 3


 
 
 
 
1JD39IH 
?????? ???
? – I, 2016-17 
SUMMATIVE ASSESSMENT – I, 2016 – 17 
???? / MATHEMATICS  
?
? – X / CLASS – X 
?????? ???:3 ??             ?????? ???:90 
Time Allowed : 3 hours               Maximum Marks: 90 
 
???? ???? : 
1. ???  ?????? ? | 
2. ??  ?
 ? 31  ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?-
? ? 4  ? ???? ?? 1 ??? ?? ??; ?-? ? 6  ? ???? ?? ?? 2 ??? 
??; ?-? ? 10  ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11  ? ???? 
?? ?? 4 ??? ? | 
3. ??  ?
 ? ??? ???  ???? ?? | 
4. ????????? ?? ??? ???$? ?? | 
 
General Instructions: 
1. All questions are compulsory. 
2. The question paper consists of 31 questions divided into four sections A, B, C and D. 
Section–A comprises of 4 questions of 1 mark each; Section- B comprises of 6 questions of 
2 marks each; Section–C comprises of 10 questions of 3 marks each and Section–D 
comprise of 11 questions of 4 marks each. 
3. There is no overall choice in this question paper. 
4. Use of calculator is not permitted. 
 
? - ? / SECTION – A 
 
 ??%? 1 ?? 4 ? ?? 1 ??? ?? | 
Question numbers 1 to 4 carry one mark each. 
 
1. ?
??? PQR ?, ?????? PQ ??? PR ?? (??? ??+?? S ??? T ?? ??? -.?? ? ?? 
ST||OR ? | ??? PS=4 cm, PQ=9 cm ??? PR=4.5 cm ??, ?? PT /?? ????? | 
In PQR, ? S and T are points on the sides PQ and PR respectively such that ST||QR. If PS = 
4cm, PQ = 9cm and PR = 4.5cm, then find PT. 
 
2. cosec48
o
 + tan88
o
 ?? 0
o
 ?? 45
o
 ?? ??? ?? ????? ?? t–???????? ?? ???? ? 34 ????? 
| 
Express cosec48
o
 + tan88
o
 in terms of t – ratios of angles between 0
o
 and 45
o
. 
 
3. ??? ? ?? ??? 0
o
 ?? 90
o
 ?? ???? ??, ?? sin? ?? ??? ?? 6? ???? ??? 
 
 
 
 
What happens to value of sin? when ? increase from 0
o
 top 90
o
. 
 
4. ?? ??????? ????? ?? ??? ???? 9?, ?????? ?? ??<? /?? ????? ???? ?9?? 
= 12.4 ?? ??< = 10.5 ???? ?? | 
Find median of the data, using an empirical relation when it is given that mode = 12.4 and 
mean = 10.5. 
 
? – ? / SECTION B 
 
 ??%? 5 ?? 10 ? ?? ?? 2 ??? ? | 
Question numbers 5 to 10 carry two marks each. 
 
5. ???$?? ?? ??? ???=? ???? ????A? ?? B? 4q+1 ?? 4q+3 ?? B? ?? ???? ??, 
???? q ??? ???=? ????A? ?? | 
Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some positive 
integer. 
 
6. ??C ????? ?? 
3 2
4
 ?? ??D???? ??%? ?? | 
Prove that 
3 2
4
 is an irrational number. 
 
7. /?? ????? ?? ??E ????? ?????? ??G ?? ??H??? ???????? ??? ?????? ?? ??+?? 
?? ??I?? ???? ?, ?????? ? ???? ?????? ?: 
2x – 3y + 6 = 0 
4x – 5y + 2 = 0 
Find whether the lines representing the following pair of linear equations intersect at a 
point are parallel or coincident: 
2x – 3y + 6 = 0 
4x – 5y + 2 = 0 
 
8. ????? ?, AD /?? ?????, AB = BC = 1cm ??? CD = 2cm ?? |  
 
In the figure, find AD if AB = BC = 1cm CD = 2cm.  
 
 
 
 
 
 
 
9. ??? 
1
cos(A+B) sin(A-B)
2
= = ?, ?? A ?? B /?? ?????, ???? ???? ??? ?? ?? A 
+ B ?? A – B K?? ??? ? | 
If 
1
cos(A+B) sin(A-B),
2
= = then find A and B, when it is given that A + B and A – B are acute 
angles. 
 
