041/IX/SA2/11/A1
Class - IX
MATHEMATICS
Time : 3 to 3½ hours
â×Ø : 3 âð 3½ ƒæ‡ÅUð
Maximum Marks : 80
¥çÏ·¤Ì× ¥´·¤ : 80
Total No. of Pages : 13
·é¤Ü ÂëcÆUæð´ ·¤è ⴁØæ : 13
General Instructions :
1.
All questions are compulsory.
2.
The question paper consists of 34 questions divided into four sections A, B, C and D.
Section - A comprises of 10 questions of 1 mark each, Section - B comprises of 8 questions of
2 marks each, Section - C comprises of 10 questions of 3 marks each and Section - D comprises
of 6 questions of 4 marks each.
3.
Question numbers 1 to 10 in Section - A are multiple choice questions where you are to select
one correct option out of the given four.
4.
There is no overall choice. However, internal choice has been provided in 1 question of two
marks, 4 questions of three marks each and 2 questions of four marks each. You have to
attempt only one of the alternatives in all such questions.
5.
Use of calculators is not permitted.
6.
An additional 15 minutes time has been allotted to read this question paper only.
âæ×æ‹Ø çÙÎðüàæ Ñ
1.
âÖè ÂýàÙ ¥çÙßæØü ãñ´Ð
2.
§â ÂýàÙ-˜æ ×ð´ 34 ÂýàÙ ãñ´, Áæð
¿æÚU ¹‡ÇUæð´ ×ð´ ¥, Õ, â ß Î ×ð´ çßÖæçÁÌ ãñÐ ¹‡ÇU - ¥ ×ð´ 10 ÂýàÙ ãñ´ ¥æñÚU ÂýˆØð·¤
¹‡ÇU - Õ ×ð´ 8 ÂýàÙ ãñ´ ¥æñÚU ÂýˆØð·¤ ÂýàÙ 2 ¥´·¤æð´ ·ð¤ ãñ´, ¹‡ÇU - â ×ð´ 10 ÂýàÙ ãñ´ ¥æñÚU ÂýˆØð·¤
ÂýàÙ 3 ¥´·¤æð´ ·¤æ ãñ, ¹‡ÇU - Î ×ð´ 6 ÂýàÙ ãñ´ ¥æñÚU ÂýˆØð·¤ ÂýàÙ 4 ¥´·¤æð´ ·¤æ ãñÐ
ÂýàÙ
1
¥´·¤ ·¤æ ãñ,
3.
Âýà٠ⴁØæ 1 âð 10 Õãéçß·¤ËÂèØ ÂýàÙ ãñ´Ð çΰ »° ¿æÚU çß·¤ËÂæð´ ×ð´ âð °·¤ âãè çß·¤ËÂ
4.
§â×ð´ ·¤æð§ü Öè âßæðüÂçÚU çß·¤Ë Ùãè´ ãñ, Üðç·¤Ù ¥æ´ÌçÚU·¤ çß·¤Ë 1 ÂýàÙ 2 ¥´·¤æð´ ×ð´, 4 ÂýàÙ 3 ¥´·¤æð´ ×ð´ ¥æñÚU 2 ÂýàÙ
¿éÙð´Ð
4 ¥´·¤æð´ ×ð´ çΰ »° ãñ´Ð ¥æ çΰ »° çß·¤ËÂæð´ ×ð´ âð °·¤ çß·¤Ë ·¤æ ¿ØÙ ·¤Úð´UÐ
ßçÁüÌ ãñÐ
5.
·ñ¤Ü·é¤ÜðÅUÚU ·¤æ ÂýØæð»
6.
