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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