041_IX_SA2_30_A1 QP Mathematics.p65

041/IX/SA2/30/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 : 11
·é¤Ü ÂëcÆUæð´ ·¤è ⴁØæ : 11
General Instructions :
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.
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1.
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2.
§â ÂýàÙ-˜æ ×ð´ 34 ÂýàÙ ãñ´, Áæð
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1
¥´·¤ ·¤æ ãñ,
3.
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4.
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6.
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ç×ÙÅU ·¤æ â×Ø çÎØæ »Øæ ãñÐ
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§â ¥ßçÏ ·ð¤ ÎæñÚUæÙ ÀUæ˜æ ·ð¤ßÜ ÂýàÙ-Â˜æ ·¤æð Âɸð´»ð
SECTION - A
Question numbers 1 to 10 carry 1 mark each. For each of the questions 1 to 10, four
alternative choices have been provided of which only one is correct. You have to
select the correct choice.
1.
2.
Which of the following is not a linear equation ?
(A)
ax1by1c50
(B)
0x10y1c50
(C)
0x1by1c50
(D)
ax10y1c50
Which of the following is a solution of the equation 4x13y516 ?
(A)
(B)
(1, 4)
(C)
(2, 4)
(D)
(1, 3)
In figure, PQRS is a rectangle. If ∠RPQ5308 then the value of (x 1 y) is
(A)
(B)
1208
(C)
1508
(D)
1808
(C)
(c)
(D)
(d)
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Two polygons have the same area in figure :
5.
(B)
(b)
Two consecutive angles of a parallelogram are in the ratio 1 : 3, then the smaller angle
is :
(A)
6.
(a)
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(A)
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4.
908
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3.
(2, 3)
508
(B)
908
(C)
608
(D)
458
In figure, PQRS is a parallelogram in which ∠PSR51258 , ∠RQT is equal to
(A)
758
041/IX/SA2/30/A1
(B)
658
(C)
2
558
(D)
1258
7.
The diagonals of rhombus are 12 cm and 16 cm. The length of the side of rhombus is
(A)
8.
12 cm
(C)
16 cm
(D)
8 cm
20 cm2
(B)
100 cm2
(C)
50 cm2
(D)
70 cm2
The length of the longest pole that can be put in a room of dimensions
10 m 3 10 m 3 5 m.
(A)
10.
(B)
The length of the diagonal of the square is 10 cm. The area of the square is
(A)
9.
10 cm
15 m
(B)
16 m
(C)
10 m
(D)
12 m
(D)
20.5
The range of the data 25.7, 16.3, 2.8, 21.7, 24.3, 22.7, 24.9 is
(A)
22
(B)
22.9
(C)
21.7
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SECTION - B
Question numbers 11 to 18 carry 2 marks each
Find the mean of factors of 24.
12.
The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the
cost of painting the walls of the room and ceiling at the rate of Rs. 50 per m2.
13.
How many litres of water flow out through a pipe having an area of cross-section of
5 cm2 in one minute, if the speed of water in pipe is 30 cm/sec.
14.
Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and
12 cm. Find the distance between them if they lie on opposite sides of centre.
15.
In a paralleloram, show that the angle bisectors of two adjacent angles intersect at
right angle.
16.
The angle between the two attitudes of parallelogram through the vertex of an obtuse
angle is 508. Find the angles of parallelogram.
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11.
OR
D is the mid point of side BC of DABC and E is the mid point of AD, then show that
ar (BED) 5
1
ar (ABC)
4
17.
Two congruent circles intersect each other at points A and B. Through A a line segment
PAQ is drawn so that P and Q lie on the two circles. Prove that BP 5 BQ.
18.
Express y in terms x in equation 2x23y512. Find the points where the line represented
by this equation cuts x-axis and y-axis.
041/IX/SA2/30/A1
3
SECTION - C
Question numbers 19 to 28 carry 3 marks each
Draw the graph of two lines whose equations are 3x22y1650 and x12y2650 on
the same graph paper. Find the area of the triangle formed by two lines and x-axis.
20.
The taxi fare in a city is as follows. For the first kilometre, the fare is Rs. 8 and for the
subsequent distance it is Rs. 5 per km. Taking the distance covered as x km and total
fare as Rs. y. Write a linear equation for this information and calculate from the equation
total fare of 15 km distance.
21.
Construct a DABC in which AB55.8 cm, BC1CA58.4 cm and ∠B 5 608 .
22.