10. ???? ?? ????? ????????? ???? ???? ??? ?? | ???? ???? ?? ?????? ????????? ???? 
????? | 
x Cf 
600 ?? ?? 
60 
500 ?? ?? 
58 
400 ?? ?? 
54 
300 ?? ??  
35 
200 ?? ?? 
22 
100 ?? ?? 
10 
Given below is a cumulative frequency distribution. Corresponding to it, make an ordinary 
frequency distribution. 
x Cf 
Below 600 60 
Below 500 58 
Below 400 54 
Below 300 35 
Below 200 22 
Below 100 10 
  
? - ? / SECTION C 
 
 ??%? 11 ?? 20 ? ?? ?? 3 ??? ?? | 
Question numbers 11 to 20 carry three marks each. 
 
11. 306 ?? 657 ?? HCF /?? ????? | HCF ?? ????? ???? ???? LCM ?? /?? 
????? | 
Find HCF of 306 and 657. Also find their LCM using their HCF. 
 
Page 4


 
 
 
 
1JD39IH 
?????? ???
? – I, 2016-17 
SUMMATIVE ASSESSMENT – I, 2016 – 17 
???? / MATHEMATICS  
?
? – X / CLASS – X 
?????? ???:3 ??             ?????? ???:90 
Time Allowed : 3 hours               Maximum Marks: 90 
 
???? ???? : 
1. ???  ?????? ? | 
2. ??  ?
 ? 31  ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?-
? ? 4  ? ???? ?? 1 ??? ?? ??; ?-? ? 6  ? ???? ?? ?? 2 ??? 
??; ?-? ? 10  ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11  ? ???? 
?? ?? 4 ??? ? | 
3. ??  ?
 ? ??? ???  ???? ?? | 
4. ????????? ?? ??? ???$? ?? | 
 
General Instructions: 
1. All questions are compulsory. 
2. The question paper consists of 31 questions divided into four sections A, B, C and D. 
Section–A comprises of 4 questions of 1 mark each; Section- B comprises of 6 questions of 
2 marks each; Section–C comprises of 10 questions of 3 marks each and Section–D 
comprise of 11 questions of 4 marks each. 
3. There is no overall choice in this question paper. 
4. Use of calculator is not permitted. 
 
? - ? / SECTION – A 
 
 ??%? 1 ?? 4 ? ?? 1 ??? ?? | 
Question numbers 1 to 4 carry one mark each. 
 
1. ?
??? PQR ?, ?????? PQ ??? PR ?? (??? ??+?? S ??? T ?? ??? -.?? ? ?? 
ST||OR ? | ??? PS=4 cm, PQ=9 cm ??? PR=4.5 cm ??, ?? PT /?? ????? | 
In PQR, ? S and T are points on the sides PQ and PR respectively such that ST||QR. If PS = 
4cm, PQ = 9cm and PR = 4.5cm, then find PT. 
 
2. cosec48
o
 + tan88
o
 ?? 0
o
 ?? 45
o
 ?? ??? ?? ????? ?? t–???????? ?? ???? ? 34 ????? 
| 
Express cosec48
o
 + tan88
o
 in terms of t – ratios of angles between 0
o
 and 45
o
. 
 
3. ??? ? ?? ??? 0
o
 ?? 90
o
 ?? ???? ??, ?? sin? ?? ??? ?? 6? ???? ??? 
 
 
 
 
What happens to value of sin? when ? increase from 0
o
 top 90
o
. 
 
4. ?? ??????? ????? ?? ??? ???? 9?, ?????? ?? ??<? /?? ????? ???? ?9?? 
= 12.4 ?? ??< = 10.5 ???? ?? | 
Find median of the data, using an empirical relation when it is given that mode = 12.4 and 
mean = 10.5. 
 
? – ? / SECTION B 
 
 ??%? 5 ?? 10 ? ?? ?? 2 ??? ? | 
Question numbers 5 to 10 carry two marks each. 
 
5. ???$?? ?? ??? ???=? ???? ????A? ?? B? 4q+1 ?? 4q+3 ?? B? ?? ???? ??, 
???? q ??? ???=? ????A? ?? | 
Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some positive 
integer. 
 
6. ??C ????? ?? 
3 2
4
 ?? ??D???? ??%? ?? | 
Prove that 
3 2
4
 is an irrational number. 
 