§â ÂýàÙ-Â˜æ ·¤æð ÂɸÙð ·ð¤ çÜ° 15
ç×ÙÅU ·¤æ â×Ø çÎØæ »Øæ ãñÐ
¥æñÚU ß𠩞æÚU-ÂéçSÌ·¤æ ÂÚU ·¤æð§ü ©žæÚU Ùãè´ çܹð´»ðÐ
1
§â ¥ßçÏ ·ð¤ ÎæñÚUæÙ ÀUæ˜æ ·ð¤ßÜ ÂýàÙ-Â˜æ ·¤æð Âɸð´»ð
SECTION – A
“Question number 1 to 10 carry 1 mark each.”
1.
2.
Equation y52x13 has :
(a)
Unique solution
(b)
No solution
(c)
Only two solutions
(d)
Infinitely many solutions
Curved surface area of hemisphere of diameter 2r is :
(a)
3.
4pr 2
(d)
8pr 2
1
7
(b)
3
7
(c)
4
7
(d)
5
7
60 cm2
(b)
50 cm2
(c)
40 cm2
(d)
30 cm2
x52
(b)
x522
(c)
y52
(d)
y522
The number of circles which can pass through three non-collinear points is :
(a)
7.
(c)
Equation of line parallel to x - axis and 2 - Units above the origin is :
(a)
6.
3pr 2
In DABC, AD is median of DABC and BE is median of DABD. If ar(DABE) 5 15 cm2
then ar(DABC) is :
(a)
5.
(b)
Out of 35 students participating in a debate 10 are girls. The probability that winner is
a boy is :
(a)
4.
2pr 2
One
(b)
Two
(c)
Many
(d)
None
In quadrilateral ABCD, AP and BP are bisectors of ∠ A and ∠ B respectively, then the
value of x is :
(a)
608
041/IX/SA2/11/A1
(b)
858
(c)
2
958
(d)
1008
8.
If area of ??gm ABCD is 80 cm2 then ar (DADP) is :
(a)
9.
12.
13.
60 cm2
(c)
50 cm2
(d)
40 cm2
208, 308
(b)
368, 608
(c)
158, 308
(d)
258, 308
In the given figure O is the centre of circle. If ∠ OAB 5 308 and ∠ OCB 5 408, then
measure of ∠ AOC is :
(a)
11.
(b)
In the given figure the value of x and y is :
(a)
10.
80 cm2
708
(b)
2208
(c)
1408
(d)
1108
SECTION – B
“Question numbers 11 to 18 carry 2 marks each.”
Three cubes of side 10 cm each are joined end to end to make cuboid. Find the surface
area of resulting solid.
If angles of quadrilateral are in ratio 1 : 2 : 3 : 4. Find measure of all the angles of
quadrilateral.
In given figure OA5OB5OC Show that
∠ x1 ∠ y5 2( ∠ z1 ∠ t)
14.
Two opposite angles of a parallelogram are (3x22)8 and (6322x)8. Find all the angles
of parallelogram.
041/IX/SA2/11/A1
3
15.
The mean of first 8 observations is 18 and last 8 observations is 20. If the mean of all
15 observations is 19, find the 8th observation.
16.
Give equation of two lines on same plane which are intersecting at point (2, 3).
17.
In given figures ‘l’ is a line intersecting two concentric circles with centre P at points
A, C, D and B show that
AC 5 DB
OR
Prove that equal chords of a circle subtend equal angles at the centre.
18.
A cone and cylinder are having equal base radius. Find the ratio of the heights of cone
and cylinder if their volume are equal.
SECTION - C
“Question number 19 to 28 carry 3 marks each”.
19.
Draw a graph of linear equation 3x12y512.
20.
Construct DABC in which BC57 cm, ∠ ABC 5 458 and AB1AC513 cm.
OR
Construct DXYZ in which ∠ Y 5 908, ∠ Z 5 308 and perimeter is 13 cm.
21.
How many meters of 5 m wide cloth will be required to make a conical tent, the radius
of whose base is 3.5 m and height is 12 m.
22.
1500 family with 2 children were selected randomly and the following data was
recorded.