In figure, ABCD is a parallelogram. The circle through A, B and C intersects CD
produced at E. Prove that AE 5 AD.
23.
XY is a line parallel to side BC of DABC. BE ?? AC and CF ?? AB meets XY is E and F
respectively. Show that ar(ABE)5ar(ACF).
OR
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19.
In figure, ABCD is a trapezium in which AB ?? DC. E is the mid point of AD and F is a
point on BC such that EF ?? DC. Prove that F is the mid point of BC.
24.
From a right circular cylinder with height 8 cm and radius 6 cm, a right circular cone
of the same height and base is removed. Find the total surface area of the remaining
solid.
25.
How many spherical lead shots each 4.2 cm diameter can be obtained from a solid
cuboid of lead with dimensions 66 cm, 42 cm and 21 cm.
OR
An iron pipe 20 cm long has external diameter equal to 25 cm. If the thickness of the
pipe is 1 cm, find the total surface area of the pipe.
041/IX/SA2/30/A1
4
26.
Three unbiased coins are tossed together. Find the probability of getting
(i)
two heads
(ii)
at least two heads
(iii)
no head
OR
A bag contains 12 balls out of which x are white. If one ball is taken out from the bag,
find the probability of getting a white ball. If 6 more white balls are added to the bag
and the probability now for getting a white ball is double the previous one, find the
value of x.
27.
The marks obtained by 40 students of class IX in Mathematics are given below :
81, 55, 68, 79, 85, 43, 29, 68, 54, 73, 47, 35, 72, 64, 95, 44, 50, 77, 64, 35, 79, 52, 45, 54,
70, 83, 62, 64, 72, 92, 84, 76, 63, 43, 54, 38, 73, 68, 52, 54
Prepare a frequency distribution table with class - size of 10 marks.
Find the median of the following data
19, 25, 59, 48, 35, 37, 30, 32, 51.
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If 25 is replaced by 52 what will be the new median.
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28.
29.
Solve for x,
OR
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3x 2 5
25x 1 7
1
5
3
5
15
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Question numbers 29 to 34 carry 4 marks each
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A and B are friends. A is elder to B by 5 years. B’s sister C is half the age of B while A’s
father D is 8 years older than twice the age of B. If the present age of D is 48 years, find
the present ages of A, B and C.
30.
Prove that the parallelograms on the same base and beween the same parallels are
equal in area.
OR
Diagonals AC and BD of a trapezium ABCD with AB ?? DC intersect each other at O.
Prove that ar(DAOD) 5 ar(DBOC)
31.
Draw a histogram of frequency polygon for the following data
Marks
10 - 15
No. of students
7
041/IX/SA2/30/A1
15 - 20
9
20 - 25
8
5
25 - 30
5
30 - 40
12
40 - 60
12
60 - 80
8
32.
In figure, diagonals AC and BD of quadrilateral ABCD intersect at O, such that
OB5OD. If AB5CD show that
(i)
(ii)
(iii)
ar (DOC) 5 ar (AOB)
ar (DCB) 5 ar (ACB)
ABCD is a parallelogram.
In figure, two circles intersect at B and C. Through B two line segments ABD and PBQ
are drawn to intersect the circles at A, D, and P, Q respectively. Prove that
∠ACP5∠QCD .
34.
A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in
the interior. The diameter of the pencil is 7 mm and the diameter of graphite is 1 mm.
If the length of the pencil is 14 cm. Find the volume of wood and that of graphite.
-oOo-
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33.
041/IX/SA2/30/A1
6
¹‡ÇU - ·¤
Âýà٠ⴁØæ 1 âð 10 Ì·¤ ÂýˆØð·¤ ·ð¤ çÜ° 1 ¥´·¤ ãñÐ 1 âð 10 Ì·¤ ÂýˆØð·¤ ÂýàÙ ·ð¤ çÜ° ¿æÚU çß·¤Ë çΰ
ãé° ãñ´ çÁÙ×ð´ âð °·¤ çß·¤Ë âãè ãñÐ ¥æ·¤æð âãè çß·¤Ë ·¤æ ¿ØÙ ·¤ÚUÙæ ãñÐ
1.
2.
(A)
ax1by1c50
(B)
0x10y1c50
(C)
0x1by1c50
(D)
ax10y1c50
çِÙçÜç¹Ì ×ð´ âð ·¤æñÙ, â×è·¤ÚU‡æ
4x13y516 ·¤æ °·¤ ãÜ ãñ?