7. /?? ????? ?? ??E ????? ?????? ??G ?? ??H??? ???????? ??? ?????? ?? ??+?? 
?? ??I?? ???? ?, ?????? ? ???? ?????? ?: 
2x – 3y + 6 = 0 
4x – 5y + 2 = 0 
Find whether the lines representing the following pair of linear equations intersect at a 
point are parallel or coincident: 
2x – 3y + 6 = 0 
4x – 5y + 2 = 0 
 
8. ????? ?, AD /?? ?????, AB = BC = 1cm ??? CD = 2cm ?? |  
 
In the figure, find AD if AB = BC = 1cm CD = 2cm.  
 
 
 
 
 
 
 
9. ??? 
1
cos(A+B) sin(A-B)
2
= = ?, ?? A ?? B /?? ?????, ???? ???? ??? ?? ?? A 
+ B ?? A – B K?? ??? ? | 
If 
1
cos(A+B) sin(A-B),
2
= = then find A and B, when it is given that A + B and A – B are acute 
angles. 
 
10. ???? ?? ????? ????????? ???? ???? ??? ?? | ???? ???? ?? ?????? ????????? ???? 
????? | 
x Cf 
600 ?? ?? 
60 
500 ?? ?? 
58 
400 ?? ?? 
54 
300 ?? ??  
35 
200 ?? ?? 
22 
100 ?? ?? 
10 
Given below is a cumulative frequency distribution. Corresponding to it, make an ordinary 
frequency distribution. 
x Cf 
Below 600 60 
Below 500 58 
Below 400 54 
Below 300 35 
Below 200 22 
Below 100 10 
  
? - ? / SECTION C 
 
 ??%? 11 ?? 20 ? ?? ?? 3 ??? ?? | 
Question numbers 11 to 20 carry three marks each. 
 
11. 306 ?? 657 ?? HCF /?? ????? | HCF ?? ????? ???? ???? LCM ?? /?? 
????? | 
Find HCF of 306 and 657. Also find their LCM using their HCF. 
 
 
 
 
 
12. ??? ?9?? 
3 2
6 6 x x x k - + + , ?9?? x- 3 ?? ???$??? ??? ?? ??? ?? k ?? ??? /?? 
?????| 
If 
3 2
6 6 x x x k - + + is completely divisible by x- 3, then find the value of k. 
 
13. ?M???? ?9?? 
2
6 9 x x + + ?? ??K? ??? a ??? ß ??? ?? ?M???? ?9?? /?? ????? 
????? ??K? a - ??? ß - ? | 
If a and ß are zeroes of a polynomial 
2
6 9, x x + + then form a polynomial whose zeroes 
are a - and . ß - 
 
14. ??E ??-?? ?????? ??G ?? ?O-???? ???? ?? ?? ?????: 
x + 2y = 2 
x – 3y = 7 
Solve the following pair of linear equations by the cross multiplication method: 
x + 2y = 2 
x – 3y = 7 
 
15. ABC ? ?? ????? ?
??? ??, ???? 90
o
B ? = ?? | AB ??? BC ?? (??? ?? ??+?? 
D ??? E -.?? ? | ??C ????? ?? 
2 2 2 2
AE CD AC DE + = + ?? | 
ABC ? is a right angled triangle in which 90 .
o
B ? = D and E are any points on AB and BC 
respectively. Prove that 
2 2 2 2
. AE CD AC DE + = + 
 
16. ??
 ? ABC ? ?? ????9 ?
??? ??, ????? ?? ???? x ???? ?? ?? | ???? ?? 
BC ?? ?? ????? P ?? Q ?? ??? ? ?? PB = BC = CQ ?? | ??C ????? ??  
 
(a) 
PQ PA
PA PB
= 
(b) 
2 2
3 PA x = 
In given figure ABC ? is an equilateral triangle, whose each side measure x units. P and Q 
are two points on BC produced such that PB = BC = CQ. 
Page 5


 
 
 
 
1JD39IH 
?????? ???
? – I, 2016-17 
SUMMATIVE ASSESSMENT – I, 2016 – 17 
???? / MATHEMATICS  
?
? – X / CLASS – X 
?????? ???:3 ??             ?????? ???:90 
Time Allowed : 3 hours               Maximum Marks: 90 
 
???? ???? : 
1. ???  ?????? ? | 
2. ??  ?
 ? 31  ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?-
? ? 4  ? ???? ?? 1 ??? ?? ??; ?-? ? 6  ? ???? ?? ?? 2 ??? 
??; ?-? ? 10  ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11  ? ???? 
?? ?? 4 ??? ? | 
3. ??  ?
 ? ??? ???  ???? ?? | 
4. ????????? ?? ??? ???$? ?? | 
 
General Instructions: 
1. All questions are compulsory. 
2. The question paper consists of 31 questions divided into four sections A, B, C and D. 
Section–A comprises of 4 questions of 1 mark each; Section- B comprises of 6 questions of 
2 marks each; Section–C comprises of 10 questions of 3 marks each and Section–D 
comprise of 11 questions of 4 marks each. 
3. There is no overall choice in this question paper. 
4. Use of calculator is not permitted. 
 