Number of girls in family
Number of family
2
475
1
814
0
211
Compute probability of a family chosen at random having
(a)
at most 1 girl
(b)
at least 2 girls
041/IX/SA2/11/A1
4
23.
24.
Give geometric representation of 2y1750 as an equation
(i)
in one, variable
(ii)
in two variables
The bisector of ∠ A of a ??gm ABCD bisect BC at P. Prove that AD 5 2CD
OR
Show that diagonal of square are equal and bisect each other at 908.
25.
For what value of “a” 12, 14, 15, 27, a12, a14, 35, 36, 40, 41 the median of the
following observation arranged in ascending order is 32.
26.
When three coins are tossed simultaneously, find the probability of getting at least two
tails.
27.
ABCD is parallelogram. On diagonal BD are points P and Q such that DP=BQ. Show
that APCQ is a parallelogram.
OR
Show that the bisectors of angles of a parallelogram form a rectangle.
28.
The radius of sphere is 5 cm. If the radius is increased by 20%. Find by how much
percent volume is increased.
SECTION - D
“Question numbers 29 to 34 carry 4 marks each”.
29.
If (2, 3) and (4, 0) lie on the graph of equation ax1by51. Find value of a and b.
Plot the graph of equation obtained.
041/IX/SA2/11/A1
5
30.
Prove that the diagonals of a parallelogram divide it into two congruent triangles.
OR
If X, Y and Z are the mid - points of sides BC, CA and AB of ∆ ABC respectively. Prove
that AZXY is a parallelogram.
31.
Water flows at the rate of 5 m per minute through a cylindrical pipe, whose diameter
is 7 cm. How long it will take to fill the conical vessel having base diameter 21 m and
depth 12 m.
32.
In given figure, AB is diameter of circle and CD is a chord equal to the radius of circle.
AC and BD when extended intersect at a point E. Prove that ∠ AEB5608.
33.
Draw a histogram of distribution table of the marks scored by 75 students of class IX.
Marks obtained Number of students
0 - 10
4
10 - 20
8
20 - 40
20
40 - 45
10
45 - 60
12
60 - 70
6
70 - 85
15
OR
The runs scored by two teams A and B in 7 overs in a cricket match are given.
Number of ball’s Team A Team B
1-6
2
5
7 - 12
1
6
13 - 18
8
2
19 - 24
9
10
25 - 30
4
5
31 - 36
5
6
37 - 42
6
3
Represent the data of both the team’s on the same graph by frequency polygon.
041/IX/SA2/11/A1
6
34.
If O is the centre of a circle as shown in given figure, then prove that x1y5z
-o0o-
041/IX/SA2/11/A1
7
¹´ÇU - ¥
ÂýàÙæð´ 1 âð 10 ×ð´ âð ÂýˆØð·¤ 1 ¥´·¤ ·¤æ ãñÐ ÂýàÙæð´ 1 âð 10 ×ð´ âð ÂýˆØð·¤ ·ð¤ çÜ°, ¿æÚU çß·¤Ë çΰ ãñ´, çÁÙ×ð´ âð
·ð¤ßÜ °·¤ ãè âãè ãñÐ ¥æ·¤æð âãè çß·¤Ë ·¤æ ¿éÙæß ·¤ÚUÙæ ãñÐ
1.
2.
â×è·¤ÚU‡æ
(a)
°·¤ ¥çmÌèØ ãÜ ãñ
(b)
·¤æð§ü ãÜ Ùãè´ ãñ
(c)
·ð¤ßÜ Îæð ãÜ ãñ´
(d)
¥ÂçÚUç×Ì L¤Â âð ¥Ùð·¤ ãÜ ãñÐ
ÃØæâ 2r ßæÜð ¥Ïü»æðÜð ·¤æ ß·ý¤ ÂëDèØ ÿæð˜æÈ¤Ü ãñ Ñ
(a)
3.