(A)
(1, 4)
(2, 3)
(B)
(C)
(2, 4)
(D)
(1, 3)
Îè ãé§ü ¥æ·ë¤çÌ ×ð´ PQRS °·¤ ¥æØÌ ãñÐ ØçÎ ∠RPQ5308 , Ìæð (x 1 y) ·¤æ ×æÙ ãñ Ñ
(A)
(B)
1208
1508
(D)
1808
(C)
(c)
(D)
(d)
du
¥æ·ë¤çÌ ×ð´ Îæð ÕãéÖéÁæð´ ·¤æ ÿæð˜æÈ¤Ü â×æÙ ãñÐ
(C)
5.
(B)
(b)
°·¤ â×æ´ÌÚU ¿ÌéÖüéÁ ·ð¤ Îæð ·ý¤×æ»Ì ·¤æð‡ææð´ ·¤æ ¥ÙéÂæÌ 1 : 3 ãñÐ ÀUæðÅðU ·¤æð‡æ ·¤æ ×æ ãñ Ñ
(A)
6.
(a)
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(A)
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4.
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3.
çِÙçÜç¹Ì ×ð´ âð ·¤æñÙ ÚñUç¹·¤ â×è·¤ÚU‡æ Ùãè´ ãñ?
508
(B)
908
(C)
608
(D)
458
¥æ·ë¤çÌ ×ð´ PQRS °·¤ â×æ´ÌÚU ¿ÌéÖüéÁ ãñ çÁâ×ð´ ∠PSR51258 , ∠RQT ·¤æ ×æ ãñ Ñ
(A)
758
041/IX/SA2/30/A1
(B)
658
(C)
7
558
(D)
1258
7.
°·¤ â׿ÌéÖüéÁ ·ð¤ çß·¤‡æü 12 âð×è °ß´ 16 âð×è ãñÐ â׿ÌéÖüéÁ ·¤è ÖéÁæ ·¤è ܐÕæ§ü ãñ Ñ
(A) 10 âð×è
(B) 12 âð×è
(C) 16 âð×è
(D) 8 âð×è
8.
°·¤ ß»ü ·ð¤ çß·¤‡æü ·¤è ܐÕæ§ü 10 âð×è ãñ, Ìæð ©â ß»ü ·¤æ ÿæð˜æÈ¤Ü ãñ Ñ
(A) 20 ß»ü âð×è
(B) 100 ß»ü âð×è
(C) 50 ß»ü âð×è
9.
°·¤ ·¤×ÚðU ·¤è çß×æ°¡ 10 ×è.310
(A)
10.
15
×è
(B)
×è. ãñ´Ð ©â ×ð´ ÚU¹ð Áæ â·¤Ùð ßæÜ𠹐Õð ·¤è ¥çÏ·¤Ì× ÜÕæ§ü ãñ Ñ
16 ×è
(C) 10 ×è
(D) 12 ×è
×è.35
¥æ¡·¤Ç¸æð´ 25.7, 16.3, 2.8, 21.7, 24.3, 22.7, 24.9 ·¤è ÂýâæÚU ãñ Ñ
(A)
22
(B)
22.9
(C)
21.7
11.
24
12.
°·¤ ·¤×ÚðU ·¤è ܐÕæ§ü, ¿æñǸæ§ü °ß´ ª¡¤¿æ§ü ·ý¤×àæÑ
°ß´
13 âð×è
ãñ´Ð
50 L¤Â°
ÂýçÌ ß»ü ×èÅUÚU ·¤è ÎÚU âð
30 âð×è
×ð´ ©â Âæ§ü âð ç·¤ÌÙð ÜèÅUÚU ÂæÙè Õãð»æ?
ÃØæâ ßæÜð ßëžæ ·¤è Îæð â×æ´ÌÚU Áèßæ°´ ·ý¤×àæÑ
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14.
1 ç×ÙÅU
3 ×è
âð×è ãñÐ ØçÎ ©â Âæ§Â ×ð´ ÂæÙè ·ð¤ ÕãÙð ·¤è »çÌ
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ÂýçÌ â𷤇ÇU ãñ, Ìæð ™ææÌ ·¤èçÁ° ç·¤
5 ᯁ
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·ð¤ »é‡æÙ¹´ÇUæð´ ·¤æ ×æŠØ ™ææÌ ·¤èçÁ°Ð
5 ×è, 4 ×è
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Âýà٠ⴁØæ 11 âð 18 Ì·¤ ÂýˆØð·¤ ·ð¤ çÜ° 2 ¥´·¤ ãñ´Ð
13.