? - ? / SECTION – A 
 
 ??%? 1 ?? 4 ? ?? 1 ??? ?? | 
Question numbers 1 to 4 carry one mark each. 
 
1. ?
??? PQR ?, ?????? PQ ??? PR ?? (??? ??+?? S ??? T ?? ??? -.?? ? ?? 
ST||OR ? | ??? PS=4 cm, PQ=9 cm ??? PR=4.5 cm ??, ?? PT /?? ????? | 
In PQR, ? S and T are points on the sides PQ and PR respectively such that ST||QR. If PS = 
4cm, PQ = 9cm and PR = 4.5cm, then find PT. 
 
2. cosec48
o
 + tan88
o
 ?? 0
o
 ?? 45
o
 ?? ??? ?? ????? ?? t–???????? ?? ???? ? 34 ????? 
| 
Express cosec48
o
 + tan88
o
 in terms of t – ratios of angles between 0
o
 and 45
o
. 
 
3. ??? ? ?? ??? 0
o
 ?? 90
o
 ?? ???? ??, ?? sin? ?? ??? ?? 6? ???? ??? 
 
 
 
 
What happens to value of sin? when ? increase from 0
o
 top 90
o
. 
 
4. ?? ??????? ????? ?? ??? ???? 9?, ?????? ?? ??<? /?? ????? ???? ?9?? 
= 12.4 ?? ??< = 10.5 ???? ?? | 
Find median of the data, using an empirical relation when it is given that mode = 12.4 and 
mean = 10.5. 
 
? – ? / SECTION B 
 
 ??%? 5 ?? 10 ? ?? ?? 2 ??? ? | 
Question numbers 5 to 10 carry two marks each. 
 
5. ???$?? ?? ??? ???=? ???? ????A? ?? B? 4q+1 ?? 4q+3 ?? B? ?? ???? ??, 
???? q ??? ???=? ????A? ?? | 
Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some positive 
integer. 
 
6. ??C ????? ?? 
3 2
4
 ?? ??D???? ??%? ?? | 
Prove that 
3 2
4
 is an irrational number. 
 
7. /?? ????? ?? ??E ????? ?????? ??G ?? ??H??? ???????? ??? ?????? ?? ??+?? 
?? ??I?? ???? ?, ?????? ? ???? ?????? ?: 
2x – 3y + 6 = 0 
4x – 5y + 2 = 0 
Find whether the lines representing the following pair of linear equations intersect at a 
point are parallel or coincident: 
2x – 3y + 6 = 0 
4x – 5y + 2 = 0 
 
8. ????? ?, AD /?? ?????, AB = BC = 1cm ??? CD = 2cm ?? |  
 
In the figure, find AD if AB = BC = 1cm CD = 2cm.  
 
 
 
 
 
 
 
9. ??? 
1
cos(A+B) sin(A-B)
2
= = ?, ?? A ?? B /?? ?????, ???? ???? ??? ?? ?? A 
+ B ?? A – B K?? ??? ? | 
If 
1
cos(A+B) sin(A-B),
2
= = then find A and B, when it is given that A + B and A – B are acute 
angles. 
 
10. ???? ?? ????? ????????? ???? ???? ??? ?? | ???? ???? ?? ?????? ????????? ???? 
????? | 
x Cf 
600 ?? ?? 
60 
500 ?? ?? 
58 
400 ?? ?? 
54 
300 ?? ??  
35 
200 ?? ?? 
22 
100 ?? ?? 
10 
Given below is a cumulative frequency distribution. Corresponding to it, make an ordinary 
frequency distribution. 
x Cf 
Below 600 60 
Below 500 58 
Below 400 54 
Below 300 35 
Below 200 22 
Below 100 10 
  
? - ? / SECTION C 
 
 ??%? 11 ?? 20 ? ?? ?? 3 ??? ?? | 
Question numbers 11 to 20 carry three marks each. 
 