2pr 2
1
7
(a)
(c)
4pr 2
(d)
8pr 2
3
7
(c)
4
7
(d)
5
7
ãñ , Ìæð
ar(DABC)
ãñ Ñ
(b)
50 cm2
(c)
40 cm2
(d)
30 cm2
y52
(d)
y522
¥Ùð·¤
(d)
·¤æð§ü Ùãè´
·ð¤ â×æ´ÌÚU ÌÍæ ×êÜçÕ´Îé âð 2 - §·¤æ§ü ª¤ÂÚU ÚðU¹æ ·¤æ â×è·¤ÚU‡æ ãñ Ñ
x52
(b)
x522
(c)
ÌèÙ ¥â´ÚðU¹è çÕ´Îé¥æð´ âð ãæð·¤ÚU ÁæÙðßæÜð ßëžææð´ ·¤è ⴁØæ ãñ Ñ
(a)
7.
(b)
60 cm2
x - ¥ÿæ
(a)
6.
3pr 2
¥æ·ë¤çÌ ×ð´, AD ç˜æÖéÁ ABC ·¤è ×æçŠØ·¤æ ãñ ÌÍæ BE ç˜æÖéÁ ABD ·¤è ×æçŠØ·¤æ ãñÐ ØçÎ ar(DABE) 5
15 cm2
5.
(b)
ßæÎçßßæÎ ÂýçÌØæðç»Ìæ ×ð´ Öæ» ÜðÙðßæÜð 35 çßlæçÍüØæð´ ×ð´ âð 10 ÜǸ緤Øæ¡ ãñ´Ð §â×ð´ ÁèÌÙð ßæÜæ °·¤ ÜǸ·¤æ ãæðÙð ·¤è
ÂýæçØ·¤Ìæ ãñ Ñ
(a)
4.
y52x13 ·ð¤/·¤æ Ñ
°·¤
(b)
Îæð
(c)
¥æ·ë¤çÌ ×ð´ çΰ ¿ÌéÖüéÁ ABCD ×ð´, AP ¥æñÚU BP ·ý¤×àæÑ ∠ A ¥æñÚU ∠ B ·ð¤ â×çmÖæÁ·¤ ãñ´Ð ÌÕ x ·¤æ ×æÙ ãñ Ñ
(a)
608
041/IX/SA2/11/A1
(b)
858
(c)
8
958
(d)
1008
8.
¥æ·ë¤çÌ ×ð´, ØçÎ â×æ´ÌÚU ¿ÌéÖüéÁ ABCD ·¤æ ÿæð˜æÈ¤Ü 80 cm2 ãñ, Ìæð ar (DADP) ãñ Ñ
(a)
9.
(b)
60 cm2
(c)
50 cm2
(d)
40 cm2
(c)
158, 308
(d)
258, 308
Îè ãé§ü ¥æ·ë¤çÌ ×ð´, x ¥æñÚU y ·ð¤ ·ý¤×àæÑ ×æÙ ãñ Ñ
(a)
10.
80 cm2
208, 308
(b)
368, 608
Îè ãé§ü ¥æ·ë¤çÌ ×ð´, O ßëžæ ·¤æ ·ð¤‹Îý ãñ, ∠ OAB5308 ¥æñÚU ∠ OCB5408
(a)
708
(b)
2208
(c)
1408
ãñÐ
ÌÕ
∠ AOC
(d)
·¤è ×æ ãñ Ñ
1108
¹´ÇU - Õ
Âýà٠ⴁØæ 11 âð 18 Ì·¤ ÂýˆØð·¤ ÂýàÙ 2 ¥´·¤æð´ ·¤æ ãñÐ
11.
ÖéÁæ 10 cm ßæÜð ÌèÙ ƒæÙæð´ ·¤æð çâÚðU âð çâÚUæ ç×Üæ·¤ÚU °·¤ ƒæÙæÖ ÕÙæØæ ÁæÌæ ãñÐ §â ÆUæðâ ·¤æ ÂëDèØ ÿæð˜æÈ¤Ü ™ææÌ
·¤èçÁ°Ð
12.