70 ß»ü âð×è
(D)
5 âð×è
°ß´
12 âð×è
ãñ´Ð
ØçÎ Áèßæ°¡ ·ð¤‹Îý çՋÎé ·ð¤
çâh ·¤èçÁ° ç·¤ °·¤ â×æ´ÌÚU ¿ÌéÖüéÁ ·ð¤ Îæð â´Ü‚Ù ·¤æð‡ææ𴠷𤠷¤æð‡æ â×çmÖæÁ·¤ ÂÚUSÂÚU â×·¤æð‡æ ÂÚU Âýç̑ÀðUÎ
16.
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15.
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â×é¹ (çßÂÚUèÌ) Âÿææð´ ×ð´ çSÍÌ ãñ, Ìæð ©Ù·ð¤ Õè¿ ·¤è ÎêÚUè ™ææÌ ·¤èçÁ°Ð
°·¤ â×æ´ÌÚU ¿ÌéÖüéÁ ·ð¤ ¥çÏ·¤ ·¤æð‡æ ßæÜð àæèáü âð ÕÙæ° »° Îæð Ü´Õæð´ ·ð¤ Õè¿ ·¤æ ·¤æð‡æ
¿ÌéÖüéÁ ·ð¤ ·¤æð‡æ ™ææÌ ·¤èçÁ°Ð
508
ãñÐ
â×æ´ÌÚU
¥Íßæ
°·¤ ç˜æÖéÁ ABC ×ð´ D ÌÍæ E ·ý¤×àæÑ BC °ß´ AD ·ð¤ ×ŠØ çՋÎé ãñ´, Ìæð çâh ·¤èçÁ° ç·¤
ÿæð˜æÈ¤Ü (BED) 5
17.
1
ÿæð˜æÈ¤Ü (ABC)
4
Îæð âßæZ»â× ßëžæ ÂÚUSÂÚU çՋÎé¥æð´ A ÌÍæ B ÂÚU Âýç̑ÀðUÎ ·¤ÚUÌð ãñ´Ð çՋÎé A âð °·¤ ÚðU¹æ¹´ÇU PAQ §â Âý·¤æÚU
ÕÙæØæ ÁæÌæ ãñ ç·¤ çՋÎé P ÌÍæ Q çßçÖóæ ßëžææð´ ÂÚU çSÍÌ ãñ´Ð çâh ·¤èçÁ° ç·¤ BP 5 BQ.
18.
â×è·¤ÚU‡æ
2x23y512
·¤è âãæØÌæ âð
y
·¤æð
x ·ð¤ M¤Â ×ð´ ÃØ€Ì ·¤èçÁ°Ð ©Ù çՋÎé¥æð´ ·ð¤ çÙÎðüàææ´·¤ ™ææÌ
·¤èçÁ° Áãæ¡ ÂÚU §â â×è·¤ÚU‡æ mæÚUæ çÙM¤çÂÌ ÚðU¹æ x-¥ÿæ °ß´ y-¥ÿæ ·¤æð ·¤æÅUÌè ãñÐ
041/IX/SA2/30/A1
8
¹‡ÇU - »
Âýà٠ⴁØæ 19 âð 28 Ì·¤ ÂýˆØð·¤ ÂýàÙ 3 ¥´·¤ ·¤æ ãñÐ
19.
20.
°·¤ ãè »ýæȤ ÂðÂÚU ÂÚU â×è·¤ÚU‡ææð´ 3x22y1650 °ß´ x12y2650 ·ð¤ ¥æÜð¹ ÕÙ槰Р§Ù Îæð ÚðU¹æ¥æð´
°ß´ x-¥ÿæ
mæÚUæ çƒæÚUè ãé§ü ç˜æÖéÁ ·¤æ ÿæð˜æÈ¤Ü ™ææÌ ·¤èçÁ°Ð
°·¤ àæãÚU ×ð´ ÂýÍ× ç·¤Üæð×èÅUÚU ·¤æ ÅñU€âè ç·¤ÚUæØæ 8 L¤ÂØð ãñ ¥æñÚU ©â·ð¤ ÕæÎ ·¤è ÎêÚUè ·¤æ ç·¤ÚUæØæ 5 L¤ÂØð ÂýçÌ
y L¤ÂØð ×æÙ ÜèçÁ°Ð §â
ç·¤Üæð×èÅUÚU ãñÐ ÌØ ·¤è »§ü ·é¤Ü ÎêÚUè ·¤æð x
ç·¤Üæð×èÅUÚU ¥æñÚU ·é¤Ü ç·¤ÚUæØð ·¤æð
ÁæÙ·¤æÚUè ·ð¤ çÜ° °·¤ ÚñUç¹·¤ â×è·¤ÚU‡æ çÜç¹° ¥æñÚU ©â â×è·¤ÚU‡æ ·¤è âãæØÌæ âð
15
ç·¤Üæð×èÅUÚU ·¤æ
ç·¤ÚUæØæ ™ææÌ ·¤èçÁ°Ð
âð×è °ß´
∠B 5 60 8 ãñ´Ð
°·¤ ç˜æÖéÁ
22.