11. 306 ?? 657 ?? HCF /?? ????? | HCF ?? ????? ???? ???? LCM ?? /?? 
????? | 
Find HCF of 306 and 657. Also find their LCM using their HCF. 
 
 
 
 
 
12. ??? ?9?? 
3 2
6 6 x x x k - + + , ?9?? x- 3 ?? ???$??? ??? ?? ??? ?? k ?? ??? /?? 
?????| 
If 
3 2
6 6 x x x k - + + is completely divisible by x- 3, then find the value of k. 
 
13. ?M???? ?9?? 
2
6 9 x x + + ?? ??K? ??? a ??? ß ??? ?? ?M???? ?9?? /?? ????? 
????? ??K? a - ??? ß - ? | 
If a and ß are zeroes of a polynomial 
2
6 9, x x + + then form a polynomial whose zeroes 
are a - and . ß - 
 
14. ??E ??-?? ?????? ??G ?? ?O-???? ???? ?? ?? ?????: 
x + 2y = 2 
x – 3y = 7 
Solve the following pair of linear equations by the cross multiplication method: 
x + 2y = 2 
x – 3y = 7 
 
15. ABC ? ?? ????? ?
??? ??, ???? 90
o
B ? = ?? | AB ??? BC ?? (??? ?? ??+?? 
D ??? E -.?? ? | ??C ????? ?? 
2 2 2 2
AE CD AC DE + = + ?? | 
ABC ? is a right angled triangle in which 90 .
o
B ? = D and E are any points on AB and BC 
respectively. Prove that 
2 2 2 2
. AE CD AC DE + = + 
 
16. ??
 ? ABC ? ?? ????9 ?
??? ??, ????? ?? ???? x ???? ?? ?? | ???? ?? 
BC ?? ?? ????? P ?? Q ?? ??? ? ?? PB = BC = CQ ?? | ??C ????? ??  
 
(a) 
PQ PA
PA PB
= 
(b) 
2 2
3 PA x = 
In given figure ABC ? is an equilateral triangle, whose each side measure x units. P and Q 
are two points on BC produced such that PB = BC = CQ. 
 
 
 
 
 
Prove that 
(a) 
PQ PA
PA PB
= 
(b) 
2 2
3 PA x = 
 
17. ??? 
5
cosec =
3
? ??, ?? ??? ??????? : 
4sec 2tan 5sin
20cos 3cosec +9cot
? ? ?
? ? ?
- +
- 
If 
5
cosec = ,
3
? evaluate: 
4sec 2tan 5sin
20cos 3cosec +9cot
? ? ?
? ? ?
- +
- 
 
18. ??C ????? ?? : 
(1 + tan A + cot A). (sin A – cos B) = sin A. tan B – cot A. cos B 
Prove that: 
(1 + tan A + cot A). (sin A – cos B) = sin A. tan B – cot A. cos B 
 
19. ?? ?P? ???? ?, ?? ??(??? ???-??? ??%? ???? ????? ?? ??S?? ? ?? ??? ??? 
?? | ??E ????????? ???? ? ????T ????? ?? ??%? ???? ??S?? ?? ??%? ???$? ?? ?? : 
?? ??S? ? ????? ?? ??%? 
10-12 12-14 14-16 16-18 18-20 
??S?? ?? ??%? 
12 25 13 10 20 
??-????? ???? ??, ?? ??S? ? ??? ?? ????? ?? ??%? ?? ??< /?? ????? | 
In a subji mandi, fruit vendors were selling apples on boxes, which carried varying number 
of apples. The following frequency distribution shows apples according to the number of 
boxes: 
No. of apples in a box 10-12 12-14 14-16 16-18 18-20 
No. of boxes 12 25 13 10 20 
 Find the mean number of apples kept in a packing box, using step deviation method. 
 
20. 50 ??U???$??? M??? ?V ????? ?? ??E??-?? ????????? ???? ?? ?9?? /?? ????? | 
?V ??? 
0-10 10-20 20-30 30-40 40-50 
??U???$??? ?? ??%? 
5 12 20 10 3 
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Maths Past Year Paper SA-1(Set -6) - 2016

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CBSE Class 10 Notes | EduRev

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Maths Past Year Paper SA-1(Set -6) - 2016

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Maths Past Year Paper SA-1(Set -6) - 2016

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CBSE Class 10 Notes | EduRev

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