ØçÎ ç·¤âè ¿ÌéÖüéÁ ·ð¤ ·¤æð‡ææð´ ·¤æ ¥ÙéÂæÌ 1 : 2 : 3 : 4 ãñ, Ìæð §â ¿ÌéÖüéÁ ·ð¤ âÖè ·¤æð‡ææð´ ·¤è ×栙ææÌ ·¤èçÁ°Ð
13.
Îè ãé§ü ¥æ·ë¤çÌ ×ð´, ØçÎ
14.
°·¤ â×æ´ÌÚU ¿ÌéÖüéÁ ·ð¤ â×é¹ ·¤æð‡æ (3x22)8 ¥æñÚU (6322x)8 ãñ´Ð
041/IX/SA2/11/A1
OA5OB5OC ãñ, Ìæð Îàææü§° ç·¤ ∠ x1 ∠ y5 2( ∠ z1 ∠ t)
9
ãñÐ
§â â×æ´ÌÚU ¿ÌéÖüéÁ ·ð¤ âÖè ·¤æð‡æ ™ææÌ ·¤èçÁ°Ð
15.
ÂýÍ×
8 Âýðÿæ‡ææð´
·¤æ ×æŠØ
18 ãñ
ÌÍæ ¥´çÌ×
8 Âýðÿæ‡ææð´
·¤æ ×æŠØ
20
ãñÐ
ØçÎ âÖè
15 Âýðÿæ‡ææð´
·¤æ ×æŠØ
19
ãñ, Ìæð
8ßæ¡
Âýðÿæ‡æ ™ææÌ ·¤èçÁ°Ð
16.
çÕ´Îé
(2, 3)
17.
Îè ãé§ü ¥æ·ë¤çÌ ×ð´, ÚðU¹æ
ÂÚU Âýç̑ÀðUÎ ·¤ÚUÙð ßæÜè °·¤ ãè ÌÜ ×ð´ Îæð ÚðU¹æ¥æð´ ·ð¤ â×è·¤ÚU‡æ çÜç¹°Ð
‘l’
·ð¤‹Îý
P
ßæÜð Îæð â´·ð¤‹ÎýèØ ßëžææð´ ·¤æð
A, C, D
¥æñÚU
B
ÂÚU Âýç̑ÀðUÎ ·¤ÚUÌè ãñÐ
Îàææü§° ç·¤
AC 5 DB ãñÐ
¥Íßæ
çâh ·¤èçÁ° ç·¤ ßëžæ ·¤è ÕÚUæÕÚU Áèßæ°¡ ·ð¤‹Îý ÂÚU ÕÚUæÕÚU ·¤æð‡æ ¥´ÌçÚUÌ ·¤ÚUÌè ãñ´Ð
18.
°·¤ àæ´·é¤ ¥æñÚU °·¤ ÕðÜÙ ·¤è ¥æÏæÚU ç˜æ’Øæ°¡ ÕÚUæÕÚU ãñ´Ð
ØçÎ §Ù·ð¤ ¥æØÌÙ ÕÚUæÕÚU ãñ´, Ìæð àæ´·é¤ ¥æñÚU ÕðÜÙ ·¤è ª¡¤¿æ§Øæð´
·¤æ ¥ÙéÂæÌ ™ææÌ ·¤èçÁ°Ð
¹´ÇU - â
Âýà٠ⴁØæ 19 âð 28 Ì·¤ ÂýˆØð·¤ ÂýàÙ 3 ¥´·¤æð´ ·¤æ ãñÐ
19.
ÚñUç¹·¤ â×è·¤ÚU‡æ
3x12y512
20.