¥æ·ë¤çÌ ×ð´ ABCD °·¤ â×æ´ÌÚU ¿ÌéÖüéÁ ãñÐ
ãñÐ çâh ·¤èçÁ° ç·¤ AE 5 AD.
23.
°·¤ ç˜æÖéÁ ABC ×ð´ ÚðU¹æ XY ÖéÁæ BC ·ð¤ â×æ´ÌÚU ãñÐ BE ?? AC °ß´ CF ?? AB, ÚðU¹æ XY ·¤æð ·ý¤×àæÑ E °ß´
A, B ÌÍæ C âð
ÁæÙð ßæÜæ ßëžæ CD ·¤æð ÕÉUæÙð ÂÚU, E ÂÚU ç×ÜÌæ
om
·¤è ÚU¿Ùæ ·¤èçÁ° çÁâ×ð´
ç×ÜÌè ãñ´Ð
çâh ·¤èçÁ° ç·¤ ÿæð˜æȤÜ
(ABE)5ÿæð˜æÈ¤Ü (ACF).
¥Íßæ
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F ÂÚU
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ABC
AB55.8 âð×è, BC1CA58.4
21.
¥æ·ë¤çÌ ×ð´ ABCD °·¤ â×Ü´Õ ãñ çÁâ×ð´ AB ?? DCÐ
çՋÎé E ÖéÁæ AD ·¤æ ×ŠØ çՋÎé ãñ ¥æñÚU ÖéÁæ BC ÂÚU
°·¤ çՋÎé F §â Âý·¤æÚU ãñ ç·¤ EF ?? DC çâh ·¤èçÁ° ç·¤ çՋÎé F ÖéÁæ BC ·¤æ ×ŠØ çՋÎé ãñÐ
24.
8 âð×è
ª¡¤¿æ§ü ¥æñÚU
6 âð×è
ç˜æ’Øæ ßæÜð °·¤ ÜÕ ßëžæèØ ÕðÜÙ âð ©ÌÙè ãè ª¡¤¿æ§ü °ß´ ©ÌÙè ãè ¥æÏæÚU ç˜æ’Øæ
·¤æ ÜÕ ßëžæèØ àæ´·é¤ çÙ·¤æÜ çÜØæ ÁæÌæ ãñÐ
25.
66
âð×è,
42
âð×è °ß´
ç·¤° Áæ â·¤Ìð ãñ´Ð
20 âð×è
21
àæðá ÆUæðâ ·¤æ ·é¤Ü ÂëDèØ ÿæð˜æÈ¤Ü ™ææÌ ·¤èçÁ°Ð
âð×è çß×æ¥æð´ ßæÜð ç‷𤠷¤è ÆUæð⠃æÙæÖ âð ç·¤ÌÙð
¥Íßæ
4.2 âð×è
ÃØæâ ßæÜð »æðÜð Âýæ#
ܐÕæ§ü ßæÜð °·¤ Üæðãð ·ð¤ Âæ§ü ·¤æ Õæs ÃØæâ 25 âð×è ãñÐ ØçÎ Âæ§ü ·¤è ×æðÅUæ§ü 1 âð×è ãñ, Ìæð Âæ§üÂ
·¤æ ·é¤Ü ÂëDèØ ÿæð˜æÈ¤Ü ™ææÌ ·¤èçÁ°Ð
041/IX/SA2/30/A1
9
26.
ÌèÙ çÙcÂÿæ ç‷𤠰·¤ âæÍ ©ÀUæÜð ÁæÌð ãñ´Ð çِÙçÜç¹Ì ·¤æð Âýæ# ·¤ÚUÙð ·¤è ÂýæçØ·¤Ìæ ™ææÌ ·¤èçÁ°Ð
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