DABC ·¤è ÚU¿Ùæ ·¤èçÁ°, çÁâ×ð´ BC57
·¤æ ¥æÜð¹ ¹è´ç¿°Ð
âð×è,
∠ ABC 5 458
¥Íßæ
DXYZ ·¤è ÚU¿Ùæ ·¤èçÁ°, çÁâ×ð´ ∠ Y 5 908, ∠ Z 5 308 ¥æñÚU
21.
22.
¥æñÚU AB1AC513 âð×è ãñÐ
ÂçÚU×æ 13 âð×è ãñÐ
¥æÏæÚU ç˜æ’Øæ 3.5 ×è ¥æñÚU ª¡¤¿æ§ü 12 ×è ßæÜð °·¤ àæ´·é¤ ·ð¤ ¥æ·¤æÚU ·¤æ Ì´Õê ÕÙæÙð ·ð¤ çÜ° 5 ×è ¿æñǸð ç·¤ÌÙð ×èÅUÚU
·¤ÂÇ¸ð ·¤è ¥æßàØ·¤Ìæ ÂǸð»è?
Îæð Փææð´ ßæÜð 1500 ÂçÚUßæÚU ØæÎëç‘ÀU·¤ M¤Â âð ¿éÙð »° ÌÍæ çِ٠¥æ¡·¤Ç¸ð ÚðU·¤æÇüU ç·¤° »° Ñ
¬Á⁄UflÊ⁄U ◊¥ ‹«∏Á∑§ÿÊ¥ ∑§Ë ‚¥ÅÿÊ
¬Á⁄UflÊ⁄UÊ¥ ∑§Ë ‚¥ÅÿÊ
2
1
0
475
814
211
UØæÎëç‘ÀU·¤ M¤Â âð ¿éÙð »° °·¤ ÂçÚUßæÚU ×ð´ çِ٠ãæðÙð ·¤è ÂýæçØ·¤Ìæ ¥çÖ·¤çÜÌ ·¤èçÁ° Ñ
(a) U¥çÏ·¤Ì× 1 UÜǸ·¤è
(b) U‹ØêÙÌ× 2 UÜǸ緤Øæ¡
041/IX/SA2/11/A1
10
23.
Uçِ٠·ð¤ M¤Â ×ð´ â×è·¤ÚU‡æ 2y1750
(i)
(ii)
24.
U°·¤
UÎæð
U¥æ·ë¤çÌ
·¤èçÁ°
¿ÚU
¿ÚUæð´
×ð´,
ç·¤
ßæÜè
ßæÜè
°·¤
U·¤æ
’Øæç×ÌèØ
çÙM¤Â‡æ
ÎèçÁ°
Ñ
â×è·¤ÚU‡æ
â×è·¤ÚU‡æ
â×æ´ÌÚU
¿ÌéÖüéÁ
AD 5 2CD
ABCD
·ð¤
∠A
U·¤æ
â×çmÖæÁ·¤
BC
·¤æð
P
ÂÚU
â×çmÖæçÁÌ
·¤ÚUÌæ
ãñÐ
çâh
ãñÐ
¥Íßæ
Îàææü§° ç·¤ °·¤ ß»ü ·ð¤ çß·¤‡æü ÕÚUæÕÚU ãæðÌð ãñ´ ÌÍæ ÂÚUSÂÚU â×·¤æð‡æ ÂÚU â×çmÖæçÁÌ ·¤ÚUÌð ãñ´Ð
25.
¥æÚUæðãè ·ý¤× ×ð´ ÃØßçSÍÌ Âýðÿæ‡ææð´ 12, 14, 15, 27, a12, a14, 35, 36, 40, 41
·¤æ ×æŠØ·¤
32
ãñÐ
a
·¤æ ×æÙ ™ææÌ
·¤èçÁ°Ð
26.
ÌèÙ ç‷¤æð´ ·¤æð °·¤ âæÍ ©ÀUæÜæ ÁæÌæ ãñÐ
27.
¥æ·ë¤çÌ ×ð´,
ABCD °·¤
â×æ´ÌÚU ¿ÌéÖüéÁ ãñÐ
Îàææü§° ç·¤
APCQ °·¤
â×æ´ÌÚU ¿ÌéÖüéÁ ãñÐ
‹ØêÙÌ× Îæð ÂÅU Âýæ# ·¤ÚUÙð ·¤è ÂýæçØ·¤Ìæ ™ææÌ ·¤èçÁ°Ð
çß·¤‡æü
BD ÂÚU
çÕ´Îé
P ¥æñÚU Q §â
Âý·¤æÚU çSÍÌ ãñ´ ç·¤
DP=BQ
ãñÐ
¥Íßæ
Îàææü§° ç·¤ °·¤ â×æ´ÌÚU ¿ÌéÖüéÁ ·ð¤ ·¤æð‡ææð´ ·ð¤ â×çmÖæÁ·¤ °·¤ ¥æØÌ ÕÙæÌð ãñ´Ð
28.
°·¤ »æðÜð ·¤è ç˜æ’Øæ 5 âð×è ãñÐ ØçÎ ç˜æ’Øæ ×ð´ 20% ·¤è ßëçh ·¤ÚU Îè Áæ°, Ìæð ™ææÌ ·¤èçÁ° ç·¤ ©â·ð¤ ¥æØÌÙ ×ð´
ç·¤ÌÙð ÂýçÌàæÌ ßëçh ãæð»è?
¹´ÇU - Î
Âýà٠ⴁØæ 29 âð 34 Ì·¤ ÂýˆØð·¤ ÂýàÙ 4 ¥´·¤æð´ ·¤æ ãñÐ
29.
ØçÎ (2, 3) ¥æñÚU (4, 0) â×è·¤ÚU‡æ ax1by51 ·ð¤ ¥æÜð¹ ÂÚU çSÍÌ ãñ´, Ìæð a ¥æñÚU b ·ð¤ ×æÙ ™ææÌ ·¤èçÁ°Ð
Âýæ# â×è·¤ÚU‡æ ·¤æ ¥æÜð¹ Öè ¹è´ç¿°Ð
041/IX/SA2/11/A1
11
§â Âý·¤æÚU
30.
çâh ·¤èçÁ° ç·¤ â×æ´ÌÚU ¿ÌéÖüéÁ ·¤æ çß·¤‡æü ©âð Îæð âßæZ»â× ç˜æÖéÁæð´ ×ð´ çßÖæçÁÌ ·¤ÚUÌæ ãñÐ
¥Íßæ
ØçÎ X, Y ¥æñÚU Z ·ý¤×àæÑ DABC ·¤è ÖéÁæ¥æð´ BC, CA ¥æñÚU AB ·ð¤ ×ŠØ çÕ´Îé ãñ´, Ìæð çâh ·¤èçÁ° ç·¤ AZXY °·¤
â×æ´ÌÚU ¿ÌéÖüéÁ ãñÐ
31.
ÃØæâ
7 âð×è ßæÜð °·¤
12 ×è ßæÜð
¥æñÚU »ãÚUæ§ü
32.
¥æ·ë¤çÌ ×ð´,
ÂÚU çÕ´Îé
33.
EU
AB Ußëžæ
ÕðÜÙæ·¤æÚU Âæ§Â âð ãæð·¤ÚU
5 ×è ÂýçÌ
ç×ÙÅU ·¤è ÎÚU âð ÂæÙè Õã ÚUãæ ãñÐ
¥æÏæÚU ÃØæâ
CD U°·¤ Áèßæ ãñ,
ç·¤ ∠ AEB5608
·¤æ °·¤ ÃØæâ ãñ ÌÍæ
ÂÚU ç×ÜÌð ãñ´Ð
çâh ·¤èçÁ°
U
Áæð ßëžæ ·¤è ç˜æ’Øæ ·ð¤ ÕÚUæÕÚU ãñÐ
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